1 
The value of lo g 10 1 + lo g 10 10 + lo g 10 10...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Special Functions
Logarithms

2 
A sequence 192, 360, 576……. is formed by multiplying the corresponding terms of two di...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP

3 
Find the value of C0 + C2 + C4 +... in the expansion of (1+x)8. Type in your answer ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Polynomials
Algebraic Identities
Binomial Theorem

4 
Consider a, b and c in a G.P. such that  a+b+ c =15 . The median of these three terms is a , and b...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP

5 
Second term of a geometric progression is 1000 and the common ratio is = 1/n, where n is a natural n...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP

6 
The maximum value of ( 3−x ) 3 ( 2−x ) 4 when ( ( 2<x<3 ) ) ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Inequations

7 
A quadratic function f( x ) attains a max of 3 at x=1 , the value of the function at x=0 is ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Graphs of Functions
Maxima and Minima

8 
How many positive integer values can x take that satisfy the inequality (x  8) (x  10) (x  12)......
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Inequations

9 
Let a+b+c=1 . Find the minimum value of ( 1 a −1)( 1 b −1)( 1 c −1). Type...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Graphs of Functions
Maxima and Minima

10 
If the first, third and thirteenth terms of an arithmetic progression are in geometric progression, ...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP
AP

11 
The sum of all the real roots of the equation  x−2  2 +  x−2 &minu...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations

12 
What is the minimum value of sum of the squares of the roots of the equation x 2 &min...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Graphs of Functions
Maxima and Minima

13 
x + y = 8 and P=5 x 2 + 11 y 2 , where x, y≥0 . W...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations

14 
For graph of f(x)= 1 x−4 , what is the value of x for which f(x) reaches infinity? ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Special Functions

15 
Find the range of p such that one root of the equation x 2 −8x+p lies between 0 and 1. ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations

16 
What is the area enclosed by the curve  x+4 + y−2 =4 (in sq. units)? Type in y...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Special Functions

17 
If x is any integer from 6 to 2 inclusive, how many values of x satisfy the following inequation:...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Inequations

18 
Which of the following inequalities has a solution set that when graphed on the number line, is a si...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations

19 
If a and b are roots of equation 3 x 2 +5x+k=0 , a 2 − b 2 =25 ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations

20 
Find the area bounded by the curves 3x = 6 + 2y and y = 3 (in sq. units) Type in your answer...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Special Functions
Modulus
Graphs of Functions

21 
If α, β be the roots of the quadratic equation x 2 − 5x + ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations

22 
Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequen...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP

23 
If x2– x – 6 < 0, x2+ 6x – 5 > 0 and x2– 10x + 16 < 0, then ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Quadratic Equations
Inequations

24 
The roots of the equation x 2 −x( a+b )+ab− b 2 =0 (where a & b ar...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations

25 
If a, b, and c are odd integers, then the roots of ax2+bx+c = 0 cannot be: A) Ration...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Polynomials
Algebraic Identities

26 
Find the values of parameter ‘a’ such that the roots α and β of th...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Quadratic Equations

27 
Find a and b such that (x + 1) and (x + 2) are factors of the polynomial x 3 +a ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Polynomials
Operations on Polynomials

28 
If log 3 2 , log 3 ( 2 x −5) and log 3 ( 2 x −7/2) are in AP, then fi...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Special Functions
Logarithms
Sequences and Series
AP, GP
AP

29 
If x and y are positive real numbers such that 12xy +21x+20y=46 , find the minimum value of ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Graphs of Functions
Maxima and Minima

30 
Find the value of a for which 4 t −(a−4) 2 t +(9/4)a<0 where ‘t’ be...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Quadratic Equations

31 
The real values of 'a' for which the quadratic equation 2x2 – (a3 + 8a 1)x +a2 &ndash...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Applications of Linear and Quadratic Equations

32 
Given the value of a1, b1, c1, a2, b2, c2 ≠ 0 and the following 2 linear equations, can the...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations

33 
The ratio of the sum to n terms of two APs is (7n+1): (4n+27), then the ratio of their 9th term...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP

34 
Let Sk be the sum of the first k terms of the arithmetic progression t1, t2, ..., tk. If Sm/Sn = m2/...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP
AP

35 
If c is positive and 2a x 2 +3bx+5c=0 doesn’t have any real root, then ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Quadratic Equations

36 
If ( 2 + 4 + 6 +... 50 terms ) (1 + 3 + ...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP

37 
If  y ≥5 and x = −( y 5 ) k  , then which one of the following is n...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations
Inequations

38 
On a fence, there are sparrows and pigeons. When five sparrows leave, there remain two pigeons for e...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations

39 
If the difference between roots of the equation x 2 +ax+1=0 is less than 5,then find the set...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Quadratic Equations

40 
Find the number of solutions when the following two inequations are satisfied: y = 6x2  13x + 6&nb...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Inequations

41 
Which of the following graphs represents the quadratic function f(x) =  x2 + 4x 4 ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Graphs of Functions
Identification of Graphs

42 
Solve the following set of linear equations in two variables 10/(x + y) + 2/(x  y) = 4 15/(...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations

43 
Find the number of nonnegative integral solutions of 3x + 10y = 200. Type in your answer as an int...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations

44 
Find the value of x and y when the solution of the following equations is given by ( 3xy+1)/3...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations

45 
A twodigit number is such that it is the product of two distinct perfect squares. The tens digit, u...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP
AP
Theory of Numbers
Numbers, Properties & Operations

46 
Let f(x)=a x 2 +bx+c , where a, b and c are Real numbers, where ‘a’ is not equal to ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Quadratic Equations

47 
Simplify ( 8.73*8.73*8.73 )+( 4.27*4.27*4.27 ) ( 8.73*8.73 )−( 8.73*4.27 )+( 4.27*...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Polynomials
Algebraic Identities

48 
2x = 4y = 8z and xyz = 288, then the value of 1/2x + 1/4y + 1/8z is ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations

49 
The sum of a number x and its reciprocal is 8/15 less than thrice the sum of another number y and th...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations

50 
How many consistent independent equations are needed to solve for n unknown variables?
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations

51 
F(x) is a fourth order polynomial with integer coefficients and with no common factor. The root...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Special Functions

52 
If α and β are the roots of the equation, 2x2 –3x –6 =0...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Quadratic Equations

53 
What should be the value of k, for the following equations to be consistent? 5x – 2y = ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations

54 
If (x1)3 is a factor of x4+ax3bx2+cx1 = 0, then find the other factor. ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Polynomials
Operations on Polynomials

55 
Solve for x: 3 ( x 2 −x) + 4 ( x 2 −x) =25 Type your answer as the sum of roo...
CAT
Quantitative Ability
Algebra

56 
If 2x+3y=10 , then the maximum value of x 2 y 3 is ( x, y>0 ) ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Inequations

57 
If the roots of 10 x 3 −c x 2 −54x−27=0 are in H.P, then find the value of c :...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP
AP

58 
If the sum of four natural numbers in AP is 60 and the sum of their squares is 920, find the smalles...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP
AP

59 
For how many values of b is the following set of equations inconsistent 4x + 6y = 14 2x + by = 7 ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations

60 
a2n  b2n , for any positive integral values of n, is always divisible by ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Polynomials
Algebraic Identities

61 
Solve x4 + 4x3 12x2 <= 0
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Inequations

62 
How many pairs of integer (p, q) are possible such that p2 – q2 = 288? ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Polynomials
Operations on Polynomials

63 
x4 – px3 + qx2 – rx + 8 = 0 divided by x + 1 leaves a remainder of 3...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Polynomials
Operations on Polynomials

64 
What is the remainder when the given polynomial p(x) is divided by x? Type in your answer as an i...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Graphs of Functions

65 
Aditya has a collection of cubeshaped toys where each of his cubes is of a different size. Before h...
CAT
Quantitative Ability
Algebra
Sequences and Series
HP and Other Sequences and Series

66 
Find the value of x if x= 1 3+ 1 3+ 1 3+ 1 3+....... ...
CAT
Quantitative Ability
Algebra

67 
Find the sum to n terms of the series 1 √1+√3 + 1 √3+√5 + 1 &radic...
CAT
Quantitative Ability
Algebra
Sequences and Series
HP and Other Sequences and Series

68 
Find the area bounded by the curves 30 = 10x  y and 20 = 4y  5x (in sq. units) Type in yo...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Special Functions
Modulus
Graphs of Functions

69 
If three positive real numbers a, b, c are in A.P. such that abc = 4, then minimum value of b ...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP
AP

70 
A quadratic function attains minimum value of –25 at x=1 . If f( 0 )=–24 , what is ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Graphs of Functions
Maxima and Minima

71 
An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral t...
CAT
Quantitative Ability
Algebra
Sequences and Series

72 
If S = 1 + x + x2+ x3+  to infinity, then x =
CAT
Quantitative Ability
Algebra
Sequences and Series

73 
Find the combined area of the 2 quadrilaterals formed by the intersection of x + 5y = 15 and 7 =...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Special Functions
Modulus
Graphs of Functions

74 
If 1/(b+c), 1/(c+a), 1/(a+b) are in A.P., then what is true about a2,b2,c2? ...
CAT
Quantitative Ability
Algebra
Sequences and Series

75 
If a, b and c are in A.P. then a 3 + c 3 −8 b 3 is equal to: ...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP
AP

76 
If [x] is the greatest integer function less than or equal to x then , [ 500 1 5 ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Special Functions

77 
If x, 2y, and 3z are in A.P. where, the distinct numbers x, y, z are in G.P., then the common ...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP
AP

78 
Find the sum of all the coefficients in the expansion of (x2+2x)20
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Polynomials, Functions and Graphs
Polynomials
Algebraic Identities
Binomial Theorem

79 
( 1− 1 3 )⋅( 1− 1 4 )⋅...⋅( 1− 1 n ) equals ...
CAT
Quantitative Ability
Algebra
Sequences and Series

80 
A child tore off one leaf from a book having page number from 1 to N. Summation of the remaining num...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP
Applications of AP and GP

81 
A test has twenty questions worth 100 points. The test consists of True/False questions worth ...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
Linear and Quadratic Equations
Linear Equations

82 
If the roots of the equation a x 3 +b x 2 +cx+d=0 are in geometric progression, then whic...
CAT
Quantitative Ability
Algebra
Equations and Polynomials
Equations
