**Ques. **If the distance of any point (x, y) from origin is defined as d(x, y) = max {|x|, |y|}, then the locus of the point (x, y), where d (x, y) = 1 is

(a) circle

(b) a square

(c) a triangle

(d) none of these

Ans. (b)

**Ques. **How many nine digit numbers can be formed by using the digits 2, 2, 3, 3, 5, 5, 8, 8, 8 so that the odd digits occupy even positions ?

(a) 7560

(b) 180

(c) 16

(d) 60

Ans. (d)

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**Ques. **The angle between two equal forces acting on a particle when the square of their resultant is three times their product is

(a) 90º

(b) 60º

(c) 120º

(d) none of these

Ans. (b)

**Ques. **If (1 + x – 2x^{2})^{6} = 1 + a_{1}x + a_{2}x^{2} + a_{3}x^{3} . . . . . then the value of a_{2} + a_{4} + a_{6} + . . . .+ a_{12} will be

(a) 32

(b) 31

(c) 64

(d) 1024

Ans. (b)

**Ques. **Number of G.P.’s having 5, 9 and 11 as it’s three terms is equal to;

(a) exactly two

(b) atmost two

(c) at least one

(d) none of these

Ans. (d)

**Ques. **If f’(x) = g(x) and g’(x) = –f(x) for all *x *and f(2) = 4 = f’(2), then f^{2} (24) + g^{2} (24) is

(a) 32

(b) 24

(c) 64

(d) 48

Ans. (a)

**Ques. **If ^{n}P_{3} + ^{n}C_{n–2} = 14n, then n =

(a) 5

(b) 6

(c) 8

(d) 10

Ans. (a)

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**Ques.** cot x – tan x =

(a) cot 2x

(b) 2 cot^{2} x

(c) 2 cot 2x

(d) cot^{2} 2x

**Ans:** (c)

**Ques. **The coefficient of x^{4} in the expansion of (1 + x + x^{2} + x^{3})^{11} is

(a) 900

(b) 909

(c) 990

(d) 999

Ans. (c)

**Ques. **The product of lengths of perpendiculars from any point of the hyperbola x^{2} – y^{2} = 8 to its asymptotes is

(a) 2

(b) 3

(c) 4

(d) 8

Ans. (c)

**Ques. **The roots of the equation 3^{2x} – 10.3^{x} + 9 = 0 are

(a) 1, 2

(b) 0, 2

(c) 0, 1

(d) 1, 3

Ans. (b)

**Ques. **Total number of ways in which four boys and four girls can be seated around a round table, so that no two girls together, is equal to

(a) 7 !

(b) (3 !) (4 !)

(c) (4 !) (4 !)

(d) (3 !) (3 !)

Ans. (b)

**Ques. **In a triangle *ABC*, the tangent of half difference of two angles is one third the tangent of half the sum of the two angles. The ratio of the sides opposite the angles in

(a) 2 : 3

(b) 1 : 3

(c) 2 : 1

(d) 3 : 4

Ans. (c)

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**Ques. **From an urn containing 3 white and 5 black balls, 4 balls are transferred into an empty urn. From this urn a ball is drawn and found to be white. The probability that out of four balls transferred, 3 are white and 1 is black, is

(a) 1/3

(b) 1/7

(c) 2/3

(d) none of these

Ans. (b)

Related:

**Ques. **The curve y – e^{xy} + x = 0 has a vertical tangent at the point

(a) (1, 1)

(b) at no point

(c) (0, 1)

(d) (1, 0)

Ans. (d)

**Ques. **If are in A.P. 10^{ax + 10} , 10^{bx + 10} , 10^{cx + 10} are in

(a) A.P.

(b) G.P. when *x* > 0

(c) G.P. for all *x*

(d) G.P. when *x* < 0

Ans. (c)

**Ques. **A man has 7 friends. In how many ways he can invite one or more of them for a tea party

(a) 128

(b) 256

(c) 127

(d) 130

Ans. (c)

**Ques. **If log 2, log (2^{n} – 1) and log (2^{n} + 3) are in A.P., then *n *=

(a) 5/2

(b) log_{2} 5

(c) log_{3} 5

(d) 3/2**
Ans:** (b)

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**Ques. **The sum of all positive divisors of 960 is

(a) 3048

(b) 3087

(c) 3047

(d) 2180

Ans. (a)

**Ques. **The area of the triangle formed by the line x + y = 3 and the angle bisectors of the pair of straight lines x^{2} – y^{2} + 2y = 1 is

(a) 2

(b) 4

(c) 6

(d) 8

Ans. (a)

**Ques. **The normal chord of a parabola y^{2} = 4ax at (x_{1},x_{1}) subtends a right angle at the

(a) Focus

(b) Vertex

(c) (–*a*, 0)

(d) None of these

Ans. (a)

**Ques. **If iz^{3} + z^{2} – z + i = 0 then the value of |z| is

(a) 1

(b) 2

(c) < 1

(d) > 1

Ans. (a)

**Ques. **Number of three digit numbers of the form *xyz* with *x* > 1 and digits are not repeated, is

(a) 640

(b) 576

(c) 800

(d) none of these

Ans. (b)

**Ques. **The graph of the function y = f(x) is symmetrical about *x* = 2, then

(a) f(x + 2) = f(x – 2)

(b) f(2 + x) = f(2 – x)

(c) f(x) = f(–x)

(d) none of these

Ans. (b)

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**Ques. **The number of distinct terms in the expansion of (x + 2y – 3z + 5w – 7u)^{n} is

(a) n + 1

(b) ^{n+4}C_{4
}(c) ^{n+4}C_{n+2}^{
}(d) none of these

Ans. (b)

**Ques. **In an election the number of candidates is 1 greater than the persons to be elected. If a voter can vote in 254 ways, then the number of candidates is

(a) 7

(b) 10

(c) 8

(d) 6

Ans. (c)

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