Question # 1

The general solution of the differential equation x dy / dx = 1 + y is:

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2

1

3

None

The period of 2 cos x is

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30π

7π

5π

2π

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If A is a skew-symmetric matrix of order n and P, any square matrix of order n, prove that P' AP is

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Skew-symmetric

Symmetric

Null

Diagonal

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I3

rI3

r

none

The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is

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2

1

-1

-2

The equation of the sphere thro' the origin and making intercepts a, b, c on co-ordinate axes is

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x²+ y²+ z²+ ax + by + cz = 0

x²+ y²+ z²- 2ax - 2 by - 2 cz = 0

x²+ y²+ z²= a + b + c

x²+ y²+ z²- ax - by - cz =0

If distance between (a,2) and (0,0) is 2 then a = _______

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0

2

4

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tan 3x + c

cot 3x + c

- cot 3x + c

If n is any positive integer then n! > 2^n-1for

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The set of integers is a subset of

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The set of natural numbers

The set of whole numbers

The set of prime numbers

The set of rational numbers

Cos 60° = ______

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1

2

1/2

3

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The constant distance of all points of the circle from its centre is called the

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Radius of the circle

Secant of the circle

Chord of the circle

Diameter of the circle

For what value of k, 3x -2y+ k= 0 is tangent to the circle x2 +y2 +6x -4y =0

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k=0

k=0 or 26

k = 26

k=-13

The square root of 2i - 20i is

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±(5 - 2i)

±(5+ 2i)

(5 - 2i)

None of these

The n numbers A₁,A₂,A₃,.....A_nare called an arithmetic means between a and b if a.A₁,A₂,A₃.....A_n, b is ______

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An arithmetic series

An arithmetic sequence

A geometric sequence

A harmonic sequence

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The function discontinuous at x = 0 is (1) tan x (II) cot x (III) sec x (iv)cosec x)

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I & III

I & IV

II & IV

II & III

The domain of an infinite sequence is a

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Set of natural numbers

R

Subset of N

None of the above

The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

The sum of the squares of three distinct real numbers, which are in G.P., is S². if their sum isαS then

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x

y

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(a - c)²= b²- c²

(a - c)²= b²+ c²

(a + c)²= b²- c²

(a + c)²= b²+ c²

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If a statement S(n) is true for n = i where i is some natural number and the truth of S(n) for n = k > i implies the truth of S(n) for n = k +1 then S(n) is true for all positive integers

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A key ring is an example of

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Permutation

Circular permutation

Combination

None

The line y = 2 x + c is a tangent to the parabola y²= 16 x if c equals

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-2

-1

0

2

The graph of a quadratic function is

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Circle

Straight line

Parabola

Triangle

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