Question # 1

tan^-1x > cot^-1x holds for

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x > 1

x < 1

x = 1

All values of x

The solution set of the equation tan^-1x - cot^-1x = cos^-1(2 - x) is

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[0, 1]

[-1, 1]

[1, 3]

None of these

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l²+ m²+ n²= 0

l²- m²+ n²= 1

l²+ m²+ n²= 1

l²+ m²- n²= 0

A tower subtends an angleαat a point on the same level as the root of the tower and at a second point, b meters above the first, the angle of depression of the foot of the tower isβ. The height of the tower is

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b cotαtanβ

b tanαtanβ

b tanαcotβ

None of these

Which of the following is a vector.

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distance

temperature

energy

acceleration

Z is a

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Infinite set

Finite set

Singleton set

Set of all integers

The number of solution of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is

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0

1

2

3

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The two parts into which 57 should be divided so that their product is 782 are

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43,14

34,23

33,24

44,13

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1

2

3

A circle passing through the vertices of any triangle is called

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Circumcirle

Incircle

Escribed circle

Unit circle

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Trichotomy property

Additive property of inequality

Transitive property

Multiplicative property

A line joining two distinct points on a parabola is called a ______ of the parabola.

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Chord

Tangent

Lust rectum

directrix

What is range of the function g (x) =|x-3|?

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[0 ,∞ )

(0 ,∞)

(-∞ ,3]

[0,∞)

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Singular

Non-singular

Adjoint

None of above

Three integers are chosen at random from the first 20 integers. Then probability that their product is even, is

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2 / 19

3 / 29

17 / 19

4 / 19

Optimal solution is found by evaluation the objective function at

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All point of feasible region

Corner point

Origin

None

The parametric equations of a circle are

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The axis of the parabola y²= 4ax is

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X = 0

Y = 0

X = y

X = -y

an - an-1 will be common difference in an A.P if

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n = 1∀n∈ N

n>1∧n∈N

n∈Z

None of the above

A fraction in which the degree of the numerator is greater than or equal to the degree of the denominator is called

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A proper fraction

An improper fraction

An equation

An identity

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none of these

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If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

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1594

792

924

2924

∫f(x) is known as:

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Definite itegral

Indefinite integral

Fixed integral

Multiple integral

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Through how many radians does the hour hand of a clock turn in one hour

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The set of first elements of the ordered pairs in a relation is called its

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domain

range

relation

function

p, q, r and s are integers. If the A.M. of the roots of x2- px + q2= 0 and G.M. of the roots of x2- rx + s2= 0 are equal, then

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q is an odd integer

r is an even integer

p is an even integer

s is an odd integer

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none of these

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