Question # 1

If 1 + Cos x = 0 then x =

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π +2n π

π + nπ

π - nπ

π/2

The general solution of the differential equation dy/dx = log x is

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Y = -x log x- x +c

Y = x log x + x²

Y = x log x -x +c

Y= 2x log x + 2x +c

The graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

If A and B are matrices of same order than (A + B)(A + B)=

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addition

multiplication

subtraction

None

The sum of the series 1+5+9+13+17+21+25+29 is:

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10 cm

20 cm

30 cm

40 cm

A relation in which the equality is true only for some values of the unknown variable is called

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An identity

An equation

A polynomial

Inverse function

The mid point of the line joining (=1,-3) to(3,-5) is

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(1, 1)

(1,-1)

(2, -8)

(1, -4)

The point (-5,3) is the center of a circle and P(7,-2) lies on the circle the radius of the circle is

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2

13

7

8

If a and b are any two distinct negative real numbers and G-ab where A.G.H represent arithmetic geometric and harmonic means then

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1

ω²

ω

0

0 (zero) is

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A irrational number

A rational number

A negative integer

A positive number

Tan (π + Tan^-1 x) =?

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Tan x

X

-x

Cot^-1 x

Ab > 0 and a > 0 then

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a > b

a < b

a = b

None

In general matrices do not satisfy

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Not a group

A group w.r.t. subtraction

A group w.r.t. division

A group w.r.t. multiplication

If 0 is not an integral multiple of π/2 then Cot⁴ θ+ Cot² θ=?

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Cosec⁴ θ -Cosec²θ

Tan θ - Tan² θ

Cosec² θ + Cosec θ

Sinθ Cosθ

What is the conjugate of -7 -2i ?

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-7 + 2i

7 + 2i

7-2i

√53

If p and r are integers P = 0, and p ≠ -r, which of the following must be true?

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p < r

p > r

p + r < 0

p - r < -0

Sin^-1 (-x) =?

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Sin^-1 x

-Sin^-1 x

Cos^-1 x

-Cos^-1 x

ω⁸⁸ = ?

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A and B are multiplicative inverse of each other

A and B are additive inverses of each other

A and B are singular matrices

A and B are equal

What is the period of Cot x?

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2π

π

π/2

4π

The number of ways in which we can courier 5 packets to 10 cities is

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2 x 5^o

5¹⁰

10⁵

2¹⁰

The value of x, and y, when (x+iy)²=5+4i

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X=2, y=-1

X=-2, y=1

X=2, y=-i

X=2, y=2

Derivative of strictly increasing function is always

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Zero

Positive

Negative

Both A and B

∫1/ax +b dx =

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1/a log |ax + b| +c

Log |ax + b| +c

1/b log |ax +b| +c

1/x log |ax + b| +c

In a school, there are 150 students. Out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for Physics class. The student enrolled for English cannot attend any other class, but the students of mathematics and Physics can take two courses at a time. Find the number of students who have taken both physics and mathematics.

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40

30

50

20

If α and β be irrational roots of a quadratic equation, then

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α = b/a and β = ca

α = a/b and β = -c/a

α² + β² = 1

α = -b/a and β= c/a

The sum of the interior angles for a 16 sided polygon is

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0

ω

1

1 / ω

Complex roots of real quadratic equation occur in

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Nilpotent matrix

Singular matrix

Non singular matrix

Diagonal matrix

The set (Q, .)

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Infinite set

Singleton set

Two points set

None

A function F(x) is called even if

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F(x) = F(-x)

F(x) = -F(x)

2F(x) = 0

One of the roots of the equation 2x² + 3x + n = 0 is the reciprocal of the other, then n = --------------------

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Both A,B have the same number of columns

Both A,B do not have the same order

Number of col A is same as number of rows of B

Number of rows of A is same as number of col of B

If Sin^-1 x + cos^-1 y = π, then x and y are

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Associative angles

Complementary angles

Reflex angles

Supplementary angles

Every prime number is also

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Rational number

even number

Irrational number

multiple of two numbers

The range of inequality x + 2 > 4 is

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(-1,2)

(-2,2)

(1,∞)

None

Which of the following is not defined?

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Arcsin 1/9

ArcCos (-4/3)

Arctan 11/12

Arccot (-4)

1+2+3+......+n=?

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n(n +1)/2

n +1/2

n(n +1)(2n +1)/6

n³

Period of Sin 2x =

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π

4π

2nπ

2π

If the angle between two vectors with magnitude 8 and 2 is 60° then their scalar product is

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12

8

16

1

The length of rectangle is twice as much as its breadth. If the perimeter is 120 cm, the length of the rectangle is

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Same as the original determinant

Additive inverse of the original determinant

Both A and B

Adj of the original matrix

Sin x + Cos x=1 x=

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π

π/2

π/3

π/4

The nth term in G.P 3,-6,12,............ is

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25, 20

20, 10

20, 5

15, 10

Sec^-1 x=

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Cos^-1 1/x

Cosec^-1 1/x

Cos-1 (-x)

Tan^-1 x

A die is thrown what is the probability that there is a prime number on the top?

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1/2

1/3

1/6

2/3

Which is a proper rational fraction

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3x - 7/x² +4

2x² - 5/x² + 4

3x⁴/2x² - 15

All are proper rational fraction

If f (x) = x/x²- 4 then which is not included in the domain of f(x)

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0

-2

1

4

In the figure angle A is =

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15

60

90

20

If the vector 2i+4j-2k and 2i +6j+xk are perpendicular then x-7

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4

8

14

7

1/x² -1 = ? (in case of making partial fraction)

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Ax +B/x² -1

A/x + B/ x- 1

A/ x+1 + B/x-1

None

If x < y, 2x = A and 2y = B then

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A =B

A < B

A< X

B < y

An angle of one radian is equivalent to

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90^o

60^o

67^o

57^o, 18^o

Two natural numbers whose sum is 25 and difference is 5, are

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25, 20

20, 10

20, 5

15, 10

The set of complex numbers forms a group under the binary operation of

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0

±1

1

{0,1}

Which of the following is the solution of Cot²x = 1/√3

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π/5

π/3

π/7

π/9

Cos^-1 (-x) =_______.

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π +cos^-1 x

π -sin^-1 x

π +sin^-1 x

π -cos^-1 x

A standard deck of 52 cards shuffled what is the probability of choosing the queen of the diamonds

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1/5

1/13

5/52

1/52

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

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-x

does not exist

1/x

0

An m x n matrix is said to be rectangular if

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Forms a group w.r.t. addition

Non commutative group w.r.t. multiplication

Forms a group w.r.t. multiplication

Doesn't form a group

Domain of Y = csc x is

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R - nπ, n ε I

R

R -nπ/2,nεI

All negative Integers

If Cⁿ_r, Pⁿ_r = 24:1 then r = ?

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1

2

3

4

If Cosθ =0, Then θ=

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nπ/2

(2n + 1)π/2

(2n - 1)π/2

(n ±1)π/2

The multiplicative inverse of x such that x = 0 is

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-x

does not exist

1/x

0

6 is

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A prime integer

An irrational number

A rational number

A odd integer

If Cosα = 3/5, Cosβ = 5/13, then

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Cos(α +β) =33/65

Sin(α +β) =56/65

sin²(α +β/2) =1/65

Cos(α +β) =63/65

Given X, Y are any two sets such that number of elements in X=28, number of elements in set Y=28, and number of elements in set X∪Y=54, then number of elements in set X∩Y=

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-7 + 2i

7 + 2i

7-2i

√53

If y = (ax)^m + b^m, then dy/dx equals

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m (ax)^m x^m-1

ma^m x^m-1

m a^m x^m-1

m a^m x^m-2

Sin^-1 √3/2 =?

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2π/3

π/2

π/3

v/5

The area of circle of unit radius=

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0

1

4

π

P(x) = 2x⁴ -3x³ +2x-1 is polynomial of degree

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1

2

3

4

The nth term of A,P:1,5,9,15...........is given by

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4n - 3

4n + 1

3n -4

4n +3

Sin-1 (√2/2)=?

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π/2

π/3

3π/4

2π

The circle (x -2)² + (y + 3)² =4 is not concentric with the circle

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(x -2)² + (y + 3)² =9

(x +2)² + (y - 3)² =4

(x -2)² + (y + 3)² =8

(x -2)² + (y + 3)² =5

Two matrices A and B are conformable for multiplication (AB) if and only if

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Addition

Multiplication

Division

Subtraction