Online Test

Question # 1

Which of the following integrals can be evaluated

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If -1 < x < 0, which of the following statements must be true?

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x < x²< x³

x < x³< x²

x²< x³< x

x²< x < x³

The multiplicative inverse of x such that x = 0 is

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-x

does not exist

1/x

0

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Ifα andβ be irrational roots of a quadratic equation, then

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In 30,60,90 triangle, if the smallest side is 6 then the side opposite to the angle of 60°is

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12

3

6

How many elements are in the sample space of two rolling dies

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6

12

18

36

Two dice are rolled. The number of possible outcome in which at least one die shows 2 is?

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5

12

11

7

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None of these

In Binomial Expansion the coefficients of the terms equidistant from beginning and end of the expansion are

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Zero

Same

Equal to preceding term

Equal to following term

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

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

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A²+ B²

A²+ B²+ 2AB

A + B

A²+ B²+ AB + BA

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

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1/5

1/13

5/52

1/52

In the expansion of (a + b)ⁿin every term the sum of the exponents of a and b is

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n

n + 1

2n - 1

2n + 1

The conic is a parabola if

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e < 1

e > 1

e = 1

e = 0

The curves y = x², y = x intersect at

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(0,0) , (1, 1)

(2, 4)

(0,3), (-1, 1)

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

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140

130

120

110

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The set {{a,b}} is

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Infinite set

Singleton set

Two points set

None

Which of the vectors have opposite direction?

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Both A and B

A fraction in which the degree of the numerator is less than the degree of the denominator is called

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Polynomial

Proper fraction

Rational fraction

Mixed fraction

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-2-i

An angle of one radian is equivalent to

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90°

60°

67°

57° 18^'

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

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25, 20

20, 10

20, 5

15, 10

In which quadrant is the solution of the equation sin x - 1 = 0

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II quadrants

II and III quadrants

III and IV quadrants

I quadrant

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Nilpotent matrix

Singular matrix

Non singular matrix

Diagonal matrix

The Domain of f(x) = log x is

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If 1 + Cos x = 0, then x =

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2

1

3

4

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1

2

3

4

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

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Function on B

Range

Domain

A into B

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An equation

Linear equation

Rational fraction

Identity

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1/2

3/5

4/5

1

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Total number of terms in the expansion of (a + b)⁵+ (a - b)⁵after simplification are

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3

1

4

7

If f₁(x) and f₂(x) are any two anti derivatives of a function F (x), then the value of f₁(x) - f₂(x) =

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A variable

A constant

undefined

infinity

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The common difference of the sequence 7,4,1, .......... is

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1

-3

5

0

The number of diagonals of a six sided figure are

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9

6

12

3

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Unit matrix

Diagonal matrix

Nilpotent matrix

Zero matrix

A point of a solution region where two of its boundary lines intersect, is called

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Boundary

Inequality

Half Plane

Vertex

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(0, e)

(0, 1)

None

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-3/4

1/16

1/4

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0

-25

5

45

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0

1

-1

2

Complex roots of real quadratic equation occur in

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Conjugate pair

ordered pair

reciprocal pair

quadratic function

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3/2 is

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An irrational number

Whole number

A positive integer

A rational number

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

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4 pie

14 pie

8 pie

2 pie

If Z = (1,2), then Z^-1= ?

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(0.2, 0.4)

(-0.2, 0.4)

(0.2 , -0.4)

(-0.2, -0.4)

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1

2

3

4

The perpendicular bisector of any chord of a circle

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Passes through the centre of the cirle

Does not pass through the centre of the circle

May or may not pass through the centre of the cirlce

None of these

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The radius of the circle (x-1)²+ (y+3)²= 64 is

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8

4

64

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None of these

Which is in the solution set of 4x - 3y < 2

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(3, 0)

(4, 1)

(1, 3)

None

The line joining (1, 3) to (a, b) has unit gradient then

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a-b = -2

a+b = 0

a-b + 5

2a+3b=1

If ab > 0 and a < 0, which of the following is negative?

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b

-b

-a

(a - b)²

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

Every prime number is also

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Rational number

even number

Irrational number

multiple of two numbers

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A positive integer

A negative integer

A natural number

An irrational number

The graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

In general matrices do not satisfy

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Commutative law w.r.t multiplication

Associative law w.r.t addition

Distributive law w.r.t addition

Multiplication of a scalar with the matrix

What is a proper rational fraction?

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All are proper rational fractions

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Free vector

Null vector

Unit vector

None of these

6 is

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A prime integer

An irrational number

A rational number

An odd integer

0 (Zero) is

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An irrational number

A rational number

A negative integer

A positive number

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

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3(-2)^n-1

2(-2)ⁿ⁺¹

3(-2)ⁿ

4(-2)^n-1

The gradient of the line joining (1, 4) and (-2, 5) is

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3/8

-2 2/3

-1/3

2

If the 19th term of A.P is 8 and the 4th term is 20, then the first term is

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20.2

25.5

27.5

37.5

The equation of the line with gradient 1 passing through the point (h, k) is

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Y = x + k - h

Y = k/h x + 1

Y = x + h - k

Ky = hx - 1

The range of inequality x + 2 > 4 is

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(-1, 2)

(-2, 2)

None

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None of these

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a + x is

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A trinomial

A binomial

A moomial

An equation

The number ways in which 5 distinct toys can be distributed among 3 children is

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3⁵

5³

C₃⁵

P₃⁵

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A + B

C²/AB

A²/BC

B²/AC

Unit vector in the positive direction of x-axis is

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All

What is the period of Cot x?

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The complement of set A relative to universal set U is the set

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A - U

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None of these

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Tan x

X

- x

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30°

45°

60°

90°

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If 2 Sin x Cos 2 x = Sin x then?

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The magnitude of a vector can never be

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Zero

Negative

Positive

Absolute

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Cos 315°=

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0.707

0.5

1

0

If the angle of a triangle are in the ratio 2:3:7, the triangle is

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Obtuse

Acute

Right angle

Isosceles

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15

60

90

20

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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

The center of a circle of radius 10 is on the origin. Which of the following points lies with in the circle

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(10, 0)

(8, 8)

(8, 4)

(0, 10)

If the sum of the roots of the equation ax²- 2x + 2a = 0 is equal to their product, then the value of a is

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1

2

3

4

If 4 - x > 5, then

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x > 1

x > -1

x < 1

x < -1

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A linear equation

A cubic equation

A quadratic equation

An equation for circle

Which of the following is the equation of a line with slope 0 and passing through the point (4, 3)

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X = 4

X = -4

Y = 3

Y = -6

If n is a positive integer, then 3+6+9+ -----------------+3n =

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A < G < H

A > G > H

A < G > H

A > G < H

Sin(a + b) + Sin (a - b) =

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Sin a Cos b

Sin a Sin b

Sin a + Cos b

Sin a - 2 Cos b

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

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2 x 5⁰

5¹⁰

10⁵

2¹⁰

The direction cosines of y-axis are

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1,0,0

0,1,0

0,0,1

1,1,1

If a statement S(n) is true for n = 1 and the truth of S(n) for n + K implies the truth of S(n) for S(n) = K + 1, then S(n) true for all

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All Real numbers

All integers

Positive integers

All complex numbers

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 = -1

X = 2, y = 2

If 0 < n < 1, n is a rational number, the number of terms in the expansion of (1 + X)ⁿare

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n + 1

2n

Infinitely many

2n²

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An irrational number

Whole number

A positive integer

A rational number

For which of the following ordered pairs (s, t) is s + t > 2 and s - t < -3?

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(3, 2)

(2, 3)

(1, 8)

(0, 3)

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The multiplicative inverse of -1 in the set {1-, 1} is

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1

-1

+1

0

A function F(x) is called even if

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F(x) = F(-x)

F(x) = -F(x)

2F(x) = 0

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p < r

p > r

p + r < 0

p - r < 0

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

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4n - 3

4n + 1

3n - 4

4n + 3

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2

1

0

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

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A = B

A < B

A < x

B < y

A farmer possesses 100 hectometers of land and wants to grow corn and wheat. Cultivation of corn requires 3 hours per hectometer while cultivation of wheat requires 2 hours pert hectometer. Working hours cannot exceed 240. If he gets a profit of Rs. 20 per hectometer for corn and Rs. 20 per hectometer for wheat. The profit function for the farmer is

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P(x,y) = 20x + 15y

P(x,y) = 2x + 3y

P(x,y) = x + y

P(x,y) = 3x + 2y

A line segment whose end points lie on a circle is called

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The secant of the circle

The arc of the circle

The chord of the circle

The circumference of the circle

Sin x + Cos x = 1 x =

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Period of Sin 2x =

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1

2

3

4

If P(E) is the probability that can event will occur, then P(E) =

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1

0.5

2

0

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

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Addition

Multiplication

Division

Subtraction

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If the sum of the roots of (a + 1)x²+ (2a + 3)x +(3a+4) = 0 is -1, then product of the roots is

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1

2

-2

-1

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The value of the polynomial 3x³+ 4x²- 5x + 4 at x = -1 is

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12

1

10

-10

Which is an explicit function

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All

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

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None

If in isosceles right angled triangle, one side is a then hypotenuse is

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a

cannot be determined by given information

If A and B are two events, then P(AUB) = ? (when A and B are disjoint)

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P(A) - P(B)

P(A) x P(B)

P(A)+P(B)

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1

0

-2

3

If c is a constant number and if f is the function defined by the equation f(x) = c for all values of x, then f is differentiable at every x and f is defined the equation f(x) = _________

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f

1

C

0

What is the domain of y = Cot^-1x?

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Set of irrational number only

Set of all real numbers

Set of intergers only

Set of complex numbers only

In the expansion of (a + b)ⁿin every term the sum of the exponents of a and b is

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n

n + 1

2n - 1

2n + 1

If any two rows (or any two columns) of a square matrix are inter changed, the determinant of the resultant matrix 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

A vector of magnitude zero is called

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Position vector

Null vector

Free vector

None of these

The constant distance of all points of the cirlce 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

If A = (3, 8) and B = (5, 6), then the distance between A and B is

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2

1

6

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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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10 cm

20 cm

30 cm

40 cm

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0

-2

1

4

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)

If A and B are matrices such that AB=BA=I then

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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

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10

20

40

26

The associative angle of 280°is

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100°

10°

If you are looking a high point from the ground, then the angle formed is

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Angle of elevation

Angle of depression

Right angle

Horizon

If the diagonal of a square has coordinates (1, 2) and (5,6) the length of a side is

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3

4

1

5

Which is not a half plane

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ax + by < c

ax + by > c

Both A and B

None

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None

Write the first four terms of the arithmetic sequence if a₁= 5 and other three consecutive terms are 23,26,29

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23, 26, 29, 32

5, 8, 11, 14

8, 11, 14, 17

None of these

If K₁: K₂= 1 : 1 then the point P dividing the line is

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Midpoint

Extreme left point

Extreme Right Point

P lies out side k₁and k₂

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15

15 i

-15 i

-15

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The difference of two consecutive terms of an A.P. is called

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Constant of series

Common ratio

Common difference

General term

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A polynomial

An inequality

An identity

A linear function

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120 degrees are equal to how many radians?

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Which of the following is the subset of all sets?

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{1, 2,3}

{0}

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

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None of these

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If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a

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Parabola

Circle

Hyperbola

Ellipse

Multiplicative inverse of "1" is

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0

+ 1

1

{0, 1}

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None

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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

The values of n such that, in the binomial expansion of (1 - x)ⁿ, co-efficient of x², co-efficient of x²is 3, are

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-2, -3

2, -3

-2, 3

None of these

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n = 3 only

n > 5

n > 3

n < 5