Question # 1

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cos x

- sin x

- cos x

tan x

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-1

0

1

Undefined

5 unbiased coins coins are tossed simultaneously. The probability of getting at least one head is

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1 / 32

31 / 32

1 / 16

None of these

w^-12= ______

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0

1

w

w²

If 2x +y + λ =0 is normal to parabola y2 =-8x,λ= _____

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12

8

24

-24

The value of k (k > 0) for which the equation x²+ kx + 64 = 0 and x²- 8x + k = 0 both will have real roots is

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8

-16

-64

16

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2x

2

Every set is an improper subset of

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Empty set

Equivalent set

Itself

Singleton set

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0

1

-1

2

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8

4

64

The product of cube roots of unity is

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Zero

1

-1

None of these

Tangent is ...............function

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Inverse

one-one

in-to

Periodic

Which of the following is not a quadrantal angle

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90°

100°

180°

270°

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none of these

The extraction of cube root of a given number is a

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Unary Operation

Binary Operation

Relation

None of these

Two sets A and B are said to be disjoint if

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0

20

90

80

Which one is quadrantal angle

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8181710°

2345°

-8181180°

-2344°

The conic is a parabola, when:

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ᵨ > 1

ᵨ < 1

ᵨ = 1

ᵨ = 0

Ifθ= 60° then

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sinθ= 1/2

tanθ= cot 30°

θ=π/4

secθ= 4

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none of these

If θ be angle between u,v and u,v determine the sides of a triangle then the third side opposite to angle θ has length

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|u+v|

|u|+|v|

|u-v|

|u|-|v|

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2

4

8

12

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cosec x + c

-cosec x + c

-sec x + c

sec x + c

The common ration of a geometric sequence cannot be

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0

1

2

3

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a = -1/2, b = -1

a = 1, b = 2

a = 2, b = 3

None of above

The product of the four fourth roots of unity is

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0

1

-1

None of these

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The central angle of an arc of a circle whose length is equal to the radius of the circle is called one

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Degree

Second

Minute

Radian

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

Archimedes approximate the function by horizontal function and the area under f by the sum of small

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Parallelograms

Squares

Retangles

Polygons

Which of the following is skew symmetric matrix

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cos h²x + sin h² x

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an even function

an odd function

an even and implicit function

neither even nor a odd

The mid point of the line segment joining the points (a,b) and (b,a) is

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csc(-π/2) = __________;

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0

1

-1

Undefined

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The graph of linear equation 2x + 3y = 10

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Parabola

Circle

Hyperbola

Straight line

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The zero vector is regarded to be parallel to

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Every vector

Is some cases

Both a,b

None

The roots of the equation will be irrational if b²- 4ac is

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Positive and perfect square

Positive but not a perfect square

Negative

Zero

If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is

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ay2 +2by+c=0

ay2+2by+4c=0

ay2+2by+c=0

ay2+by+4c=0

sin5θ+sin3θ = _______;

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2sin 4θ cosθ

2cos 4θ sinθ

2cos 4θ cosθ

-2sin 4θ sinθ

The number of different ways of describing a set is

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One

Two

Three

Four

Which is the proper rational function

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The nth term of an A.P., is 12-4n. Its common difference is

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8

4

16

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The contra positive of p → q is

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q → p

~q→~q

~p→~q

None of these

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5x^{4 + c}

1/6 x⁶+ c

5x²+ c

1/5 x⁶+ c

If the cutting plane is slightly tilted and cuts only one nappe of the cone, the resulting section is:

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an ellipse

Circle

a hyperbola

a parabola

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Principle of equality of fractions

Rule for product of fractions

Golden rule for fractions

Rule for quotient of fractions

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5

-5

none

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If a = {2m/2m < 9 ,m€ p} , the (n A) =

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{2,3,4,5,6,7,8}

{2,4,6,8............16}

{ 4, 6}

{2,3,5,7}

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

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x > 1

x < 1

x = 1

All values of x

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The coordinates of a point P(x,y) referred to XY-system are

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(x+y,y+k)

(x-h,y-k)

(x,y)

(x-h,y-k)

Φ set is the _______ of all sets

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Subset

Union

Universal

Intersection

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π

π/6

-π/2

2π

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If in the expansion of (1+x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

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4

5

6

7

If a₁= 3, r = 2, then the nth term of the G.P. is

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2.3^n-1

3.2ⁿ

3.2ⁿ⁺¹

3.2^n-1

If a 1-1 correspondence can be established b/w two sets A and B, then they are called

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Equal sets

Equivalent sets

Over lapping sets

None of these

The set {1, -1, i, -i}

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Form a group w.r.t addition

Form a group w.r.t multiplication

Does not form a group w.r.t multiplication

Not closed under multiplication

The three noncollinear points through which a circle passe are known, then we can find the:

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Variables x and y

Value of x and c

three constants f,g and c

inverse of the circle

How many term are there in the A.P, in which a₁ = 11 , a_n =68, d=3

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30

27

20

21

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Sum of all the four forth roots of unity is

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1

-1

i

0

The consecutive terms of a progressions are 30, 24, 20. The next term of the progression is

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{0} is a

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Empty set

Singleton set

Zero set

Null Set

A sequence whose reciprocal is an A.P is called

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Oscillator

H.P

G.P

None of these

The positive real number which is the measure of the length of a vector is called the

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Unit vector

Modulus

Inverse

None of these

The set { {a, b} } is

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Infinite set

Singleton set

Two points set

Empty set

An open sentence formed by using the sign of equality "=" is called

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Equation

In equation

True sentence

False sentence

The number of subsets of a set having three elements is

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4

6

8

none of these

The sum of all even numbers less than 100 is

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2450

2352

2272

2468

Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

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BA

A²

AB

B²

If (1+x-2x³)⁶= 1+a₁x + a₂x²+ a₃x³+ ..... the the value of a₂+ a₄+ a₆+ .....+a₁₂will be

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32

31

64

1024

Domain of 1+cot2θ=csc2θ is

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[0,π]

R-{x/x=nπ,n∈ z}

(-∞,+∞)

[-1,1]

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A onto B

both a & c

A into B

none of these

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0

1

8

∞

The equation of the normal to the circle x²+ y²= 25 at (4, 3) is

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3x - 4y =0

3x - 4y =5

4x + 3y = 5

4x + 3y = 25

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The function ø(x) is ananti derivativeof function f (x),x∈Df if

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ø′(x) =∫f(x)dx

ø(x) =∫f(x)dx

ø′(x) =f(x)

ø(x) =∫′(x)dx

The unit vector along y-axis is

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none of these

If x, y, z are the pth, qth, rth terms of an A.P. and also of G.P., then x^y-z. y^z-x. z^x-yeqals

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xyz

0

1

None of these

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The value of sin [ arc cos (-1/2)] is

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No term of a geometric sequence can be

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0

1

2

3

(7,9) +(3,-5) =

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(4,4)

(10,4)

(9,-5)

(7,3)

Every identity matrix is

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Row-vector

Scalar

Column-vector

All

Number of selections of n different things out of n

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1

nPr

n!

nPr

Find a if 1 is a root of the equation x²+ ax + 2 = 0

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3

-3

2

0

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If a particle moves according to the law s = t³- t², then its velocity at time t = 1.5 is

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9/2

15/4

5

None

If a₁, r are first term and the common ratio respectively then the sum of an infinite geometric series is

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A key ring is an example of

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Permutation

Circular permutation

Combination

None

If A is any matrix then its additive inverse is

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A

A^-1

A^t

-A

Derivative of a w.r.t x is

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0

1

x