We provide quadratic equations practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on quadratic equations skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of quadratic equations Questions

Question No | Questions | Class |
---|---|---|

1 | If ( alpha ) and ( beta ) are the roots of ( a x^{2}+b x+ ) ( c=0 ) then find the roots of the equation ( a x^{2}-b x(x-1)+c(x-1)^{2}=0 ) | 10 |

2 | 75. A boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. The speed of the boat in still water is (1) 6.5 km/hour (2) 5.5 km/hour (3) 6 km/hour (4) 5 km/hour | 10 |

3 | If the one of the roots of the equation is zero find ‘a’ ( boldsymbol{x}^{2}-2 boldsymbol{a} boldsymbol{x}+boldsymbol{a}^{2}+boldsymbol{a}-boldsymbol{2}=mathbf{0} ) Selective the positive answer. | 10 |

4 | Find the roots of the equation ( x ) ( frac{1}{3 x}=frac{1}{6},(x neq 0) ) | 10 |

5 | Solve the following equations: ( boldsymbol{x} boldsymbol{y}+boldsymbol{x}+boldsymbol{y}=boldsymbol{2} boldsymbol{3} ) ( boldsymbol{x} boldsymbol{z}+boldsymbol{x}+boldsymbol{z}=boldsymbol{4} mathbf{1} ) ( boldsymbol{y} boldsymbol{z}+boldsymbol{y}+boldsymbol{z}=mathbf{2 7} ) A. ( x=4,-2 ; y=2 ; 6 ; z=6,-5 ) в. ( x=2,-4 ; y=2,4 ; z=2,-6 ) c. ( x=5,-7 ; y=3,-5 ; z=6,-8 ) D. ( x=3,4 ; y=2,-5 ; z=2,-7 ) | 10 |

6 | If ( boldsymbol{a}(boldsymbol{p}+boldsymbol{q})^{2}+2 boldsymbol{b} boldsymbol{p} boldsymbol{q}+boldsymbol{c}=boldsymbol{0} ) and ( boldsymbol{a}(boldsymbol{p}+ ) ( r)^{2}+2 p b r+c=0(a neq 0), ) then A ( cdot q r=p^{2} ) B ( cdot q r=p^{2}+frac{c}{a} ) c. ( q r=-p^{2} ) D. None of the above | 10 |

7 | 6. (3x – 8)(3x+2)-(4x-11)(2x+1)=(x-3)(x + 7) | 10 |

8 | Solve ( 3 x^{2}+20 x+8 ) | 10 |

9 | > is 62. The difference of two factors for the expression a4 + – (1) -4 12) – 2 (3) 2 (4) 4 | 10 |

10 | Solve ( : 3^{4 x+1}-2 times 3^{2 x+2}-81=0 ) A. ( x=-3 ) B. ( x=9 ) c. ( x=-1 ) D. ( x=1 ) | 10 |

11 | The roots of the equation ( sqrt{3 x+1} ) ( mathbf{1}=sqrt{boldsymbol{x}} ) are ( mathbf{A} cdot mathbf{0} ) B. c. ( 0, ) D. None | 10 |

12 | The graph of an equation is given above. What is the degree of the polynomial? ( A ) B. ( c ) ( D ) | 10 |

13 | The value of ( m ) for which one of the roots of ( x^{2}-3 x+2 m=0 ) is double of one of the roots of ( x^{2}-x+m=0 ) is A . -2 B. ( c cdot 2 ) D. None of the above | 10 |

14 | Add the following ( mathbf{2} p^{2} boldsymbol{q}^{2}-mathbf{3} boldsymbol{p} boldsymbol{q}+boldsymbol{4}=mathbf{0}, mathbf{5}+mathbf{7} boldsymbol{p} boldsymbol{q} ) ( 3 p^{2} q^{2}=0 ) | 10 |

15 | Solve : [ boldsymbol{x}^{2}-boldsymbol{8} boldsymbol{x}+mathbf{1 2}=mathbf{0} ] | 10 |

16 | If ( a-b=1 ) and ( a b=12, ) find the value of ( left(a^{2}+b^{2}right) ) | 10 |

17 | If the roots of the equation ( x^{2}+p x- ) ( 6=0 ) are 6 and -1 then the value of ( p ) is A . 2 B. 3 ( c .-5 ) D. 5 | 10 |

18 | Determine the nature of roots of the given quadratic equation ( 3 x^{2}+ ) ( mathbf{2} sqrt{mathbf{5}} boldsymbol{x}-mathbf{5}=mathbf{0} ) | 10 |

19 | Factorise ( 63 a^{2}-112 b^{2} ) | 10 |

20 | Find ( k, ) so that ( (k-12) x^{2}+2(k- ) 12) ( x+2=0 ) has equal roots, where ( k neq 12 ) ( mathbf{A} cdot k=4 ) B. ( k=12 ) c. ( k=14 ) D. none of these | 10 |

21 | 7. If y = x2 + 2x – 3, y-x graph is X (6) (c) -3 -X (d) – 1-3 | 10 |

22 | Find the exact position solution of the equation ( x^{2}+x=30 ) | 10 |

23 | If ( 4 y^{2}+4 y+1=0, ) then ( y=0 ) A. Yes B. No c. Ambiguous D. Data insufficient | 10 |

24 | 24. Let a, b, c be real numbers with a 70 and let a, ß be the roots of the equation ax? + bx + c = 0. Express the roots of aºx2 + abex + c = 0 in terms of a, B. (2001 – 4 Marks) | 10 |

25 | The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is -2 is: A ( cdot x^{2}+3 x-2=0 ) B . ( x^{2}-2 x+3=0 ) c. ( x^{2}-3 x+2=0 ) D. ( x^{2}-3 x-2=0 ) | 10 |

26 | The values of k for which the roots are real and equal of the following equation ( 3 x^{2}-5 x+2 k=0 ) is ( k=frac{25}{24} ) A. True B. False | 10 |

27 | Find the values of ( K ) so that the quadratic equations ( x^{2}+2(K-1) x+ ) ( K+5=0 ) has atleast one positive root A. ( k leq-1 ) B. ( k leq 1 ) c. ( k geq-1 ) D. ( -1 leq k leq 1 ) | 10 |

28 | The number of values ( k ) for which ( left[x^{2}-right. ) ( left.(k-2) x+k^{2}right]left[x^{2}+k x+(2 k-1)right] ) is a perfect square is ( A cdot 2 ) B. ( c cdot 0 ) D. None of these | 10 |

29 | Let ( x=2 ) be a root of ( y=4 x^{2}-14 x+ ) ( boldsymbol{q}=mathbf{0} . ) Then ( boldsymbol{y} ) is equal to A ( cdot(x-2)(4 x-6) ) В. ( (x-2)(4 x+6) ) c. ( (x-2)(-4 x-6) ) D. ( (x-2)(-4 x+6) ) | 10 |

30 | Factorize: ( 2 m^{2}+39 m+19 ) | 10 |

31 | By increasing the speed of a car by 10 ( k m / h r, ) the time of journey for a distance of ( 72 k m ) is reduced by 36 minutes. Write an equation for the given information and check if it is a Quadratic Equation? | 10 |

32 | If 2,8 are the roots of ( x^{2}+a x+beta=0 ) and 3,3 are the roots of ( x^{2}+alpha x+b= ) 0 then find the roots of ( x^{2}+a x+b=0 ) A . -1,-9 в. 1,9 c. -2,-8 D. 2,8 | 10 |

33 | If ( 3 x^{2}+10=11 x, ) then ( x=2, frac{5}{3} ) A. Yes B. No c. Ambiguous D. Data insufficient | 10 |

34 | Solve the given quadratic equation by using the formula method, ( (2 x+ ) ( mathbf{3})(mathbf{2} boldsymbol{x}-mathbf{2})+mathbf{2}=mathbf{0} ) | 10 |

35 | 71. There is a square field whose side is 44 m. A square flowerbed is prepared in its centre, leaving a gravel path of uniform width all around the flowerbed. The total cost of laying the flowerbed and gravelling the path at Rs. 2 and Re. 1 per square metre respec- tively is Rs. 3536. Find the width of the gravelled path. (1) 1 metre (2) 1.5 metre (3) 2 metre (4) 2.5 metre | 10 |

36 | Find the discriminant of the following quadratic equations and hence determine the nature of the roots of the equation: ( frac{1}{4} x^{2}-2 x+1=0 ) | 10 |

37 | If the following quadratic equation has two equal and real roots then find the value of ( mathrm{k}: ) ( 4 x^{2}-5 x+k=0 ) | 10 |

38 | If ( (3-2 x) ) and ( (5 x+8) ) are factors of ( left(-10 x^{2}+h x-kright), ) then the values of ( h ) and ( k ) are respectively A. -1 and 24 B. 1 and 24 c. -1 and -24 D. 1 and -24 | 10 |

39 | if ( alpha ) and ( beta ) are sum and product of roots of the given equation respectively, then ( (-boldsymbol{alpha} boldsymbol{beta}) ) is A. always a prime number B. always an odd integer c. always an irrational number D. dependent on value of a | 10 |

40 | Determine the set of values of ( k ) for which the given quadratic equation has real roots: ( mathbf{2} boldsymbol{x}^{2}+boldsymbol{k} boldsymbol{x}-boldsymbol{4}=mathbf{0} ) | 10 |

41 | Find the value of ( p ) such that quadratic equation ( (boldsymbol{p}-mathbf{1 2}) boldsymbol{x}^{2}-boldsymbol{2}(boldsymbol{p}-mathbf{1 2}) boldsymbol{x}+ ) ( 2=0 ) has equal | 10 |

42 | The positive root ( x^{2}+b x+8=0 ) is twice the other root then ( b= ) A. 6 B. – – c. 12 D. -12 | 10 |

43 | By selling an article for Rs.24, a trader loses as much percent as the cost price of the article. Write an equation to express this information and check if it is convertible to a Quadratic Equation. | 10 |

44 | ( x^{2}+6 x+9=0 ) ( x=? ) | 10 |

45 | If ( 6 x-x^{2}=1, ) then the value of ( (sqrt{x}- ) ( left.frac{1}{sqrt{x}}right) ) is ( A cdot 2 ) B. 3 c. 1 D. – | 10 |

46 | For the equation ( boldsymbol{x}^{2}-(boldsymbol{k}+mathbf{1}) boldsymbol{x}+left(boldsymbol{k}^{2}+right. ) ( k-8)=0 ) if one root is greater then 2 and other is less than 2 , then ( k ) lies between A . ( -2 & 3 ) B. 2 & – 2 c. ( 2 &-3 ) D. None of these | 10 |

47 | Solve for ( x: x^{5}+242=frac{243}{x^{5}}, ) where ( x ) is real number. | 10 |

48 | Find the discriminant for the given quadratic equation: ( boldsymbol{x}^{2}+boldsymbol{x}+mathbf{1}=mathbf{0} ) A . -3 B. – 5 ( c .-7 ) D. – – | 10 |

49 | If ( boldsymbol{h}=mathbf{5}, boldsymbol{k}=mathbf{3} ) then find the value of ( frac{k^{3}}{9}+frac{h k}{10} ) | 10 |

50 | Find the product of the roots of equation ( left(frac{x}{sqrt{2}}-2right)(x-sqrt{2})=0 ) ( mathbf{A} cdot mathbf{4} ) B. 3 c. 2 ( D ) | 10 |

51 | 21. Let p,q e{1,2,3,4}. The number of equations of the form 3 px2 + qx+1=0 having real roots is (1994) (a) 15 (b) 9 (C) 7 let, (d) 8 | 10 |

52 | Check whether ( boldsymbol{x}^{2}+frac{1}{2} boldsymbol{x}=mathbf{0} ) is a quadratic equation. | 10 |

53 | Which of the following is not a quadratic equation A ( cdot x-frac{3}{2 x}=5 ) в. ( 4 x-frac{5}{8}=x^{2} ) c. ( _{x+frac{1}{x}=9} ) D. ( 4 x-frac{2}{3 x}=4 x^{2} ) | 10 |

54 | Assertion Let equations ( a x^{2}+b x+c= ) ( mathbf{0}(boldsymbol{a}, boldsymbol{b}, boldsymbol{c} in boldsymbol{R}) & boldsymbol{x}^{2}+mathbf{2} boldsymbol{x}+mathbf{5}=mathbf{0} ) have common root, then ( frac{boldsymbol{a}+boldsymbol{c}}{boldsymbol{b}}=frac{mathbf{1}}{mathbf{3}} ) Reason If both roots of ( A x^{2}+B x+K_{1}=0 & ) ( boldsymbol{A}^{prime} boldsymbol{x}^{2}+boldsymbol{B}^{prime} boldsymbol{x}+boldsymbol{K}_{2}=mathbf{0} ) are identical ( operatorname{then} frac{boldsymbol{A}}{boldsymbol{A}_{1}}=frac{boldsymbol{B}}{boldsymbol{B}_{1}}=frac{boldsymbol{K}_{1}}{boldsymbol{K}_{2}}left(text { where } boldsymbol{A}, boldsymbol{B}, boldsymbol{K}_{1}right. ) and ( left.A^{prime}, B,^{prime} K_{2} in Rright) ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect, Reason is correct | 10 |

55 | Roots of quadratic equation ( 5 x^{2}- ) ( 22 x-15=0 ) are A ( cdot_{-5,} frac{-3}{5} ) в. ( _{5,} frac{3}{5} ) c. ( _{5}, frac{-3}{5} ) D. None of these | 10 |

56 | If the roots of the equation ( 5 x^{2}-7 x+ ) ( k=0 ) are mutually reciprocal then ( k= ) A . 5 B. 2 ( c cdot frac{1}{5} ) D. None of these | 10 |

57 | Find a two-digit number which exceeds by 12 the sum of the squares of its digits and by 16 the doubled product of its digits. | 10 |

58 | Find the value of ( K ), If the roots of the following quadratic equation are equal ( : x^{2}+K x^{2}+1=0 ) | 10 |

59 | When will the quadratic equation ( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+boldsymbol{c}=boldsymbol{0} ) NOT have Real Roots? A. ( b^{2}-4 a c geq 0 ) B . ( b^{2}-4 a c>0 ) c. ( b^{2}-4 a c<0 ) D. None of these | 10 |

60 | If ( a, b, c ) are real and ( b^{2}-4 a c ) is perfect square then the roots of the equation ( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+boldsymbol{c}=mathbf{0}, ) will be: A. Rational & distinct B. Real & equal C. Irrational & distanct D. Imaginary & distinct | 10 |

61 | Given that ( z^{2}-10 z+25=9, ) what is ( z ) ( ? ) A .3,4 в. 1,6 ( c .2,6 ) D. 2, | 10 |

62 | Find the roots using factorisation ( 9 x-x^{2}=0 ) A . 1,9 B. 0,9 ( c .9,9 ) D. | 10 |

63 | A two digit number is such that the product of its digits is ( 18 . ) When 63 is subtracted from the number, the digits interchange their places. Find the number | 10 |

64 | State the following statement is True or False The digit at ten’s place of a two digit number exceeds the square of digit at units place ( (x) ) by 5 and the number formed is ( 61, ) then the equation is ( mathbf{1 0}left(boldsymbol{x}^{2}+mathbf{5}right)+boldsymbol{x}=mathbf{6 1} ) A. True B. False | 10 |

65 | The two sides of a right-angled triangle are ( boldsymbol{x}, boldsymbol{x}+mathbf{1} ) and hypotenuse, the longest side is ( sqrt{1} 3 . ) Find the area of the triangle. A ( cdot 1 mathrm{m}^{2} ) B. ( 2 mathrm{m}^{2} ) ( c cdot 3 m^{2} ) D. ( 4 mathrm{m}^{2} ) | 10 |

66 | From ( 2012-2016, ) the amount (in crores) spent on natural gas ( mathrm{N} ) and electricity ( mathrm{E} ) by Indian residents can be described by the following expressions, where t is the number of years since 2012 Gas spending model, ( mathrm{N}=2.13 t^{2}-4.21 t+37.40 ) Electricity spending model, ( mathrm{E}=-0.209 t^{2}+5.393 t+307.735 ) What is the total amount A spent on natural gas and electricity by Indian residents from 2012 to 2016? A. ( 1.467 t^{2}+7.423+121.721 ) 1 B. ( 1.339 t^{2}-8.729 t+76.245 ) c. ( 1.01 t^{2}+7.083+97.83 ) D. ( 1.921 t^{2}+1.183 t+345.135 ) | 10 |

67 | If the roots of the equation ( x^{2}+p x+ ) ( c=0 ) are (2,-2) and the roots of the equation ( boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+boldsymbol{q}=mathbf{0} ) are ( (-mathbf{1},-mathbf{2}) ) then the roots of the equation ( x^{2}+ ) ( b x+c=0 ) are A ( .-3,-2 ) в. -3,2 c. 1,-4 D. -5,1 | 10 |

68 | For what values of ( k, ) the roots of the quadratic equation ( (boldsymbol{k}+mathbf{4}) boldsymbol{x}^{2}+(boldsymbol{k}+ ) 1) ( x+1=0 ) are equal? | 10 |

69 | 32. Let a, b, c be the sides of a triangle where a #bec and 2 R. If the roots of the equation x2 +2(a+b+c)x +32 (ab + bc+ca)= 0 are real, then (2006 – 3M, -1) (6) and | 10 |

70 | If the equation ( k x^{2}+4 x+1=0 ) has real and distinct roots, then: ( mathbf{A} cdot k4 ) ( mathbf{c} cdot k leqslant 4 ) D. ( k geqslant 4 ) | 10 |

71 | A train travels a distance of ( 480 k m ) at a uniform speed. If the speed had been ( 8 k m / h r ) less, then it would have taken 3 hours more to cover the same distance. Formulate the quadratic equation in terms of the speed of the train. | 10 |

72 | Find the value ( frac{left(x^{2}-4right)}{(x+2)} ) A ( .2 x-2 ) B. ( x-2 ) c. ( x+2 ) D. None of these | 10 |

73 | Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i) ( 2 x^{2}-3 x+5=0 ) (ii) ( 3 x^{2}-4 sqrt{3} x+4=0 ) (iii) ( 2 x^{2}-6 x+3=0 ) | 10 |

74 | ( sqrt{2} sec x+tan x=1 ) | 10 |

75 | Check whether ( 3 x-10=0 ) is a quadratic equation. | 10 |

76 | For what value of ( k ) does ( (k-12) x^{2}+ ) ( mathbf{2}=mathbf{0} ) have equal roots? | 10 |

77 | Consider quadratic equation ( a x^{2}+ ) ( (2-a) x-2=0, ) where ( a in R ) If exactly one root is negative, then the range of ( a^{2}+2 a+5 ) is ( A cdot[4, infty) ) B ( cdot[-2, infty) ) c. ( (-infty, 4] ) ( D cdot(5, infty) ) | 10 |

78 | 21. Let a, b, c be real. If ax2+bx+c=0 has two real roots a. and B, where a 1, then show that 1++ <0. a al (1995 – 5 Marks) where 24-1 med p21. then she was release | 10 |

79 | If one of the roots of ( a x^{2}+b x+c=0 ) is ( mathbf{7}+sqrt{mathbf{2}} ) then find the other root A. ( -7+sqrt{2} ) B. ( 7-sqrt{2} ) c. ( -7-sqrt{2} ) D. Cannot be determined | 10 |

80 | Roots of the equation ( boldsymbol{x}^{3}-(boldsymbol{a}+boldsymbol{b}+ ) ( c) x^{2}+(a b+b c+c a) x-a b c=0 ) ( x^{2}+2 x+7=0 ) and ( a x^{2}+b x+c=0 ) have a common root, where ( a, b, c in R, ) can be A .4,8,28 В. 1,2,7 c. 1,4,36 D. None of the above | 10 |

81 | Check whether ( 6 x^{3}+x^{2}=2 ) is a quadratic equations | 10 |

82 | The roots of ( x^{2}+k x+k=0 ) are real and equal, find ( k ) | 10 |

83 | If ( x^{2}-b x+c=0 ) has equal integral roots, then This question has multiple correct options A. ( b ) and ( c ) are integers B. ( b ) and ( c ) are even integers ( mathrm{c} . b ) is an even integer and ( c ) is a perfect square of an integer D. none of these | 10 |

84 | Determine the nature of the roots of the given equation from their discriminants. ( 2 y^{2}+11 y-7=0 ) A. Real and equal B. Real and unequal c. one real and one imaginary D. Both imaginary | 10 |

85 | Find ( p in R ) for ( x^{2}-p x+p+3=0 ) has A. One positive and one negative root. B. Both roots are negative c. one root ( >2 ) and the other root ( <2 ) D. None of the above | 10 |

86 | Find the value of ( k ) for which the given equations has real and equal roots: (i) ( (k-12) x^{2}+2(k-12) x+2=0 ) (ii) ( k^{2} x^{2}-2(k-1) x+4=0 ) | 10 |

87 | Find the discriminant of the equation and the nature of roots. Also find the roots. ( 6 x^{2}+x-2=0 ) A ( cdot D=49, ) Real and distinct roots: ( frac{1}{5}, frac{-2}{3} ) B. ( D=39 ), Real and distinct roots: ( frac{1}{2}, frac{-2}{3} ) C. ( D=49 ), Real and distinct roots: ( frac{1}{3}, frac{-7}{3} ) D. ( D=49 ), Real and distinct roots: ( frac{1}{2}, frac{-2}{3} ) | 10 |

88 | The roots of the equation ( x^{2}-2 sqrt{2} x+ ) ( mathbf{1}=mathbf{0} ) are- A. Real and distinct B. Imaginary and different c. Real and equal D. Rational and different | 10 |

89 | The given quadratic equations have real roots and the roots are ( -sqrt{2}, frac{-5}{sqrt{2}} ) ( sqrt{2} x^{2}+7 x+5 sqrt{2}=0 ) A. True B. False | 10 |

90 | Amy is 5 years older than her sister Julie. If the product of their ages is 6 Find the age of Julie. A. 1 year B. 2 years c. 3 years D. 4 years | 10 |

91 | Solve:6 ( +7 b-3 b^{2} ) | 10 |

92 | 6. Ifx—2-2—2, then x is equal to? x-2 | 10 |

93 | If ( x^{2}+a x+b ) is an integer for every integer ( boldsymbol{x} ) then A. ( a ) is always an integer but b need not be an integer B. ( b ) is always an integer but a need not be an integer ( mathrm{c} cdot a+b ) is always an integer D. none of these | 10 |

94 | If the roots of the equation ( p x^{2}+q x+ ) ( r=0 ) are in the ratio ( =l: m ) ( left(l^{2}+m^{2}right) p r+l mleft(2 p r-q^{2}right)=0 ) | 10 |

95 | If the equation ( 16 x^{2}+6 k x+4=0 ) has equal roots, then the value of ( k ) is ( mathbf{A} cdot pm 8 ) в. ( pm frac{8}{3} ) ( c cdot_{pm frac{3}{8}} ) D. 0 | 10 |

96 | If ( x=2+2^{frac{1}{3}}+2^{frac{2}{3}}, ) then the values of ( boldsymbol{x}^{3}-mathbf{6} boldsymbol{x}^{2}+boldsymbol{6} boldsymbol{x} ) is ( mathbf{A} cdot mathbf{3} ) B. 4 ( c cdot-2 ) D. | 10 |

97 | If the equation ( x^{2}+4+3 cos (a x+ ) ( b)=2 x ) has at least one solution where ( boldsymbol{a}, boldsymbol{b} in[mathbf{0}, mathbf{5}], ) then the value of ( (boldsymbol{a}+boldsymbol{b}) ) equal to This question has multiple correct options A ( .5 pi ) в. ( 3 pi ) c. ( 2 pi ) D. | 10 |

98 | Write the Quadratic equation to find two consecutive odd positive integers, whose product is 323 | 10 |

99 | Roots of the equations ( x^{2}-3 x+2=0 ) are A. 1,-2 B . -1,2 c. -1,-2 D. 1,2 | 10 |

100 | If the roots of the equation ( (x-a)(x-b)+(x-b)(x-c)+ ) ( (x-c)(x-a)=0 ) are equal, then ( a^{2}+b^{2}+c^{2} ) is equal to ( mathbf{A} cdot a+b+c ) B . ( 2 a+b+c ) c. ( 3 a b c ) D. ( a b+b c+c a ) E ( . a b c ) | 10 |

101 | The roots of the equation ( x^{2}+2 sqrt{3} x+ ) ( mathbf{3}=mathbf{0} ) are A . real and unequal B. rational and equal c. irrational and equal D. irrational and unequal | 10 |

102 | 68. If p2 += 47, then the nu- merical value of P+ will be (1) 6 (2) 7 13) Ž (4) 3 | 10 |

103 | Find the roots of each of the following quadratic equations by the method of completing the squares ( 2 x^{2}-5 x+3=0 ) A. ( x=2, x=-7 ) В. ( x=-1, x=3 ) c. ( x=1, x=frac{3}{2} ) D. ( x=1, x=frac{1}{2} ) | 10 |

104 | If ( a<b<c<d, ) then for any real non- zero ( lambda ), the quadratic equation ( (x- ) ( a)(x-c)+lambda(x-b)(x-d)=0 ) has This question has multiple correct options A. Non-real roots B. One real root between ( a ) and ( c ). c. one real root between ( b ) and ( d ) D. Irrational roots. | 10 |

105 | If the equation ( a x^{2}+2 b x+c=0 ) has real roots, ( a, b, c ) being real numbers and if ( m ) and ( n ) are real number such that ( m^{2}>n>0 ) then show that the equation ( a x^{2}+2 m b x+n c=0 ) has real roots. | 10 |

106 | expand: ( 9(x-y)^{2}+6(y-x) ) | 10 |

107 | The average weight of 15 Oarsmen in a boat is increased by ( 1.6 mathrm{kg} ) when one of the crew, who weigh ( 42 mathrm{kg} ) is replaced by a new man. Find the weight of the new man (in kg). A . 65 B. 66 c. 43 D. 67 | 10 |

108 | The product of two consecutive integers is ( 600 . ) Find the second integer. A .24 B . 23 c. 25 D. 26 | 10 |

109 | Is the following equation quadratic? ( mathbf{1 3}=-mathbf{5} boldsymbol{y}^{2}-boldsymbol{y}^{boldsymbol{3}} ) A. Yes B. No c. Ambiguous D. Data insufficient | 10 |

110 | The value of ( a ) for which the equation ( a^{2}+2 a+csc ^{2} pi(a+x)=0 ) has a solution, is/are ( mathbf{A} cdot mathbf{0} ) B. ( c cdot-1 ) D. | 10 |

111 | Solve for ( a, b ) ( boldsymbol{a}^{2}+boldsymbol{b}^{2}-mathbf{4} boldsymbol{a}+mathbf{1 6} boldsymbol{b}+mathbf{6 8}=mathbf{0} ) | 10 |

112 | The values of ( k ) for which the equation ( 2 x^{2}+k x+x+8=0 ) will have real and equal roots are ( A cdot 10 ) and -6 B. 7 and -9 ( c cdot 6 ) and -10 D. -7 and 9 | 10 |

113 | If the roots of ( frac{1}{x+a}+frac{a}{x+b}=frac{1}{c}, ) are equal in magnitude and opposite in sign, then the product of the roots is : A ( cdot-frac{1}{2}left(a^{2}+b^{2}right) ) B. ( frac{1}{2}left(a^{2}+b^{2}right) ) c. ( -frac{3}{2}left(a^{2}+b^{2}right) ) D. None | 10 |

114 | If ( alpha ) and ( beta ) are two zeroes of the polynomial ( boldsymbol{x}^{2}-mathbf{7} boldsymbol{x}+boldsymbol{k} ) where ( boldsymbol{alpha}-boldsymbol{beta}= ) ( 5, ) find value of ( k ) | 10 |

115 | Divide:- ( boldsymbol{X}^{2}+mathbf{5} boldsymbol{X}+mathbf{6} boldsymbol{b} boldsymbol{y} boldsymbol{X}+mathbf{2} ) | 10 |

116 | For ( a, b, c in Q ) and ( b+c neq a, ) the roots of ( boldsymbol{a} boldsymbol{x}^{2}-(boldsymbol{a}+boldsymbol{b}+boldsymbol{c}) boldsymbol{x}+(boldsymbol{b}+boldsymbol{c})=mathbf{0} ) are A. Rational and unequal B. rational and equal c. complex numbers D. none | 10 |

117 | Area enclosed by curves ( y=2^{x} ) and ( boldsymbol{y}=|boldsymbol{x}+mathbf{1}| ) in the first quadrant is? A ( cdot frac{1}{2}-frac{1}{log 2} ) B. ( frac{3}{2}-frac{1}{2 log 2} ) c. ( frac{3}{2}-frac{1}{log 2} ) D. ( frac{1}{2}+frac{3}{log 2} ) | 10 |

118 | State the following statement is True or False The length of a rectangle ( (x) ) exceeds its | 10 |

119 | Solve the following equations: ( sqrt{4 x^{2}-7 x-15}-sqrt{x^{2}-3 x}= ) ( sqrt{x^{2}-9} ) | 10 |

120 | If ( a x^{2}+b x+6=0 ) does not have two distinct real roots, where ( boldsymbol{a} in boldsymbol{R}, boldsymbol{b} in boldsymbol{R} ) then the least value of ( 3 a+b ) is A .4 B. – 1 ( c .1 ) D. – 2 | 10 |

121 | If ( left(p^{2}-2 p+1right) x^{2}-left(p^{2}-3 p+2right) x+ ) ( p^{2}-1=0 ) has more then two roots then ( p= ) | 10 |

122 | The product of two consecutive integers is ( 156 . ) Find the integers. A. 10 and 13 B. 12 and 13 c. 12 and 11 D. 1 and 13 | 10 |

123 | Three consecutive natural numbers are such that the square of the middle number exceeds the difference of squares of the other, two by ( 60 . ) Find the numbers. | 10 |

124 | Find the roots ( 4 x^{2}+4 sqrt{3 x}+3=0 ) | 10 |

125 | Find the value of ( k ) for which the equation ( 2 x^{2}-k x+3=0 ) will have two real and equal roots. | 10 |

126 | If ( a, b, c ) are non-zero, unequal rational numbers, then the roots of the equation ( a b c^{2} x^{2}+left(3 a^{2}+b^{2}right) c x-6 a^{2}-a b+ ) ( 2 b^{2}=0 ) are A . rational B. imaginary C. irrational D. none of these | 10 |

127 | if sum=1 product ( =-6 ) then find the 2 numbers. | 10 |

128 | The length of a rectangle is ( 3 mathrm{cm} ) more than its width and area is ( 54 mathrm{cm}^{2} ). Find the perimeter of the rectangle. ( mathbf{A} cdot 25 mathrm{cm} ) B. ( 30 mathrm{cm} ) c. ( 35 mathrm{cm} ) D. ( 40 mathrm{cm} ) | 10 |

129 | If ( r ) be the ratio of the roots of the equation ( a x^{2}+b x+c=0, ) then ( frac{(r+1)^{2}}{r}= ) A ( cdot frac{a^{2}}{b c} ) в. ( frac{b^{2}}{c a} ) c. ( frac{c^{2}}{a b} ) D. None of these | 10 |

130 | 1 7. 4x +17 Solve: 18 13x – 2 17x-32 -= – x 3 =- 7x 12 x+16 36 | 10 |

131 | Check whether the given equation is a quadratic equation or not. ( x^{2}+2 sqrt{x}-3 ) A. True B. False | 10 |

132 | Which of the following is not a quadratic equation? A ( cdot x^{2}+6 y+2 ) B. ( (x-2)+(x+2)^{2}+3 ) c. ( (3 x-2)^{3}+frac{1}{2} x-4 ) D. ( 3 x^{2}-6 x+frac{1}{2} ) | 10 |

133 | If the roots of the equation ( x^{2}-2 a x+ ) ( a^{2}+a-3=0 ) are real and less than 3 then A ( . a<2 ) в. ( 2 leq a leq 3 ) c. ( 34 ) | 10 |

134 | Check whether the following is quadratic equation. ( boldsymbol{x}^{2}-mathbf{2} boldsymbol{x}=(-mathbf{2})(boldsymbol{3}-boldsymbol{x}) ) | 10 |

135 | Let ( boldsymbol{alpha}, boldsymbol{beta} ) be the roots of ( boldsymbol{a x}^{2}+boldsymbol{b x}+boldsymbol{c}= ) ( 0 ; gamma, delta ) be the roots of ( p x^{2}+q x+r=0 ) and ( D_{1}, D_{2} ) are the respective discriminants of these equations. If the ( boldsymbol{alpha}, boldsymbol{beta}, boldsymbol{gamma}, boldsymbol{delta} ) are in AP, then ( boldsymbol{D}_{1}: boldsymbol{D}_{2} ) is equal to ( mathbf{A} cdot frac{a^{2}}{b^{2}} ) B. ( frac{a^{2}}{p^{2}} ) ( ^{mathbf{C}} cdot frac{b^{2}}{q^{2}} ) D. ( frac{c^{2}}{r^{2}} ) | 10 |

136 | If ( alpha, beta ) are zeroes of polynomial ( f(x)= ) ( x^{2}+p x+q ) then polynomial having ( frac{1}{alpha} ) and ( frac{1}{beta} ) as its zeroes is: A ( cdot x^{2}+q x+p ) B. ( x^{2}-p x+q ) c. ( q x^{2}+p x+1 ) D. ( p x^{2}+q x+1 ) | 10 |

137 | Sum of a number and its reciprocal is ( mathbf{5} frac{1}{mathbf{5}} . ) Then the required equation is A ( cdot y^{2}+frac{1}{y}=frac{26}{5} ) B. ( 5 y^{2}-26 y+5=0 ) c. ( y^{2}+frac{1}{y}+frac{26}{5}=0 ) D. ( 5 y^{2}+26 y+5=0 ) | 10 |

138 | State the nature of the given quadratic equation ( 3 x^{2}+4 x+1=0 ) A. Real and Distinct Roots B. Real and Equal Roots c. Imaginary Roots D. None of the above | 10 |

139 | For what value of ( mathrm{k} ), does the equation ( left[k x^{2}+(2 k+6) x+16=0right] ) have equal roots? A. 1 and 9 B. -9 and -1 c. -1 and 9 D. -1 and -9 | 10 |

140 | f ( x+y+z=0 ) then what is the value of ( frac{1}{x^{2}+y^{2}-z^{2}}+frac{1}{y^{2}+z^{2}-x^{2}}+ ) ( frac{1}{z^{2}+x^{2}-y^{2}} ) A ( cdot frac{1}{x^{2}+y^{2}+z^{2}} ) в. c. -1 D. | 10 |

141 | Solve the following quadratic equation by factorization, the roots are: ( 0, a+b ) ( frac{x-a}{x-b}+frac{x-b}{x-a}=frac{a}{b}+frac{b}{a} ) A. True B. False | 10 |

142 | If 8 is a root of the equation ( x^{2}-10 x+ ) ( k=0, ) then the value of ( k ) is : A . 2 B. 8 ( c .-8 ) D. 16 | 10 |

143 | Find the nature of the roots of ( 3 x^{2}- ) ( 4 sqrt{3} x+4=0 ) | 10 |

144 | The roots of the equation ( 2 x^{2}+x- ) ( 4=0 ) are ( mathbf{A} cdot 1,-4 ) в. ( -3, frac{1}{sqrt{3}} ) c. ( frac{sqrt{33}-1}{4}, frac{-sqrt{33}-1}{4} ) D. None | 10 |

145 | Solve ( frac{2 x+3}{2 x-3}+frac{2 x-3}{2 x+3}=frac{17}{4} ) | 10 |

146 | The ( _{text {一一一一一一 }} ) product rule says that when the product of two terms is zero, then either of the terms is equal to zero. A. one B. two c. three D. zero | 10 |

147 | Given reason whether the following is an equation or not: ( (x-2)^{2}=x^{2}-4 x+4 ) | 10 |

148 | Solve :- [ x^{2}-2 cos alpha+cos 2 alpha=0 ] | 10 |

149 | If the roots of ( left(a^{2}+b^{2}right) x^{2}-2 b(a+ ) ( c) x+left(b^{2}+c^{2}right)=0 ) are equal, then ( a, b, c ) are in A. A.P в. G.P. c. н.P. D. none of these | 10 |

150 | The roots of the following quadratic equation are not real ( 2 x^{2}-3 x+5=0 ) A . True B. False | 10 |

151 | I: If ( a, b, c ) are real, the roots of ( (b- ) ( c) x^{2}+(c-a) x+(a-b)=0 ) are real and equal, then ( a, b, c ) are in A.P. Il: If ( a, b, c ) are real and the roots of ( left(a^{2}+right. ) ( left.boldsymbol{b}^{2}right) boldsymbol{x}^{2}-boldsymbol{2} boldsymbol{b}(boldsymbol{a}+boldsymbol{c}) boldsymbol{x}+boldsymbol{b}^{2}+boldsymbol{c}^{2}=boldsymbol{0} ) are real and equal, then ( a, b, c ) are in H.P. Which of the above statement(s) is(are) true? A. only। B. only II c. both I and II | 10 |

152 | Find the root of ( x^{2}-20 x+100 ) | 10 |

153 | The roots of the equation ( x^{sqrt{x}}=(sqrt{x})^{x} ) are A. 0 and 1 B. 0 and 4 c. 1 and 4 D. 0,1 and 4 | 10 |

154 | Solve the following quadratic equations by factorization method: ( mathbf{3}left(x^{2}-6right)=x(x+7)-3 ) A ( cdotleft{-frac{3}{2}, 5right} ) в. ( left{frac{3}{2}, 5right} ) ( ^{c} cdotleft{-frac{3}{2},-5right} ) D. None of these | 10 |

155 | Solve for ( x: sqrt{7 x^{2}}-6 x-13 sqrt{7}=0 ) | 10 |

156 | Write the suitable quantifier for all values of ( x ) there is no real number such that ( x^{2}+2 x+2=0 ) A. Universal quantifier (forall) B. Existential quantifier c. Both D. None | 10 |

157 | If ( boldsymbol{alpha} neq boldsymbol{beta}, boldsymbol{alpha}^{2}=mathbf{5} boldsymbol{alpha}-mathbf{3}, boldsymbol{beta}^{2}=mathbf{5} boldsymbol{beta}-mathbf{3} ) then the equation whose roots are ( boldsymbol{alpha} / boldsymbol{beta} ) ( & boldsymbol{beta} / boldsymbol{alpha} ) is A ( cdot x^{2}+5 x-3=0 ) B. ( 3 x^{2}+12 x+3=0 ) c. ( 3 x^{2}-19 x+3=0 ) D. None of these | 10 |

158 | Solve : [ boldsymbol{x}^{2}+4 boldsymbol{x}+boldsymbol{4}=mathbf{0} ] | 10 |

159 | Solve the equation obtained ( x^{2}-x- ) ( 6=0 ) and hence find the dimensions of the verandah. Verandah is in rectangular shape having area and perimeter equal. A. ( x=3 ; ) length ( =6 mathrm{m} ) and breadth ( =3 mathrm{m} ) B. ( x=3 ; ) length ( =6 mathrm{m} ) and breadth ( =4 mathrm{m} ) c. ( x=3 ; ) length ( =4 mathrm{m} ) and breadth ( =3 mathrm{m} ) D. ( x=4 ; ) length ( =6 mathrm{m} ) and breadth ( =3 mathrm{m} ) | 10 |

160 | Find the least positive value of ( k ) for which the equation ( x^{2}+k x+4=0 ) has real roots. | 10 |

161 | 12. Which of the following is not the quadratic equation whose roots are cosecand sec-e? a. x2 – 6x + 6 = 0 b. x2 – 7x + 7 = 0 c. x2 – 4x + 4 = 0 d. none of these | 10 |

162 | Find the roots of the equations by the method of completing the square. ( boldsymbol{x}^{2}+mathbf{7} boldsymbol{x}-mathbf{6}=mathbf{0} ) | 10 |

163 | Determine whether the equation ( 5 x^{2}= ) ( 5 x ) is quadratic or not. A. Yes B. No c. complex equation D. None | 10 |

164 | fsum ( =-12, ) product ( =-28 . ) Then find the 2 numbers. | 10 |

165 | 58. Two runners cover the samed tance at the rate of 15 km a 16 km per hour respectively. Find the distance travelled when one takes 32 minutes longer than the other. (1) 128 km (2) 64 km (3) 96 km (4) 108 km | 10 |

166 | Solve ( 6 x^{2}-5 x-25=0 ) | 10 |

167 | The following equation is a qudratic equation. ( 16 x^{2}-3=(2 x+5)(5 x-3) ) A. True B. False | 10 |

168 | If the roots of the equation ( p x^{2}+q x+ ) ( boldsymbol{r}=mathbf{0} ) are in the ratio ( l: boldsymbol{m} ) prove that ( (l+m)^{2} p r=l m q^{2} ) | 10 |

169 | If ( n^{2}=(n+6), ) then find the value of ( n ) A. ( n=-2,-3 ) в. ( n=3,2 ) c. ( n=-3,2 ) D. ( n=-2,3 ) | 10 |

170 | A family is going to a theme park having ( t ) members in the family. Each ticket costs ( $ 80, ) and the number of tickets needs to be bought can be calculated from the expression ( t^{2}- ) ( 4 t-90=6 ) when ( t>0 . ) What is the total cost of the theme park tickets that the family paid? A. ( $ 640 ) B. ( $ 800 ) c. ( $ 960 ) D. ( $ 1,120 ) | 10 |

171 | The mentioned equation is in which form? ( mathbf{3} boldsymbol{y}^{2}-mathbf{7}=sqrt{mathbf{3}} boldsymbol{y} ) A. linear B. Quadratic c. Cubic D. None | 10 |

172 | The real values of ( a ) for which the quadratic equation ( 2 x^{2}-left(a^{3}+8 a-right. ) 1) ( x+a^{2}-4 a=0 ) possesses roots of opposite signs are given by : ( mathbf{A} cdot a>6 ) B . ( a>9 ) c. ( 0<a<4 ) D. ( a<0 ) | 10 |

173 | Which of the following is a Quadratic Equation? A ( .5 x+8=0 ) B ( cdot 6 x^{2}+7 x=19 ) ( mathbf{c} cdot x+1 ) D. None of these | 10 |

174 | Solve ( x^{2}-6 x+2=0 ) | 10 |

175 | 13. If cosec -cot 0=, then the value of cosec O is a. q+ 1980 b. q- – q 1 + – d. none of these | 10 |

176 | Which of the following equations are not quadratic? ( mathbf{A} cdot x(2 x+3)=x+2 ) B ( cdot(x-2)^{2}+1=2 x-3 ) ( mathbf{c} cdot y(8 y+5)=y^{2}+3 ) D. ( y(2 y+15)=2left(y^{2}+y+8right) ) | 10 |

177 | John and jivanti together have 45 marbles. Both of them lost 5 marbles each , and the product of the number of marbles they now have is ( 128 . ) Form the quadratic equation. | 10 |

178 | Solve the following. ( 3 a^{2} x^{2}+8 a b x+4 b^{2}=0,(a neq 0) ) | 10 |

179 | Solve ( 4 x^{2}-7 x+5 ) | 10 |

180 | Say true or false. f ( x(x-4)=0, ) then ( x=0 ) or ( x=4 ) A. True B. False | 10 |

181 | Check whether ( 2 x^{2}-3 x+5=0 ) has real roots or no. A. The equation has real roots. B. The equation has no real roots. c. Data insufficient D. None of these | 10 |

182 | The value ( (s) ) of ( k ) for which the quadratic equation ( k x^{2}-k x+1=0 ) has equal roots is ( mathbf{A} cdot k=0 ) B. ( k=4 ) c. ( k=0,4 ) D. ( k=-4 ) | 10 |

183 | Say true or false. ( x^{2}+6=5 x, ) then ( x=3 ) or ( x=2 ) A. True B. False | 10 |

184 | Find the discriminant for the given equation: ( mathbf{3} boldsymbol{x}^{2}+mathbf{2} boldsymbol{x}-mathbf{1}=mathbf{0} ) A . 11 B. 13 c. 15 D. 16 | 10 |

185 | The roots of the equation ( a x^{2}+b x+ ) ( c=0 ) will be in reciprocal if ( mathbf{A} cdot a=b ) B . ( a=b c ) ( mathbf{c} cdot c=a ) D. ( c=b ) | 10 |

186 | Choose the quadratic equation in ( boldsymbol{p} ) whose solutions are 1 and 7 A ( cdot p^{3}-p x+6=0 ) B . ( p^{2}-p x+6=0 ) c. ( p^{2}-8 p+7=0 ) D. ( p^{2}-5 p+7=0 ) | 10 |

187 | Which of the following is a quadratic equation? ( mathbf{A} cdot x^{frac{1}{2}}+2 x+3=0 ) B. ( left(x^{2}-1right)(x+4)=x^{2}+1 ) C ( cdot x^{2}-3 x+5=0 ) D. ( left(2 x^{2}+1right)(3 x-4)=6 x^{2}+3 ) | 10 |

188 | An equation whose maximum degree of variable is two is called ( ldots ). equation. | 10 |

189 | Let there be two integers such that one integer is 3 more than the other and their product is ( 70 . ) Find the two integers. A. 7 and 10 B. 6 and 9 c. 10 and 13 D. 12 and 14 | 10 |

190 | John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is ( 124 . ) Form the quadratic equation we can find that John had 36 or 9 marbles. A. True B. False | 10 |

191 | Solve ( 7 x^{2}-5 x-3=0 ) | 10 |

192 | If ( alpha ) and ( beta ) are the roots of the equation ( x^{2}-p x+q=0, ) then find the equation whose roots are ( frac{boldsymbol{q}}{boldsymbol{p}-boldsymbol{alpha}} ) and ( frac{boldsymbol{q}}{boldsymbol{p}-boldsymbol{beta}} ) | 10 |

193 | Find a quadratic polynomial with ( frac{1}{4},-1 ) as the sum and product of its zeroes respectively. | 10 |

194 | Find ( a ) so that roots of ( x^{2}+2(3 a+ ) 5) ( x+2left(9 a^{2}+25right)=0 ) are real. | 10 |

195 | Determine the values of ‘ ( a^{prime} ) for which both roots of the quadratic equation ( left(a^{2}+a-2right) x^{2}-(a+5) x-2=0 ) exceed the number minus one. | 10 |

196 | Obtains all other zeroes of ( x^{4}-3 x^{3}- ) ( x^{2}+9 x-6, ) if two of its zeroes are ( sqrt{3} ) and ( -sqrt{3} ) | 10 |

197 | If the value of ( b^{2}-4 a c^{prime} ) is greater than zero, the quadratic equation ( a x^{2}+b x+ ) ( c=0 ) will have A. Two Equal Real Roots. B. Two Distinct Real Roots. c. No Real Roots. D. No Roots or Solutions. | 10 |

198 | The roots of the equation ( 2 y^{2}+y- ) ( mathbf{2}=mathbf{0} ) are A. ( frac{-1-sqrt{17}}{2}, frac{-1-sqrt{17}}{2} ) B. ( frac{-1-sqrt{17}}{4}, frac{-1+sqrt{17}}{4} ) c. ( -1-sqrt{17},-1+sqrt{17} ) D. None | 10 |

199 | If the roots of the equation ( x^{2}-8 x+ ) ( a^{2}-6 a=0 ) are real, then the value of ( a ) will be A ( .-2<a<8 ) в. ( -2 leq a leq 8 ) ( mathbf{c} cdot 2<a<8 ) D. ( 2 leq a leq 8 ) | 10 |

200 | The mentioned equation is in which form? ( (y-2)(y+2)=0 ) A. cubic B. quadratic c. linear D. none of these | 10 |

201 | STATEMENT -1: Roots of the quadratic equation ( 3 x^{2}-2 sqrt{6}+2=0 ) are same STATEMENT -2: A quadratic equation ( a x^{2}+b x=c=0 ) has two distinct real roots, if ( b^{2}-4 a c>0 ) A. Statement – 1 is True, Statement- – 2 is True, Statement 2 is a correct explanation for Statement – 1 B. Statement – 1 is True, Statement – 2 is True : Statement 2 is NOT a correct explanation for Statement- – c. statement- 1 is True, Statement – 2 is False D. Statement-1 is False, Statement- – 2 is True | 10 |

202 | A root of the equation ( (x-1)(x- ) 2) ( =frac{30}{49} ) is A ( -frac{17}{7} ) B. ( frac{15}{7} ) c. ( frac{13}{7} ) D. ( frac{11}{7} ) | 10 |

203 | Solve [ boldsymbol{x}^{2}+mathbf{5}=-mathbf{6} boldsymbol{x} ] | 10 |

204 | Assertion (A): The roots of ( (x-a)(x- ) ( b)+(x-b)(x-c)+(x-c)(x-a)= ) 0 are real Reason (R): A quadratic equation with non-negative discriminant has real roots A. Both (A) and (R) are true and (R) is the correct explanation of (A) B. Both (A) and (R) are true and (R) is not the correct explanation of ( (A) ) ( c cdot(A) ) is true but (R) is false D. (A) is false but (R) is true | 10 |

205 | Find the roots of the following quadratic equation, if they exist, using the quadratic formula of Shridhar Acharya. ( 2 x^{2}-2 sqrt{2} x+1=0 ) | 10 |

206 | If ( a+b+c=2 s, ) then the value of ( (s- ) ( a)^{2}+(s-b)^{2}+(s-c)^{2} ) will be A ( cdot s^{2}+a^{2}+b^{2}+c^{2} ) B. ( a^{2}+b^{2}+c^{2}-s^{2} ) c. ( s^{2}-a^{2}-b^{2}-c^{2} ) D. ( 4 s^{2}-a^{2}-b^{2}-c^{2} ) | 10 |

207 | If the product of all solution of the equation ( frac{(2009) x}{2010}=(2009)^{log _{x}(2010)} ) can be expressed in the lowest form as ( frac{m}{n} ) then the value of ( (boldsymbol{m}+boldsymbol{n}) ) is | 10 |

208 | Factorise ( : boldsymbol{m}^{2}-mathbf{1 0 m}-mathbf{1 4 4} ) | 10 |

209 | Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is ( A cdot 4 ) B. 5 ( c cdot 6 ) D. 10 | 10 |

210 | Which of the following equations has two distinct real roots ? A ( cdot 2 x^{2}-3 sqrt{2} x+frac{9}{4}=0 ) В. ( x^{2}+x-5=0 ) c. ( x^{2}+3 x+2 sqrt{2}=0 ) D. ( 5 x^{2}-3 x+1=0 ) | 10 |

211 | Solve ( : a^{2}-(b+5) a+5 b=0 ) | 10 |

212 | In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was? A. ( x^{2}+10 x+9=0 ) B . ( x^{2}-10 x+16=0 ) c. ( x^{2}-10 x+9=0 ) D. None of the above | 10 |

213 | If ( a=frac{1}{3-2 sqrt{2}}, b=frac{1}{3+2 sqrt{2}} ) then the value of ( boldsymbol{a}^{mathbf{3}}+boldsymbol{b}^{mathbf{3}} ) is: A ( cdot 194 ) B. 200 c. 198 D. 196 | 10 |

214 | For what positive values of ‘ ( m ) ‘ roots of given equation is equal, distinct, imaginary ( boldsymbol{x}^{2}- ) ( boldsymbol{m} boldsymbol{x}+boldsymbol{9}=mathbf{0} ) | 10 |

215 | Let ( f(x)=x^{2}-3 x+4, ) then the value of ( boldsymbol{x} ) which satisfies ( boldsymbol{f}(mathbf{1})+boldsymbol{f}(boldsymbol{x})= ) ( boldsymbol{f}(mathbf{1}) boldsymbol{f}(boldsymbol{x}) ) is A . B. c. 1 or 2 D. 1 and 0 | 10 |

216 | The sum of the values of k for which the roots are real and equal of the following equation ( 4 x^{2}-2(k+1) x+(k+4)=0 ) is | 10 |

217 | Is the given equation quadratic? Enter 1 for True and 0 for False. ( boldsymbol{x}^{2}+boldsymbol{4} boldsymbol{x}=mathbf{1 1} ) | 10 |

218 | Find the value of ( k ) for which the equation ( boldsymbol{x}^{2}+boldsymbol{k}(boldsymbol{2} boldsymbol{x}+boldsymbol{k}-mathbf{1})+boldsymbol{2}=mathbf{0} ) has real and equal roots. | 10 |

219 | The product of two consecutive natural numbers is ( 12 . ) The equation form of this statement is A. ( x^{2}+2 x-12=0 ) B . ( x^{2}+1 x-12=0 ) c. ( x^{2}+1 x+12=0 ) D. ( x^{2}+2 x+12 ) | 10 |

220 | The value of ( a ) for which one root of the quadratic equation ( left(a^{2}-5 a+3right) x^{2}+ ) ( (3 a-1) x+2=0 ) is twice as large as the other is A ( cdot-frac{2}{3} ) в. ( frac{1}{3} ) ( c cdot-frac{1}{3} ) D. ( frac{2}{3} ) | 10 |

221 | Find the discriminant of the equation and the nature of roots. Also find the roots, if they are real: ( 3 x^{2}-2 x+frac{1}{3}=0 ) A. Roots are imaginary B. ( mathrm{D}=0, ) Roots are real and equal ( frac{1}{3}, frac{1}{3} ) ( mathrm{c} cdot_{mathrm{D}=} frac{2}{5}, ) Roots are real and unequal ( frac{1}{5}, frac{1}{2} ) D. Cannot be determined | 10 |

222 | Find the roots of each of the following quadratic equations by the method of completing the squares ( sqrt{5} x^{2}+9 x+4 sqrt{5}=0 ) A. ( -sqrt{7}, frac{-17}{sqrt{3}} ) в. ( -sqrt{5}, frac{-4}{sqrt{5}} ) c. ( -sqrt{5}, frac{-14}{sqrt{3}} ) D. ( -sqrt{7}, frac{-13}{sqrt{5}} ) | 10 |

223 | 1 U0 WUL LUI DU 16. Let a, b, c be real numbers, a = 0. o, c be real numbers, a = 0. If a is a root of +bx+c = 0. B is the root of a2x2 – bx -c= 0 and 0<a<B, then the equation a2x2 +2bx +2c=0 has a root y that always satisfies (1989- 2 Marks) (a) = (b) y = a +5 (d) a <y<B. (c) yra | 10 |

224 | Check whether ( x^{2}-frac{29}{4} x+5=0 ) is a quadratic equation | 10 |

225 | Let ( p, q in{1,2,3,4} . ) The number of equation of the form ( p x^{2}+q x+1=0 ) having real roots, is A . 15 B. 9 c. 8 D. 7 | 10 |

226 | The number of real roots of the equation ( (x-1)^{2}+(x-2)^{2}+(x- ) ( mathbf{3})^{2}=mathbf{0} ) is : ( mathbf{A} cdot mathbf{1} ) B . 2 ( c .3 ) D. None of these | 10 |

227 | f ( p ) and ( q ) are positive then the roots of the equation ( x^{2}-p x-q=0 ) are A. imaginary B. real & both positive c. real & both negative D. real & of opposite sign | 10 |

228 | 5. Find the solution for 5. Find the solution for | 10 |

229 | The graph of ( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{2}-boldsymbol{4} boldsymbol{x}+boldsymbol{3} ) represents A. a line segment B. parabola c. a line D. a ray | 10 |

230 | If ( 3 x^{2}+4 k x+1>0 ) for all real values of ( x, ) then ( k ) lies in the interval. A ( cdotleft(frac{-sqrt{3}}{2}, frac{sqrt{3}}{2}right) ) в. ( left(frac{-1}{4}, frac{1}{4}right) ) ( ^{c} cdotleft[frac{-sqrt{3}}{2}, frac{sqrt{3}}{2}right] ) D. ( left(frac{-1}{2}, frac{1}{2}right) ) | 10 |

231 | Which of the following is quadratic polynomial ( mathbf{A} cdot x+2 ) B. ( x^{2}+2 ) c. ( x^{3}+2 ) D. ( 2 x+2 ) | 10 |

232 | The formula of discriminant of quadratic equation ( a x^{2}+b x+c=0 ) is ( D= ) | 10 |

233 | In a square box, a glass is to be surrounded by a ( 2 mathrm{cm} ) glass border. If the total area of the square is ( 121 mathrm{cm}^{2} ) Find the dimension of the glass box. A. ( 5 mathrm{cm} ) в. ( 6 mathrm{cm} ) ( c cdot 7 mathrm{cm} ) D. ( 8 mathrm{cm} ) | 10 |

234 | Verify: ( (a+b)^{2}-(a-b)^{2}=4 a b, ) for ( a= ) ( mathbf{4}, boldsymbol{b}=mathbf{3} ) | 10 |

235 | For what value of ( ^{prime} boldsymbol{k}^{prime},left(boldsymbol{k}^{2}-mathbf{4}right) boldsymbol{x}^{2}+ ) ( 2 x-9=0 ) can not be quadratic equation? | 10 |

236 | Solve the following quadratic equation for ( x ) ( 4 x^{2}+4 b x-left(a^{2}-b^{2}right)=0 ) | 10 |

237 | Solve the equation ( mathbf{5}^{x^{2}+3 x+2}=mathbf{1} ) find the difference between the roots of the equation. | 10 |

238 | If the area of rectangle is given by ( x^{2}+ ) ( 5 x+6 ) then write the possible length and breadth. | 10 |

239 | The Discriminant value of equation ( mathbf{5} boldsymbol{x}^{2}-mathbf{6} boldsymbol{x}+mathbf{1}=mathbf{0} ) is A . 16 B. ( sqrt{56} ) ( c cdot 4 ) D. 56 | 10 |

240 | Determine the nature of roots of the equation ( x^{2}+2 x sqrt{3}+3=0 ) A. Real and distinct B. Non-real and distinct c. Real and equal D. Non-real and equal | 10 |

241 | Check whether the given equation is a quadratic equation ( x+frac{3}{x}=x^{2} ) | 10 |

242 | Determine the nature of the roots of the follwoing quadratic equation: ( 2 x^{2}-6 x+3=0 ) | 10 |

243 | ( frac{1}{(x-1)(x-2)}+frac{1}{(x-2)(x-3)}= ) ( frac{2}{3}, x neq 1,2,3 . ) Find sum of values of ( x ) | 10 |

244 | Solve the given quadratic equation by factorization method ( boldsymbol{x}^{2}-mathbf{9}=mathbf{0} ) | 10 |

245 | Find the roots of the quadratics equation ( 3 x^{2}-4 sqrt{3} x+4=0 ) | 10 |

246 | Solve ( 6 m^{2}-11 m+6=0 ) | 10 |

247 | If ( a<c<b ) then the roots of the equation ( (a-b)^{2} x^{2}+2(a+b- ) ( 2 c) x+1=0 ) are A. Imaginary B. Real c. one real and one Imaginary D. Equal and Imaginary | 10 |

248 | If the roots of ( a x^{2}-b x-c=0 ) change by the same quantity, then the expression in ( a, b, c ) that does not change is A ( cdot frac{b^{2}-4 a c}{a^{2}} ) в. ( frac{b-4 c}{a} ) c. ( frac{b^{2}+4 a c}{a^{2}} ) D. none of these | 10 |

249 | Find the value of ( k ) for which the equation ( x^{2}-6 x+k=0 ) has distinct roots. ( mathbf{A} cdot k>9 ) B. ( k=6,7 ) only c. ( k<9 ) ( mathbf{D} cdot k=9 ) | 10 |

250 | Solve by factorization ( sqrt{mathbf{3}} boldsymbol{x}^{2}+mathbf{1 1} boldsymbol{x}+ ) ( mathbf{6} sqrt{mathbf{3}}=mathbf{0} ) | 10 |

251 | The number of points ( (p, q) ) such that ( boldsymbol{p}, boldsymbol{q} in{1,2,3,4} ) and the equation ( p x^{2}+q x+1=0 ) has real roots is ( A cdot 7 ) B. 8 c. 9 D. none of these | 10 |

252 | State the following statement is True or False The sum of a natural number ( x ) and its | 10 |

253 | Solve ( 12 x^{2}-27=0 ) | 10 |

254 | Calculate ( frac{1}{x_{1}^{3}}+frac{1}{x_{2}^{3}}, ) where ( x_{1} ) and ( x_{2} ) are roots of the equation ( 2 x^{2}-3 a x- ) ( mathbf{2}=mathbf{0} ) | 10 |

255 | For what value of ( k,(4-k) x^{2}+ ) ( (2 k+4) x+(8 k+1)=0 ) is a perfect square: | 10 |

256 | 18. Let a, ß be the roots of the equation (x-a)(x-6)=c,c*0.- Then the roots of the equation (x-a) (x-B)+c=0 are (1992 – 2 Marks) (a) a, (b) b,c (c) a b (d) at c,b+c | 10 |

257 | Find the value ( (s) ) of ( k ) so that the equation ( x^{2}-11 x+k=0 ) and ( x^{2}- ) ( 14 x+2 k=0 ) may have a common root. | 10 |

258 | Figure shows a square with total area of 121 square units. Calculate the value of ( boldsymbol{x} ) begin{tabular}{|c|c|} hline & \ ( 7 x ) & 49 \ hline( x^{2} ) & ( 7 x ) \ hline end{tabular} ( A ) B. ( c ) D. 1 ( E ) | 10 |

259 | Solve ( 2 cos ^{2} theta-sqrt{3} sin theta+1=0 ) | 10 |

260 | I: The roots of ( a(b-c) x^{2}+b(c-a) x+ ) ( c(a-b)=0 ) are real and equal, then ( a, b, c ) are in G.P. II: The number of solutions of ( mid x^{2}- ) ( 2 x+2 mid=3 x-2 ) is 4 Which of the above statement(s) is/are true? A. only। B. only II c. both I and II D. neither I nor II | 10 |

261 | If the roots of a quadratic expression ( a x^{2}+b x+c ) are complex, then A ( cdot b^{2}4 a c ) c. ( b^{2}=4 a c ) ( mathbf{D} cdot a=0 ) | 10 |

262 | Solve: ( sqrt{7 sqrt{7 sqrt{7 sqrt{7 sqrt{7 ldots ldots}}}}}=k . ) Find k. | 10 |

263 | If ( a, b, c ) are real numbers such that ac ( neq 0, ) then show that at least one of the equations ( a x^{2}+b x+c=0 ) and ( -a x^{2}+b x ) ( +c=0 ) has real roots. | 10 |

264 | Factorise: ( 5 x^{2}-x-4 ) | 10 |

265 | 71. 1+2 72 + 73 73+ 74 will be equal to (1) 1 (2) -3 (3) Both of above (4) None of the above | 10 |

266 | Solve: ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=mathbf{5} ) | 10 |

267 | The values of he equation afor which both the roots of the equation ( (a- ) 6)( x^{2}=a(x-3) ) are positive are given by в. ( left(0, frac{72}{11}right) ) c. ( left(6, frac{72}{11}right) ) D. ( left(frac{72}{13}, 6right) ) | 10 |

268 | The number of point of intersection of the two curves ( y=2 sin x ) and ( y= ) ( 5 x^{2}+2 x+3 ) is ( ? ) ( A cdot infty ) B. 0 c. 1 D. less than two | 10 |

269 | If ( a ) and ( b ) are the roots of ( x^{2}-p x+q= ) ( 0, ) then ( a^{2}+b^{2} ) is A ( cdot p^{2}+q^{2} ) B . ( p^{2}+2 q ) c. ( p^{2}-q^{2} ) D. ( p^{2}-2 q ) | 10 |

270 | if ( [mathrm{x}] ) is the integral part of ( mathrm{x} ), then solve ( left[mathbf{4}-[boldsymbol{x}]^{2}right]-[boldsymbol{x}]^{2}=mathbf{2} ) find the number of integers satisfying the equation. | 10 |

271 | Which of the following statements has the truth value ( ^{prime} F^{prime} ? ) A. A quadratic equation has always a real root B. The number of ways of seating 2 persons in two chairs out of ( n ) persons in ( P(n, 2) ) C. The cube roots of unity are in GP D. None of the above | 10 |

272 | Determine ( k ) for which the quadratic equation has equal roots ( k x^{2}-5 x+ ) ( boldsymbol{k}=mathbf{0} ) | 10 |

273 | If ( frac{1}{a}+frac{1}{b}+frac{1}{c}=frac{1}{a+b+c} ) where ( (a+ ) ( b+c) neq 0 ) and ( a b c neq 0 . ) What is the value of ( (boldsymbol{a}+boldsymbol{b})(boldsymbol{b}+boldsymbol{c})(boldsymbol{c}+boldsymbol{a}) ? ) ( mathbf{A} cdot mathbf{0} ) B. ( c cdot-1 ) ( D ) | 10 |

274 | Find the value of ‘p’ for which the quadratic equatio has equal roots, ( (p+1) n^{2}+2(p+3) n+(p+8)=0 ) | 10 |

275 | Simplify ( frac{a}{x-a}+frac{b}{x-b}=frac{2 c}{x-c} ) | 10 |

276 | 2. A number which satisfies the given equation is called solutions or root of the equation. | 10 |

277 | 18. For a s 0, determine all real roots of the equation x2 – 2a x – al-3a2 = 0 (1986 – 5 Marks) | 10 |

278 | If the roots of the equation ( x^{2}-15- ) ( boldsymbol{m}(mathbf{2} boldsymbol{x}-mathbf{8})=mathbf{0} ) are equal, then ( boldsymbol{m}= ) A. 3,-5 в. 3,5 c. -3,5 D. -3,-5 | 10 |

279 | For ( a>0, ) all the real roots of the equation ( boldsymbol{x}^{2}-mathbf{3} boldsymbol{a}|boldsymbol{x}-boldsymbol{a}|-mathbf{7} boldsymbol{a}^{2}=mathbf{0} ) are ( mathbf{A} cdot 4 a, 5 a ) в. ( -4 a, 5 a ) ( mathbf{c} .-4 a,-5 a ) D. ( 4 a,-5 a ) | 10 |

280 | If one root of ( x^{2}-x-k=0 ) is square of the other, then ( k= ) A ( .2 pm sqrt{5} ) B . ( 2 pm sqrt{3} ) ( c cdot 3 pm sqrt{2} ) D. ( 5 pm sqrt{2} ) | 10 |

281 | For what value of ( k ) will the quadratic equation: ( k x^{2}+4 x+1=0 ) have real and equal roots? A .2 B. 3 ( c cdot 4 ) ( D ) | 10 |

282 | 71. Which one of the following is a root of equation x + x + 1 = 0? (1) x=0 (2) x= 1 (3) Both of above (4) none of the above | 10 |

283 | If ( A ) and ( B ) are whole numbers such that ( 9 A^{2}=12 A+96 ) and ( B^{2}=2 B+3, ) find the value of ( 5 A+7 B ) A . 31 B. 37 c. 41 D. 43 | 10 |

284 | Find the quadratic equation in ( x, ) whose solutions are 3 and 2 A ( cdot x^{3}-5 x+6=0 ) B. ( x^{2}-5 x+6=0 ) c. ( x^{2}-3 x+6=0 ) D. ( x^{2}-5 x+7=0 ) | 10 |

285 | The product of two consecutive even numbers is ( 120 . ) Can you express this information in the form of a Quadratic Equation? If yes, what would be the resulting Quadratic Equation? | 10 |

286 | Show that the equation ( 2left(a^{2}+b^{2}right) x^{2}+ ) ( 2(a+b) x+1=0 ) has no real roots, when ( a neq b ) | 10 |

287 | The area of a rectangular field is given as 300 square metres. It is also given that the breadth of the field is 3 metres more than its length. Can this information be expressed mathematically as a Quadratic Equation. If yes, what would be the resulting Quadratic Equation? | 10 |

288 | f ( a, b, c in R^{+} ) and ( 2 b=a+c, ) then check the nature of roots of equation ( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{2} boldsymbol{b} boldsymbol{x}+boldsymbol{c}=mathbf{0} ) | 10 |

289 | One year ago a man was eight times old as his son. Now his age is equal to the square of his son’s age. Represent this situation in form of a quadratic equation | 10 |

290 | Solve: ( 28-31 x-5 x^{2}=0 ) | 10 |

291 | All the values of ‘a’ for which the quadratic expression ( a x^{2}+(a- ) 2) ( x-2 ) is negative for exactly two integral values of ( x ) may lie in A. ( (1,3 / 2) ) B. ( (3,2 / 2) ) c. (1,2) (i) 5 D. (-1,2) | 10 |

292 | f ( a(a+2)=24 ) and ( b(b+2)=24 ) where ( a neq b, ) then ( a+b= ) A . – 48 B . – – ( c cdot 2 ) D. 46 E. 48 | 10 |

293 | 1. If l, m, n are real, em, then the roots by the equation: (l-mx2–5 (+ m)x-2 (1-m)=0 are (1979) (a) Real and equal (6) Complex (c) Real and unequal (d) None of these. | 10 |

294 | Solve the following quadratic equation by factorization, the roots are ( boldsymbol{x}^{2}-(sqrt{mathbf{3}}+mathbf{1}) boldsymbol{x}+sqrt{mathbf{3}}=mathbf{0} ) A . 3,1 в. ( sqrt{2}, ) c. ( sqrt{3}, 1 ) D. ( sqrt{5}, ) | 10 |

295 | If ( frac{5 x-7 y+10}{1}=frac{3 x+2 y+1}{8}= ) ( frac{11 x+4 y-10}{9}, ) then what is the ( x+y ) equal to? A . 1 B. 2 ( c cdot 3 ) D. – | 10 |

296 | Find the value of ‘k’ so that the equation ( boldsymbol{x}^{2}+mathbf{4} boldsymbol{x}+(boldsymbol{k}+mathbf{2})=mathbf{0} ) has one root equal to zero. | 10 |

297 | The value of k for which the quadratic equation, ( k x^{2}+1=k x+3 x-11 x^{2} ) has real and equal roots are A. ( -11 .-3 ) 3 ( 3.31-31-3 ) B. 5,7 c. 5,-7 D. None of these | 10 |

298 | 4. If (y – 4)² = 16 then find the value of y. 10 | 10 |

299 | The rectangular fence is enclosed with an area ( 16 mathrm{cm}^{2} . ) The width of the field is ( 6 mathrm{cm} ) longer than the length of the fields. What are the dimensions of the field? A. length ( =2 mathrm{cm}, ) width ( =6 mathrm{cm} ) B. length ( =1 mathrm{cm}, ) width ( =8 mathrm{cm} ) c. length ( =2 mathrm{cm}, ) width ( =8 mathrm{cm} ) D. length ( =3 mathrm{cm}, ) width ( =8 mathrm{cm} ) | 10 |

300 | If one of the zeroes of the quadratic polynomial ( (k-1) x^{2}+k x+1 ) is -3 then the value of ( k ) is. A ( cdot frac{4}{3} ) в. ( frac{-4}{3} ) ( c cdot frac{2}{3} ) D. ( frac{-2}{3} ) | 10 |

301 | What is the absolute value of the difference between the roots of ( x^{2}+6 x+5=0 ? ) | 10 |

302 | If the roots of the quadratic equation ( x^{2}+6 x+b=0 ) are real and distinct and they differ by atmost 4 then the least value of ( b ) is A . 5 B. 6 ( c cdot 7 ) D. 8 | 10 |

303 | f ( p, q, r ) are real and ( p neq q, ) then roots of the equation ( (boldsymbol{p}-boldsymbol{q}) boldsymbol{x}^{2}+mathbf{5}(boldsymbol{p}+boldsymbol{q}) boldsymbol{x}- ) ( mathbf{2}(boldsymbol{p}-boldsymbol{q})=mathbf{0} ) are A. Real and equal B. Complex c. Real and unequal D. None of these | 10 |

304 | 58. I 2×2 +5x+2, value of 1) 2 (3) -2 (4-2 | 10 |

305 | Check whether the following is Quadratic equations: ( (x+1)^{2}=2(x-3) ) | 10 |

306 | Find a quadratic equation with real coefficient whose one root is ( 3-2 i ) | 10 |

307 | Two candidates attempt to solve a quadratic equation of the ( a x^{2}+b x+ ) ( c=0 ) One starts with a wrong value of ( b ) and find the roots to be 2 and 6 . The other starts with the wrong values of ( c ) and find the roots to be ( +2,-9 . ) The correct roots of the equation are | 10 |

308 | ( sqrt{x^{2}+1} ) | 10 |

309 | 20. Solve ? +4x+31 +2x + 5 = 0 (1988 – 5 Marks) | 10 |

310 | Factorize ( 3 x^{2}+14 x+15 ) | 10 |

311 | Solve the equation using formula. ( 2 x^{2}+frac{x-1}{5}=0 ) A ( cdot x=frac{-1 pm sqrt{10}}{4} ) B. ( x=frac{-1 pm sqrt{41}}{20} ) c. ( x=frac{1 pm sqrt{41}}{20} ) D. ( _{x}=frac{1 pm sqrt{10}}{4} ) | 10 |

312 | Factorise: ( 12 a x-4 a b+18 b x-6 b^{2}= ) 0 | 10 |

313 | Find the values of ( k ) for which the given equation has real and equal roots ( mathbf{2} boldsymbol{x}^{2}-mathbf{1} mathbf{0} boldsymbol{x}+boldsymbol{k}=mathbf{0} ) | 10 |

314 | 53. If (3a + 1)2 + (b – 1)2 + (20-3)2 = 0, then the value of (3a + b + 2c) is equal to : (1) 3 (2)-1 (3) 2 (4)5 | 10 |

315 | If ( x ) is real, ( x+frac{1}{x} neq 0 ) and ( x^{3}+frac{1}{x^{3}}=0 ) then the value of ( left(boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}right)^{mathbf{4}} ) is ( mathbf{A} cdot mathbf{4} ) B. 9 c. 16 D. 25 | 10 |

316 | If ( x=5+2 sqrt{6}, ) then the value of ( left(sqrt{boldsymbol{x}}-frac{1}{sqrt{x}}right)^{2} ) A ( .4 sqrt{6} ) B. 8 c. 16 D. 12 E. None of these | 10 |

317 | ( mathbf{f} boldsymbol{x}=frac{1}{mathbf{5}+frac{mathbf{1}}{mathbf{5}+frac{mathbf{1}}{mathbf{5}+} cdots cdots}}^{text {then }} ) A ( cdot x^{2}+5 x-1=0 ) B . ( x^{2}-5 x-1=0 ) C ( cdot x^{2}-5 x+1=0 ) D. ( x^{2}+5 x+1=0 ) | 10 |

318 | ( frac{41 x-12}{x^{2}-16}=frac{4 x+3}{x-4} ) | 10 |

319 | 63. The value of 20+ V20 + 120+……. is: (1) 4 (2) 3 h (3) 5 (4) 0 | 10 |

320 | A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number. | 10 |

321 | If one root of the equation ( x^{2}+p x+ ) ( 12=0 ) is 4 while the equation ( x^{2}+ ) ( p x+q=0 ) has equal roots, then one value of ( q ) is ( mathbf{A} cdot mathbf{3} ) в. 12 c. ( frac{49}{4} ) D. 4 | 10 |

322 | ( x^{2}+(a+b+c) x+a b+b c ) | 10 |

323 | If ( a-b=5 ) and ( a^{2}+b^{2}=53, ) find the value of ( a b ) | 10 |

324 | ( boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}-left(boldsymbol{a}^{2}+boldsymbol{a}-boldsymbol{6}right)=mathbf{0} ) | 10 |

325 | A farmer wishes to start a 100 sq.m rectangular vegetable garden. since he has only ( 30 mathrm{m} ) barbed wire, he fences the sides of the rectangular garden letting his house compound wall act as the fourth side fence. Find the dimension of the garden. A. ( 20 m, 5 m ) or ( 10 m, 10 m ) В. ( 2 m, 5 m ) or ( 10 m, 10 m ) ( mathrm{c} .20 mathrm{m}, 5 mathrm{m} ) or ( 1 mathrm{m}, 10 mathrm{m} ) D. None of these | 10 |

326 | Is the following equation a quadratic equation? ( 16 x^{2}-3=(2 x+5)(5 x-3) ) A. Yes B. No c. Ambiguous D. Data insufficient | 10 |

327 | ( f(m)=2, ) find the value of ( m^{2}-m+1 ) | 10 |

328 | The value of ( mathrm{k} ) for which polynomial ( x^{2}-k x+4 ) has equal zeroes is This question has multiple correct options A .4 B . 2 ( c .-4 ) D. – | 10 |

329 | ( frac{1-frac{9}{y^{2}}}{1-frac{3}{y}}-frac{3}{y}, ) where ( (y neq 0)= ) A. ( frac{y-3}{y} ) в. ( frac{y+3}{y} ) ( c cdot 3 ) D. E ( .3 y-1 ) | 10 |

330 | Solve : ( sqrt{2} x^{2}-sqrt{3} x-3 sqrt{2} ) | 10 |

331 | Factories: ( x^{2}+6 x+9 ) | 10 |

332 | If one of the zeroes of the polynomial ( boldsymbol{f}(boldsymbol{z})=boldsymbol{p}^{2} boldsymbol{z}^{2}+boldsymbol{8} boldsymbol{z}+boldsymbol{1} boldsymbol{6} ) is reciprocal of the other, then the value of ( p ) is: ( A ldots pm 4 ) B. – 5 ( c cdot 6 ) D. – | 10 |

333 | If the sum of the roots of the equation ( x^{2}-x=k(2 x-1) ) is zero, find ( k ) | 10 |

334 | If the equation ( x^{2}+b x+c=0 ) and ( boldsymbol{x}^{2}+boldsymbol{c} boldsymbol{x}+boldsymbol{b}=mathbf{0},(boldsymbol{b} neq boldsymbol{c}) ) have a common root then A. ( b+c=0 ) B. ( b+c=1 ) c. ( b+c+1=0 ) D. None of these | 10 |

335 | Number of solutions of the equation ( (sqrt{3}+1)^{2 x}+(sqrt{3}-1)^{2 x}=2^{3 x} ) is | 10 |

336 | The roots of ( a^{2} x^{2}+a b x=b^{2}, a neq ) ( mathbf{0}, boldsymbol{b} neq mathbf{0} ) are: A. Equal B. Non- real c. Unequal D. None of these | 10 |

337 | 17. Solve for x; (5+276)+2-3 +(5-216)*2-3 = 10 (1985 – 5 Marks) | 10 |

338 | Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials: ( x+x^{2}-4 ) | 10 |

339 | If Sum of two numbers ( =-21 ) and Product ( =-100 ) Then find the two numbers | 10 |

340 | State whether the given algebraic expressions are polynomials? Justify. ( x^{2}+7 x+9 ) | 10 |

341 | If ( a>0, ) then the expression ( a x^{2}+ ) ( b x+c ) is positive for all values of ( x ) provided A ( . b^{2}-4 a c>0 ) В. ( b^{2}-4 a c<0 ) ( mathbf{c} cdot b^{2}-4 a c=0 ) D. ( b^{2}-a c<0 ) | 10 |

342 | The roots of the equation ( a x^{2}+b x+ ) ( c=0 ) will be imaginary if A. ( a>0, b=0, c0, b=0, c>0 ) c. ( a=0, b>0, c>0 ) D. ( a>0, b>0, c=0 ) | 10 |

343 | State true or false: ( x^{2}-5 x+6 ) cannot be written as a product of two linear factors. A . True B. False | 10 |

344 | The angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown by Bheeshm on him and with six other arrows he killed the rath driver of Bheeshm. With one arrow each, he knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrows he laid Bheeshm unconscious on an arrow bed. Find the total number of arrows Arjun had. | 10 |

345 | For what value of ( k ) will ( x^{2}- ) ( (3 k-1) x+2 k^{2}+2 k=11 ) have equal roots? ( mathbf{A} cdot 9,-5 ) В. -9,5 ( c .9,5 ) D. -9,-5 | 10 |

346 | If the equation ( a x^{2}+b x+c=0 ) ( a, b, c in R ) have non-real roots, then This question has multiple correct options A ( cdot c(a-b+c)>0 ) B. ( c(a+b+c)>0 ) c. ( c(4 a-2 b+c)>0 ) D. None of the above | 10 |

347 | Which of the following is a quadratic equation? A ( cdot x^{frac{1}{2}}+2 x+3=0 ) B ( cdot(x-1)(x+4)=x^{2}+1 ) ( mathbf{c} cdot x^{4}-x+5=0 ) D. ( (2 x+1)(3 x-4)=2 x^{2}+3 ) | 10 |

348 | Find the roots of the equation ( 2 x^{2}- ) ( boldsymbol{x}+frac{mathbf{1}}{mathbf{8}}=mathbf{0} ) | 10 |

349 | If ( a^{2}-5 a-1=0 ) and ( a neq 0 ; ) find: ( (i) a-frac{1}{a} ) ( (mathrm{ii}) boldsymbol{a}+frac{mathbf{1}}{boldsymbol{a}} ) | 10 |

350 | Find the value of ( mu ) for which one root of the quadratic equation ( mu x^{2}-14 x+ ) ( 8=0 ) in 6 times the other. | 10 |

351 | Which of the following is not a quadratic equation? A ( cdot 2(x-1)^{2}=4 x^{2}-2 x+1 ) B. ( left(x^{2}+1right)^{2}=x^{2}+3 x+9 ) ( mathbf{C} cdotleft(x^{2}+2 xright)^{2}=x^{4}+3+4 x^{3} ) D ( cdot x^{2}+9=3 x^{2}-5 x ) | 10 |

352 | What is a Quadratic Equation? | 10 |

353 | Find a quadratic equation whose roots ( operatorname{are} alpha, beta ) such that ( alpha+beta=3 ) and ( alpha^{3}+ ) ( boldsymbol{beta}^{mathbf{3}}=mathbf{9} ) | 10 |

354 | For the expression ( a x^{2}+7 x+2 ) to be quadratic, the necessary condition is ( mathbf{A} cdot a=0 ) B. ( a neq 0 ) ( ^{c} cdot_{a}>frac{7}{2} ) D. ( a<-1 ) | 10 |

355 | The values of ( k, ) so that the equations ( 2 x^{2}+k x-5=0 ) and ( x^{2}-3 x-4=0 ) have one root in common, are A ( cdot_{3, frac{27}{2}} ) в. ( 9, frac{27}{4} ) c. ( _{-3, frac{-27}{4}} ) D. ( -3, frac{4}{27} ) | 10 |

356 | The given equation ( (x+1)^{2}=2(x-3) ) is A . linear B. quadratic c. cubic D. none of these | 10 |

357 | Find the value of ( s, ) if ( 3 s^{2}+8 s+3 ) | 10 |

358 | Find the equation whose roots are the reciprocals of the roots of ( 3 x^{2}-5 x+ ) ( mathbf{7}=mathbf{0} ) A ( cdot 7 x^{2}-5 x+3=0 ) B . ( 7 x^{2}+5 x+3=0 ) c. ( 4 x^{2}-5 x+3=0 ) D. ( 7 x^{2}-5 x+7=0 ) | 10 |

359 | If ( left(2 x^{2}-3 x+1right)left(2 x^{2}+5 x+1right)=9 x^{2} ) A. For real root B. Two real and two imaginary root c. Four imaginary roots D. None of the above | 10 |

360 | 7. The solution of the equation 5x^2(2x– 7) = 2(3x-1) + | 10 |

361 | If 1 lies between the roots of the equation ( y^{2}-m y+1=0 ) and ( [x] ) is the GIF function, then the value of ( left[left(frac{4|x|}{|x|^{2}+16}right)^{m}right], ) is ( mathbf{A} cdot mathbf{0} ) B. ( c cdot 2 ) D. None of the above | 10 |

362 | Solve: ( x+frac{1}{x}=25 frac{1}{25} ) | 10 |

363 | Choose best possible option. ( left(x+frac{1}{2}right)left(frac{3 x}{2}+1right)= ) ( frac{6}{2}(x-1)(x-2) ) is quadratic. A. Yes B. No c. Complex equation D. None | 10 |

364 | Solve the equation ( x^{2}-2 b x+left(b^{2}-right. ) ( left.boldsymbol{a}^{2}right)=mathbf{0} ) | 10 |

365 | 62. The speed of the current is 5 km hour. A motorboat goes 10 km upstream and back again to the starting point in 50 minutes. The speed, in km/hour, of the mo- torboat in still water is (1) 20 (2) 26 (3) 25 (4) 28 | 10 |

366 | Check whether ( 5-6 x=frac{2}{5} x^{2} ) is a quadratic equation. | 10 |

367 | Solve the following by using the method of completing square. ( 6 x^{2}-11 x+3=0 ) | 10 |

368 | Which of the following equations have no real roots ? A ( cdot x^{2}-2 sqrt{3}+5=0 ) B ( cdot 2 x^{2}+6 sqrt{2} x+9=0 ) c. ( x^{2}-2 sqrt{3}-5=0 ) D ( cdot 2 x^{2}-6 sqrt{2} x-9=0 ) | 10 |

369 | The given quadratic equation have real roots and the roots are ( -2 sqrt{3}, frac{-sqrt{3}}{2} ) ( mathbf{2} boldsymbol{x}^{2}+mathbf{5} sqrt{mathbf{3}} boldsymbol{x}+mathbf{6}=mathbf{0} ) A. True B. False | 10 |

370 | 15. If one root of the quadratic equation ax2 + bx+c=0 is equal to the n-th power of the other, then show that (ac”)”+1 +(a” c)2+1 +b=0 (1983 – 2 Marks) | 10 |

371 | Solve: ( x^{2}+y^{2}-4 x-4 y+8=0 ) | 10 |

372 | The nature of the roots of the equation ( x^{2}-5 x+7=0 ) is A. No real roots B. 1 real root and 1 imaginary c. Real and unequal D. Real and equal | 10 |

373 | Two types of boxes ( A, B ) are to be placed in a truck having capacity of 10 tons. When 150 boxes of type ( A ) and 100 boxes of type ( B ) are loaded in the truck, it weighs 10 tons. But when 260 boxes of type ( A ) are loaded in the truck, it can still accommodate 40 boxes of type ( B ) so that it is fully loaded. Find the weight of each type of box. | 10 |

374 | If the quadratic equation ( x^{2}+b x+ ) ( mathbf{7 2}=mathbf{0} ) has two distinct integer roots, then the number of all possible values of bis A . 12 B. 9 c. 15 D. 18 | 10 |

375 | The set of values of ( p ) for which the roots of the equation ( 3 x^{2}+2 x+p(p-1)= ) 0 are of opposite sign is ( A cdot(-infty, 0) ) B. (0,1) c. ( (1, infty) ) D. ( (0, infty) ) | 10 |

376 | If sec ( alpha ) and ( csc alpha ) are the roots of ( x^{2}- ) ( boldsymbol{p} boldsymbol{x}+boldsymbol{q}=boldsymbol{0} ) then A ( cdot p^{2}=q(q-2) ) B . ( p^{2}=q(q+2) ) c. ( p^{2}+q^{2}=2 q ) D・ ( p^{2}+q^{2}=1 ) | 10 |

377 | Assertion If the roots of the equations ( x^{2}-b x+ ) ( c=0 ) and ( x^{2}-c x+b=0 ) differ by the same quantity, then ( b+c ) is equal to -4 Reason If ( alpha, beta ) are the roots of the equation ( A x^{2}+B x+C=0, ) then ( alpha-beta= ) ( frac{sqrt{boldsymbol{B}^{2}-boldsymbol{4} boldsymbol{A} boldsymbol{C}}}{boldsymbol{A}} ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 10 |

378 | The length of a rectangular verandah is ( 3 m ) more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter. Taking ( x ) as the breadth of the verandah, write an equation in ( x ) that represents the above statement. A ( cdot x^{2}-x-6=0 ) B. ( x^{2}-x+6=0 ) c. ( x^{2}-x+5=0 ) D. ( x^{2}-x-5=0 ) | 10 |

379 | Find the number of all real solution to the quadratic equation ( x^{2}+2 x=-1 ) | 10 |

380 | Which of the following steps should be followed to convert a given word problem into a Quadratic Equation? A. Represent the unknown quantity/ies with variables ( (x ) y etc. B. Express the information of the problem mathematically in the form of an equation. c. check if the equation formed is in one variable and the degree of the equation is 2 D. All of the above | 10 |

381 | 16. Find all real values of x which satisfy x2-3x+2> 0 and x-2x-450 (1983 – 2 Marks) | 10 |

382 | The expression ( 21 x^{2}+a x+21 ) is to be factored into two linear prime binomial factors with integer coefficients. This can be done if a is: A. odd number B. zero c. even number D. None | 10 |

383 | Before Robert Norman worked on ‘Dip and Field Concept’, his predecessor thought that the tendency of the magnetic needle to swing towards the poles was due to a point attractive. However, Norman showed with the help of experiment that nothing like point attractive exists. Instead, he argued that magnetic power lies is lodestone. Which one of the following is the problem on which Norman and others worked? A. Existence of point attractive B. Magnetic power in lodestone c. Magnetic power in needle D. swinging of magnetic needle | 10 |

384 | Find the value of x for which the expression 2 – 3x – 4×2 has the greatest value. (1) 16 | 10 |

385 | Is the following equation a quadratic equation? ( (x+2)^{3}=x^{3}-4 ) A. Yes B. No c. Ambiguous D. Data insufficient | 10 |

386 | Check whether the following are Quadratic equations ( (x+2)^{3}=2 xleft(x^{2}-1right) ) | 10 |

387 | The sum of all real values of ( x ) satisfying the equation ( left(x^{2}-5 x+5right)^{x^{2}+4 x-60}=1 ) is? | 10 |

388 | If ( a^{2}-a b=0, ) which of the following is the correct conclusion? ( mathbf{A} cdot a=0 ) B . ( a=b ) ( mathbf{c} cdot a^{2}=b ) D. either ( a=0 ) or ( a=b ) | 10 |

389 | Using the identity ( a^{2}-b^{2}= ) ( (a+b)(a-b) ) solve ( left(7 frac{3}{4}right)^{2}-left(2 frac{1}{4}right)^{2} ) | 10 |

390 | The product of 2 consecutive integers is 20 find them | 10 |

391 | 63. The current of a stream runs at the rate of 4 km an hour. A boat goes 6 km and comes back to the starting point in 2 hours. The speed of the boat in still water is (1) 6 km/hour (2) 8 km/hour (3) 7.5 km/hour (4) 6-8 km/hour | 10 |

392 | f ( p=-2, ) find the value of: ( -3 p^{2}+4 p+7 ) | 10 |

393 | Find the root of the quadratic equation ( x^{2}+2 sqrt{2 x}+6=0 ) by using the quadratic formula A . ( x=sqrt{2} pm 2 i ) B. ( x=-sqrt{2} pm 2 i ) c. ( x=-sqrt{4} pm 2 i ) D. ( x=-sqrt{2} pm 4 i ) | 10 |

394 | The expression ( frac{5-x}{x^{2}-x-20} ) when simplified equals A ( cdot frac{1}{(x+4)} ) в. ( frac{1}{(x-4)} ) c. ( -frac{1}{(x+4)} ) D. ( frac{1}{(x-5)} ) | 10 |

395 | For what values of ( m in R, ) both roots of the equation ( x^{2}-6 m x+9 m^{2}- ) ( 2 m+2=0 ) exceed ( 3 ? ) B. ( left(frac{11}{9}, inftyright) ) c. ( [1, infty] ) D. ( [0, infty] ) | 10 |

396 | If ( x^{4}+frac{1}{x^{4}}=119, ) then the value of ( x- ) ( frac{1}{-} ) is ( x ) ( A cdot 6 ) B. 12 c. 11 D. | 10 |

397 | If the sum of the roots of the quadratic equation ( a x^{2}+b x+c=0 ) is equal to the sum of the square of their reciprocals, then ( frac{a}{c}, frac{b}{a} ) and ( frac{c}{b} ) are in A . GP в. нР c. АGР D. AP | 10 |

398 | Check whether the following are Quadratic equations ( x^{2}+3 x+1=(x-2)^{2} ) | 10 |

399 | Greatest ratio of roots of ( 4 x^{2}-2left(a^{2}+right. ) ( left.b^{2}right) x+a^{2} b^{2}=0 ) if ( a=2 b ) | 10 |

400 | Find the roots of the equation ( 2 x^{2}+ ) ( x-6=0 ) by factorisation. | 10 |

401 | The number of roots of the equation ( 2^{x}+2^{x-1}+2^{x-2}=7^{x}+7^{x-1}+7^{x-2} ) is- | 10 |

402 | Solve: ( frac{2 x-1}{x+4}-2 x-5 x+3=0 ) | 10 |

403 | Find the value of ( k ) for which the equation ( 3 x^{2}-6 x+k=0 ) has distinct and real root. | 10 |

404 | Solve ( boldsymbol{x}+mathbf{2}+boldsymbol{y}+mathbf{3}+ ) ( sqrt{(x+2)(y+3)}=39 ) ( (x+2)^{2}+(y+3)^{2}+(x+2)(y+ ) 3)( =741 ) | 10 |

405 | A quadratic equation in ( x ) is ( a x^{2}+ ) ( boldsymbol{b} boldsymbol{x}+boldsymbol{c}=mathbf{0}, ) where ( boldsymbol{a}, boldsymbol{b}, boldsymbol{c} ) are real numbers and the other condition is ( mathbf{A} cdot a neq 0 ) в. ( b neq 0 ) c. ( c neq 0 ) ( mathbf{D} cdot b=0 ) | 10 |

406 | Find the quadratic function ( boldsymbol{f}(boldsymbol{x}) boldsymbol{i} boldsymbol{f} boldsymbol{f}(boldsymbol{0})=mathbf{1}, boldsymbol{f}(1)=mathbf{0}, boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{f}(boldsymbol{3})= ) ( mathbf{5} ) | 10 |

407 | Find the value of discriminant for ( sqrt{3} x^{2}+2 sqrt{2} x-2 sqrt{3}=0 ) | 10 |

408 | Which of the following is a quadratic polynomial in one variable? A. ( sqrt{2 x^{3}}+5 ) . B. ( 2 x^{2}+2 x^{-2} ) c. ( x^{2} ) D. ( 2 x^{2}+y^{2} ) | 10 |

409 | Ifa, ß are the roots of x2 + px +q=0 and y, 8 are the roots of r+rx+s=0, evaluate (a-ya-8)(-y) (B-8) in terms of p, q, r and s. Deduce the condition that the equations have a common (1979) root. | 10 |

410 | Equation of the tangent at (4,4) on ( x^{2}= ) 4y is A. ( 2 x+y+4=0 ) В. ( 2 x-y-4=0 ) c. ( 2 x+y-12=0 ) D. ( 2 x+y+12=0 ) | 10 |

411 | Find the value(s) of ( k ) for which the equation ( boldsymbol{x}^{2}+mathbf{5} boldsymbol{k} boldsymbol{x}+mathbf{1 6}=mathbf{0} ) has equal roots. | 10 |

412 | 63. 11 (*+ +* +- 4 = 0. then possible of x will be (x+0. x# 1) (1) 5485 2 515 (3 3445 (4) – 3415 | 10 |

413 | In the following, determine the value of ( k ) for which the given value is a solution of the equation. ( mathbf{3} boldsymbol{x}^{2}+mathbf{2} boldsymbol{k} boldsymbol{x}-mathbf{3}=mathbf{0}, boldsymbol{x}=-frac{mathbf{1}}{mathbf{2}} ) | 10 |

414 | If the quadratic equation ( k x^{2}-2 k x+ ) ( 6=0 ) has equal roots, then find the value of ( k ) | 10 |

415 | The sum of the real roots of the equation ( |boldsymbol{x}-mathbf{2}|^{2}+|boldsymbol{x}-mathbf{2}|-mathbf{2}=mathbf{0} ) ( A cdot 2 ) B. 3 ( c cdot 4 ) D. | 10 |

416 | Divide 18 into 2 parts such that their product is 81 A. 9,-9 в. 3,27 c. ( 9, frac{1}{9} ) D. 9,9 | 10 |

417 | If ( boldsymbol{A}=boldsymbol{x}^{2}+boldsymbol{x}+mathbf{1}, boldsymbol{B}=boldsymbol{x}^{2}-boldsymbol{x}+mathbf{1} ) then ( boldsymbol{A}-mathbf{2} boldsymbol{B} ) | 10 |

418 | 7. Find all integers x for which (5x-1)<(x+1)2 < (Tx-3). | 10 |

419 | Discriminant of the equation ( -3 x^{2}+ ) ( 2 x-8=0 ) is A . -92 B. -29 c. 39 D. 49 | 10 |

420 | Find the value of ( k ) for which the quadratic equation ( (k-2) x^{2}+ ) ( 2(2 k-3) x+5 k-6=0 ) has equal roots ( A ) B. 3 c. A and B both D. none of these | 10 |

421 | If ( alpha ) and ( beta ) are zeroes of the polynomial ( 2 x^{2}+3 x+7 . ) Find a quadratic polynomial whose zeroes are ( frac{1}{alpha^{2}} & frac{1}{beta^{2}} ) A ( cdot 49 x^{2}+18 x+4 ) B . ( 49 x^{2}-18 x+4 ) c. ( 49 x^{2}-23 x-4 ) D. ( 49 x^{2}-21 x+4 ) | 10 |

422 | Determine the nature of roots of the following quadratic equation: ( 2 x^{2}+5 x+5=0 ) | 10 |

423 | The solution of the equation ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=mathbf{2} ) will be A .2,-1 в. ( _{0,-1,-frac{1}{5}} ) ( mathrm{c} cdot_{-1,-frac{1}{5}} ) D. None of these | 10 |

424 | Negetive of Discriminant of the following quadratic equation is : ( x^{2}-x+1=0 ) | 10 |

425 | If one root of ( x^{2}+a x+8=0 ) is 4 and the equation ( x^{2}+a x+b=0 ) has equal roots, then ( b= ) A . 7 B. 9 ( c .1 ) D. 3 | 10 |

426 | Which is a quadratic equation? A ( cdot x+frac{1}{x}=2 ) B . ( x^{2}+1=(x+3)^{2} ) c. ( x(x+2) ) D. ( _{x+frac{1}{x}} ) | 10 |

427 | If ( n ) is a positive integer and ( n in[5,100] ) then the number of integral roots of the equation ( x^{2}+2 x-n=0 ) are A . 4 B. 6 c. 8 D. 10 | 10 |

428 | If the equation ( 2 x^{2}-6 x+p=0 ) has real and different roots, then the values of ( p ) are given by ( ^{A} cdot_{p}frac{9}{2}} ) ( mathrm{D} cdot_{p} geq frac{9}{2} ) | 10 |

429 | Let ( a, b, c ) be the sides of a triangle. No two of them are equal and ( lambda epsilon R ) If the roots of the equation ( x^{2}+2(a+b+ ) ( c) x+3 lambda(a b+b c+c a)=0 ) are real then. | 10 |

430 | Check whether the following is a quadratic equation or not ( (x+1)^{2}=2(x-3) ) | 10 |

431 | If both roots of the equation ( a x^{2}+ ) ( 2 x a+1+a^{2}-16=0 ) are opposite in ( operatorname{sign}, ) then the range of ( a ) is ( A cdot(-infty,-4) cup(4, infty) ) B . (-4,4) ( mathbf{c} cdot(-infty,-4) cup(0,4) ) D ( cdot(0,4) ) | 10 |

432 | The trinomial ( a x^{2}+b x+c ) has no real roots, ( a+b+c<0 . ) Find the sign of the number ( c ) | 10 |

433 | The sign of the quadratic polynomial ( a x^{2}+b x+c ) is always positive, if? ( mathbf{A} cdot ) a is positive and ( b^{2}-4 a c leq 0 ) B. a is positive and ( b^{2}-4 a geq 0 ) ( mathrm{C} cdot ) a can be any real number and ( b^{2}-4 a c leq 0 ) D. a can be any real number and ( b^{2}-4 a c geq 0 ) | 10 |

434 | The roots of ( a x^{2}+b x+c=0, ) where ( a neq 0, b, c epsilon R ) are non real complex and ( a+c 2 b )B . ( 4 a+c<2 b ) c. ( 4 a+c=2 b ) D. None of these | 10 |

435 | ( boldsymbol{x}^{2}-(boldsymbol{m}-mathbf{3}) boldsymbol{x}+boldsymbol{m}=mathbf{0}(boldsymbol{m} in boldsymbol{R}) ) be a quadratic equation. Find the value of ( boldsymbol{m} ) for which both the roots are equal: A ( cdot{1,9} ) B. ( c .3 ) D. {4,11} | 10 |

436 | The value of ( k, ) of the roots of the equation ( 2 k x^{2}+2 k x+2=0 ) are equal is ( A cdot frac{4}{5} ) B. 4 c. 1 D. | 10 |

437 | ( frac{x-a}{x-b}+frac{x-b}{x-a}= ) | 10 |

438 | The given quadratic equations have real roots and roots are Real and equal, ( sqrt{frac{3}{2}} ) ( mathbf{2} boldsymbol{x}^{2}-mathbf{2} sqrt{mathbf{6} boldsymbol{x}}+mathbf{3}=mathbf{0} ) A. True B. False | 10 |

439 | If ( boldsymbol{alpha}, boldsymbol{beta} in boldsymbol{C} ) are the distinct roots, of the equation ( x^{2}-x+1=0, ) then ( alpha^{101}+ ) ( beta^{107} ) is equal to A . B. 2 ( c cdot-1 ) D. | 10 |

440 | Identify which of the following is/are a quadratic polynomial function: This question has multiple correct options ( mathbf{A} cdot f(x)=(x+1)^{3}-(x+2)^{3} ) ( g(x)=left{begin{array}{cc}frac{x^{4}}{x^{2}} & text { if } x neq 0 \ 0 & text { if } x=0end{array}right. ) C ( cdot h(x)=(x+1)^{2}-(x+2)^{2} ) D. All of these | 10 |

441 | Solve the equation: ( 4 x^{2}-4 p x+left(p^{2}-q^{2}right)=0 ) | 10 |

442 | f ( x=3 t, y=1 / 2(t+1), ) then the value of ( t ) for which ( x=2 y ) is ( A cdot 1 ) B. ( 1 / 2 ) ( c .-1 ) D. ( 2 / 3 ) | 10 |

443 | Is the given equation quadratic? Enter 1 for True and 0 for False. ( boldsymbol{n}-mathbf{3}=mathbf{4} boldsymbol{n}^{2} ) | 10 |

444 | If the roots of the equation ( frac{alpha}{x-alpha}+ ) ( frac{beta}{boldsymbol{x}-beta}=1 ) be equal in magnitude but opposite in ( operatorname{sign}, ) then ( alpha+beta ) is equal to: A. B. 1 ( c cdot 2 ) D. | 10 |

445 | Decide whether ( m^{2}+m+2=4 m ) is a quadratic equation | 10 |

446 | The number of solutions of the equation, ( 2{x}^{2}+5{x}-3=0 ) is A. No solution B. ( c cdot 2 ) D. Infinite | 10 |

447 | The number of quadratic equation which are unchanged by squaring their roots is | 10 |

448 | ( boldsymbol{x}^{2}-(boldsymbol{m}-mathbf{3}) boldsymbol{x}+boldsymbol{m}=mathbf{0}(boldsymbol{m} in boldsymbol{R}) ) be a quadratic equation. Find the value of ( boldsymbol{m} ) for which, both the roots lie in the interval of (1,2) A. ( (10, infty) ) ) в. ( (-infty, 0) ) ( c cdot(-infty, infty) ) D. None of the above | 10 |

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