A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

- 18 months
- 19 months
- 20 months
- 21 months

If α ≠ β but α^{2} = 5α - 3 and β^{2} = 5β - 3, then the equation having α/β and β/α as its roots is

- 3x
^{2}- 19x - 3 = 0 - 3x
^{2}- 19x + 3 = 0 - x
^{2}- 5x + 3 = 0 - 3x
^{2}+ 19x - 3 = 0

Let a and b be roots of the equation px^{2} + qx + r, p ≠ 0. If p, q, r are in A.P. and 1/a + 1/b = 4, then the value of |a - b| is

- 2√17 / 9
- √61 / 9
- √34 / 9
- 2√13 / 9

The domain of the function f(x) = 1/√(|x| - x) is

- (0,∞)
- (-∞,0)
- (-∞,∞)
- (-∞,∞) - {0}

The function f(x) = log (x + √(x^{2} +1)) is

- an even function
- an odd function
- neither an even nor an odd function
- a periodic function

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

- not symmetric
- transitive
- reflexive
- a function

If a ϵ R and the equation -3(x - [x])^{2} + 2(x - [x]) + a^{2} = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval

- (-1, 0) U (0, 1)
- (-2, -1)
- (1, 2)
- (-∞, -2) U (2, ∞)

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is

- 510
- 256
- 275
- 219

If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then

- B = C
- A = C
- A ∩ B = φ
- A = B

A function f from the set of natural numbers to integers defined by

f(n) = (n-1)/2, when n is odd

f(n) = -n/2, when n is even

- one-one and onto both
- one-one and but not onto
- neither one-one nor onto
- onto but not one-one

For real x, let f(x) = x^{3} + 5x + 1, then

- f is one-one and onto R
- f is onto R but not one-one
- f is neither one-one nor onto R
- f is one-one but not onto R

If ((1 + i)/(1 - i))^{x} = 1, then

- x = 4n, where n is any positive integer.
- x = 2n, where n is any positive integer.
- x = 4n + 1, where n is any positive integer.
- x = 2n + 1, where n is any positive integer.

If |z - 4| < |z - 2|, its solution is given by

- Re(z) > 3
- Re(z) > 0
- Re(z) < 0
- Re(z) > 2

If (1 – p) is a root of quadratic equation x^{2} + px + (1 – p) = 0, then its roots are

- 0, -1
- 1, 1
- 0, 1
- 2, 1

If a, b, c are distinct +ve real numbers and a^{2} + b^{2} + c^{2} = 1, then ab + bc + ca is

- greater than 1
- equal to 1
- less than 1
- any real number

If A^{2} – A + I = 0, then the inverse of A is

- A - I
- A
- I + A
- I - A

Number greater than 1000 but less than 4000 is formed using the digits 0, 2, 3, 4 when repetition allowed is

- 105
- 125
- 128
- 625

Let S(k) = 1 + 3 + 5 + .. + (2k – 1) = 3 + k^{2} . Then which of the following is true?

- principle of mathematical induction can be used to prove the formula
- S(k) implies S(k + 1)
- S(k) implies S(k - 1)
- S(1) is correct

Let f(x) = 4 and f′(x) = 4. Then Lim_{x→2} (x f(2) − 2 f(x)) / (x − 2) is given by

- -4
- 2
- 3
- -2

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u and the other from rest with uniform acceleration f. Let α be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time

- t = (u sin α)/f
- t = (f cos α)/u
- t = (u sin α)
- t = (u cos α)/f

The area of the region bounded by the parabola (y – 2)^{2} = x – 1, the tangent to the parabola at the point (2, 3) and the x-axis is

- 3
- 6
- 9
- 12

The order and degree of the differential equation (1 + 3dy/dx)^{2/3} = 4d^{3}y/dx^{3} are

- (3, 3)
- (3, 1)
- (1, 2)
- (1, 2/3)

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?

- 74
- 65
- 68
- 73

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then median of the new set

- is two times the original median
- is increased by 2
- remains the same as that of the original set
- is decreased by 2

A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is

- 1/3
- 1/2
- 3/4
- 2/3

Events A, B, C are mutually exclusive events such that P(A) = (3x + 1)/3, P(B) = (x - 1)/4, P(C) = (1 - 2x)/4. The set of possible values of x are in the interval

- [1/3, 1/2]
- [1/3, 13/3]
- [0, 1]
- [1/3, 2/3]

The number of solution of tan x + sec x = 2 cos x in [0, 2π) is

- 0
- 1
- 2
- 3

The negation of the statement "If I become a teacher, then I will open a school" is

- I will not become a teacher or I will open a school
- Either I will not become a teacher or I will not open a school
- Neither I will become a teacher nor I will open a school
- I will become a teacher and I will not open a school

A triangle with vertices (4, 0), (-1, -1), (3, 5) is

- right angled but not isosceles
- neither right angled nor isosceles
- isosceles and right angled
- isosceles but not right angled

If the two circles (x-1)^{2} + (y-3)^{2} = r^{2} and x^{2} + y^{2} - 8x + 2y + 8 = 0 intersect in two distinct point, then

- 2 < r < 8
- r = 2
- r > 2
- r < 2

A plane which passes through the point (3, 2, 0) and the line (x-4)/1 = (y-7)/5 = (z-4)/4 is

- 2x - y + z = 5
- x + 2y - z = 1
- x - y + z = 1
- x + y + z = 5

The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is:

- 1880
- 1120
- 1240
- 1960

If 2+3i is one of the roots of the equation 2x^{3} – 9x^{2} + kx – 13 = 0, k ∈ R, then the real root of this equation:

- does not exist
- exists and is equal to 1/2
- exists and is equal to -1/2
- exists and is equal to 1

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is:

- 26.5
- 28
- 29.5
- 31

If the coefficients of the three successive terms in the binomial expansion of (1+x)^{n} are in the ratio 1:7:42, then the first of these terms in the expansion is:

- 6th
- 7th
- 8th
- 9th

What is the sum of the squares of the roots of the equation x^{2} + 2x - 143 = 0?

- 170
- 180
- 190
- 290

If the difference between the roots of ax^{2} + bx + c = 0 is 1, then which one of the following is correct?

- b
^{2}= a(a + 4c) - a
^{2}= b(b + 4c) - a
^{2}= c(a + 4c) - b
^{2}= a(b + 4c)

If α and β are the roots of the equation x^{2} - q(1+x) - r = 0, then what is (1+α)(1+β) equal to?

- 1 - r
- q - r
- 1 + r
- q + r

If \( A = \begin{bmatrix}1 & 2 \\2 & 3 \end{bmatrix} \) and \( B = \begin{bmatrix}1 & 0 \\1 & 0 \end{bmatrix} \) then what is determinant of AB?

- 0
- 1
- 10
- 20

A and B are two matrices such that AB = A and BA = B then what is B^{2} equal to?

- B
- A
- I
- -I

If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

- 4/3
- 1
- 7/4
- 8/5

Let P be the point on the parabola, y^{2} = 8x which is at a minimum distance from the centre C of the circle, x^{2} + (y + 6)^{2} = 1. Then the equation of the circle, passing through C and having its centre at P is:

- x
^{2}+ y^{2}– x + 4y – 12 = 0 - x
^{2}+ y^{2}– x/4 + 2y – 24 = 0 - x
^{2}+ y^{2}– 4x + 9y + 18 = 0 - x
^{2}+ y^{2}– 4x + 8y + 12 = 0

The system of linear equations

x + λy – z = 0

λx – y – z = 0

x + y – λz = 0

has a non-trivial solution for:

- exactly one value of λ.
- exactly two values of λ.
- exactly three values of λ.
- infinitely many values of λ.

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal half of the distance between its foci, is:

- 4/√3
- 2/√3
- √3
- 4/3

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

- 3a
^{2}– 32a + 84 = 0 - 3a
^{2}– 34a + 91 = 0 - 3a
^{2}– 23a + 44 = 0 - 3a
^{2}– 26a + 55 = 0

The integral \( \int \dfrac{2x^{12}+5x^9}{(x^5+x^3+1)^3} dx \) is equal to:

- \( \dfrac{-x^5}{(x^5+x^3+1)^2} + C \)
- \( \dfrac{x^{10}}{2(x^5+x^3+1)^2} + C \)
- \( \dfrac{x^5}{2(x^5+x^3+1)^2} + C \)
- \( \dfrac{-x^{10}}{2(x^5+x^3+1)^2} + C \)

If the line, (x-3)/2 = (y+2)/-1 = (z+4)/3, lies in the plane, lx + my – z = 9, then l^{2} + m^{2} is equal to:

- 18
- 5
- 2
- 26

If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation

cosx + cos2x + cos3x + cos4x = 0 is:

- 5
- 7
- 9
- 3