Question # 1

Two cards are drawn at random from a well shuffled pack of cards. The probability that at least one of them is a face card is

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3 / 17

5 / 17

7 / 17

9 / 17

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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 positive integer just greater than (1+0.0001)¹⁰⁰⁰⁰is

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4

5

2

3

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

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

The seventh term of an A.P whose first term is P and common difference is q. is

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P-6q

P+6q

P-4q

P-nq

The total number of subsets that can be formed out of the set {a, b, c} is

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1

4

8

12

Domain of sinθis

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Set of real numbers

Set of complex numbers

Set of natural numbers

Set of even numbers

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In a country, 55% of the male population has houses in cities while 30% have houses both in cities and in village. Find the percentage of the population that has house only in villages.

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45

30

25

50

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5 / 12

3 / 8

5 / 8

7 / 4

If f(x) = x²- x then f(2) is

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4

6

2

0

An airplane flying at height of 300 meters above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60° and 45° respectively. Then the height of the lower plane from the ground is (in meters).

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The graph of y < 2 is the

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Left half plane

upper half plane

Right half plane

Lower half plane

There is no element common in

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N and W

E and W

N and O

Q and Q'

The Principal value of sin-1 (-1/1/2)

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π/2

-π/2

π

-π

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Associative law of multiplication

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ab - ba

a(bc) = (ab) c

a(b + c) = ab +ac

(a +b)c = ac + bc

The element range of sequence are called

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Series

progression

Members

Terms

The equation of the circle with centre (-h, -k) and radius r is

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(x +h)²+ (y+k)²= r²

(x +h)²+ (y-k)²= r²

(x -h)²+ (y+k)²= r²

(x -h)²+ (y-k)²= r²

cos^-1(cos x) =

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x

cos x

x = 1/x

cos^-2 x

√2 is a number

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Rational

Irrational

Even

Odd

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0

1

-1

If distance of (a,b) from x-axis is 2 then

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a = 2

b = 2

a = b

b = 4

f (x) = | x | is a/an

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Injective function

Bijective function

Surjective function

Implicit function

The set {{a,b}} is

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Infinite set

Singleton set

Two points set

None

A triangle has six

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side

elements

angle

tangents

If the sum of two unit vectors is a unit vector the the magnitude of their difference is

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√2

√3

1

None of these

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

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A = B

A < B

A < x

B < y

The modulus of 12-5i is:

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7

13

√7

119

The set of real numbers is a subset of

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The set of natural numbers

The set of rational numbers

The set of integers

The set of complex numbers

The coefficient of x¹⁰in the expansion (x³+3/x²)¹⁰is

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1700

17023

17027

17010

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2

6

If sin x + sin²x = 1, then the value of Cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x + 2 cos⁴x + cos²x-2 is equal to

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0

1

2

sin²x

The slope of the normal at (5 cos, 0, 5 sin 0) to the circle. x²+y² = 25 is:

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tan𝜽

cos𝜽 /sin𝜽

-cot𝜽

- tan𝜽

The distance between the points A(-8,3) and B(2,-1) is

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116

none of these

A box contains 10 red 30 white and 20 black marbles When a marble is drawn at random the probability that it is either red or white is

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1/6

1/3

1/2

2/3

The lotus of intersection of perpendicular tangents to the parabola y² = 4ax is:

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Axis of the parabola

Focal chord of the parabos

The tangent at vertex of the parabola

a directrix of the parabola

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

Range of sin x is ______

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[-1, 1]

R

Negative real numbers

None of these

The function {f(x,y)|y = ax2 +bx +c} is

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One-one function

Constant function

Onto function

Quadratic function

Form a group of 5 men and 3 women, a committee of 4 persons is to be selected randomly. The probability that there is a majority of men is

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1/4

1/3

1/2

1/6

The distance of the point (a, b) from x-axis is

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a

b

a + b

∀a,b,c∈R and c>0,then

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a>b ⇒ ac < bc

a>b ⇒ ac > bc

a<b ⇒ ac > bc

None of these

(1+w)(1+w2)(1+w4)(1+w8)....50 factors

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0

-1

1

2

The third term in the expansion of (1+2x) is

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-2x2

-4x2

2x2

4x2

The conic is a parabola, when:

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ᵨ > 1

ᵨ < 1

ᵨ = 1

ᵨ = 0

In R, the multiplicative inverse of a is

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0

1

-a

1/a

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28 / 81

28 / 243

81 / 28

243 / 82

The point of concurrency of the medians of a triangle is called

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incentre

circumcentre

e-centre

centroid

A square matrix A = [aij] is upper triangular when

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cij = 0

bij = 0

aij = 0 for all i > j

dij = 0

Identity w.r.t intersection in a power set of any set is

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∅

Set itself

Singleton set

{0}

The three consecutive numbers a,√ab,b are in

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G.P

H.P

G.M

None of these

A person standing on the bank of a river observes that the angle subtended by a tree of the opposite bank is 60°, when he retreats 40 m from the bank, he finds the angle to be 30°. The height of the tree and the breadth of the river are

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One-to-one and onto

One-to-one but not on to

Onto but not one-to-one

Neither one-to-one nor onto

A sequence of number whose reciprocals form an arithmetic sequence is called

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Geometric sequence

Arithmetic series

Harmonic sequence

Harmonic series

The coordinates of the point that divides the join of A(-6,3) and B(5, -2) in the ratio 2:3 internally

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Period of sin x is

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i is equal

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(1 , 0)

(0 , 1)

(1 , 1)

(0 , 0)

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0

1

13

Range of 3 cot x is ______

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[-1, 1]

[-3, 3]

R

None of these

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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There are ______ types of rational fraction

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Three

Four

Five

Two

Range of cot x is ______

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[-1, 1]

R

Negative real numbers

R - {x | - 1 < x < 1}

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x-axis

y-axis

z-axis

None of these

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-1

0

1

undefined

In how many ways can 5 persons be seated at a round table

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5!

4!

3!

120

The distance of the point (-2 , 3) from y-axis is

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2

-2

3

1

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Z is a group under

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Subtraction

Multiplication

Addition

None of these

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0

undefined

If cosα= 4/5, then cosα/2

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√25 is a number

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Rational

Irrational

Natural

Odd

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If A = {2m/m³= 8 , m€ Z} then A =

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{1,8,27}

{4}

(2,4,6}

{2,16,54}

When a selection of object is made without paying regard to the order of selection, it is called

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Sequence

Series

Combination

Permutation

The number of subsets of a set having three elements is

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4

6

8

none of these

The equation of a line parallel to the tangent to the circle x²+ y²= 16 at the point (2, 3) and passing thro' the origin is

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2x + 3y = 0

2x - 3y = 0

3x + 2y = 0

3x - 2y = 0

The value of cos(cos-1 1/2) is

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1/2

√3/2

-1/2

1/√2

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If the lower limit of an integral is a constant and the upper limit is a variable, then the integral is a

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Constant function

Variable value

Function of upper limit

All

In R the right cancellation property w.r.t. addition is

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The transpose of a zero matrix is a ______

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Column matrix

Zero matrix

Row matrix

Scalar matrix

1 + 2 + 3 + ...... + n = ______

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The corner point of the boundary lines, x-2y

2x + y = 2 is:

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(2,6)

(6,2)

(-2,2)

(2,-2)

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The identity element of a set X with respect to intersection in P(x) is

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X

Does not exist

∅

None of these

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2^x

2^xIn x

2^xIn 2

Domain of 1+cot2θ=csc2θ is

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[0,π]

R-{x/x=nπ,n∈ z}

(-∞,+∞)

[-1,1]

One degree is denoted by

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1⁰

1'

1"

1 rad

The sum of the even coefficients in the expansion (1 + x)ⁿis

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n²

2^n-2

2^n-1

2ⁿ