Question # 1

Let a₁, a₂, a₃, a₄and a₅be such that a₁, a₂, and a₃are in A.P., a₂, a₃and a₄are in G.P and a₃, a₄and a₅are in H.P. Then, a₁, a₃and a₅are in

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G.P.

A.P.

H.P.

None of these

If there is one-one correspondence between A and B, then we write.

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A = B

A⊆ B

A⊇ B

A ∼ B

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

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At

-A

A

A-1

The domain of the function x/x² -4 is given by

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R

R + 2

[R - (+2)

R-4

If the exponent in the binomial expansion is 6, then the middle term is

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2nd

3rd

4th

5th

√23 is

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A rational number

A irrational number

An even integer

A factor of 36

A = B iff

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All elements of A also the elements of B

A and B should be singleton

A and B have the same number of elements

If both have the same element

The intercepts of the plane 2x - 3y + 4z = 12 on the co-ordinate axes are given by

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2, -3, 4

6, -4, -3

6, -4, 3

3, -2, 1.5

6! = ______

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360

720

6.5.4

None of these

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A

B

U

None of these

Additive inverse of - a - b is

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a

-a + b

a - b

a + b

If ΔABC is right triangle then the law of Cosines reduces to

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The Pythagoras Theorem

The law of Sines

The law of cosines

The law of tangents

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real part of z

imaginary part of z

conjugate of z

modulus of z

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

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Period of Tangent function is

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0°

-π

π

2π

The number of standard parabolic functions are is

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4

2

3

1

The point R dividing internally the line joining the points P(x₁, y₁) and Q(x₂, y₂) in the ratio K₁: K₂has the coordinates

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E-radius corresponding to < B is

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If you are looking a bird in the tree from the ground then the angle formed is called angle of______;

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Elevation

Depression

Right angle

None of these

The sum even binomial coefficient of (3+2x)5 is ______term

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16

30

8

32

The periods of the function f(x) = x[x] is

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1

2

Non periodic

None of these

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15/23

7/15

7/8

15/7

The physical quantity which can be specified by a number alongwith unit is called a

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scalar

vector

constant

none of these

1,1/3,1/5,1/7,1/9..... is a

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geometric sequence

finite sequence

infinite sequence

arithmetic series

A key ring is an example of

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Permutation

Circular permutation

Combination

None

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4x + 1

4x

2x³

none of these

The sets {1, 2, 4} and {4, 6, 8, 10} are

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Equal sets

Equivalent sets

Disjoint sets

Over lapping sets

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additive property

multiplicative property

additive identity

multiplicative identity

If we have a statement "if p then q" then q is called

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Conclusion

Implication

Unknown

Hypothesis

The solution set of trigonometric equation contains

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one element

two elements

three elements

Infinite elements

A number A is called the arithmetic mean between a and b if a, A, b is ______

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Arithmetic sequence

Geometric sequence

Harmonic sequence

Arithmetic sequence

If a₁, r and a_nare the first term, common ratio and the nth term respectively of a G. P. then a_n=

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a₁rⁿ

a₁r^n-1

a₁rⁿ⁺¹

a₁r

Which of the following is factor of x11+a11, where n is an odd integer

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x-a

x+a

2x-a

2x+a

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Reflexive property

Symmetric property

Transitive property

Additive property

For non-trival solution |A| is

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non zero

A = 0

|A| = 0

At = 0

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A polynomial P(x)has a factor (x-a)if P(a) =

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a

x

1

0

The angle of depression of a point situated at a distance of 70 meters from the base of a tower is 45°. The height of the tower is

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70 m

85 m

35 m

None of these

(a,b) +(-a,-b) =

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(0,0)

(a,b)

(-a,-b)

(1,1)

Name the property used in 4 x (5 x 8) = ( 4 x 5) x 8

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Associative property of addition

Associative property of multiplication

Additive identity

Multiplicative identity

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Associative law of addition

Commutative law of addition

Additive identity

Closure law of addition

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direction ratios

direction cosines

direction angles

none of these

The sum of the roots of the equation x2 -6x +2 = 0 is

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-6

2

-2

6

The order axioms are satisfied by set of

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C

C and R

R

None of these

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3

2

8

0

6 is

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A prime integar

An irrational number

A rational number

An odd integer

Three unbiased coins are tossed. Then the probabilities of getting two heads is

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3/8

1/8

1/4

None of these

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Period of Cotangent function is

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π

-π

0

-2π

sin(3π/2 -θ)=_______;

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sinθ

cosθ

-sinθ

-cosθ

The equation |x + 4| = x has solution

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x = -2

x = 2

x = -4

x = 4

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sin h x

cos h x

sec h x

cosec h x

If a≠ , b≠ 0 and|a=b|=|a-b|,then vectors a and b are:

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Parallel to each other

Perpendicular to each other

Inclined at 60^o

neither parallel nor perpendicular

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If A⊆ B, and B is a finite set, then

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n (a) < n(B)

n(B)<(A)

n(A)≤ n (B)

n(A)≥ n(B)

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

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1700

17023

17027

17010

Derivative of strictly increasing function is always

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Zero

Positive

Negative

Both (A) and (B)

If |a x b|2 + (a,b)2 = _____

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|a|2 + |b|2

|a|2- |b|2

|a|2|b|2

None

The only function which is both even and odd is

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f(x) =α

f(x) = x

f(x) =0

Both A & B

Range of cotθis

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(+∞to -∞)

(-1 to +1)

(-5 to +5)

Set of even numbers only

The maximum value of sinθcosθis

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1

1/2

1/4

1/6

Area of the circle with ends of a diameter at (-3,2) and (5,-6)

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128π sq. units

64π sq. units

32π sq.units

None of these

A prime number can be a factor of a square only if it occurs in the square at least

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Once

Thirce

Twice

None of these

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 1}

The sum of co-efficient in (1+x-3x²)⁴¹⁶³is

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0

1

-1

None

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1

0

5

2

tan^-1(1/4) + tan^-1(2/9) is equal to

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1/2 cos^-1(3/5)

1/2 sin^-1(3/5)

1/2 tan^-1(3/5)

tan^-11/2

In one hour, the hour hand of a clock turns through

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The set of real roots of the equation log_{(5x + 4)}(2x +3)³- log_{(2x + 3)}(10x²+ 23x + 12) = 1 is

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{-1}

{-3/5}

Empty set

{-1/3}

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(-28,12) divides the join of A(-6,3) and B(5,-2) in ratio

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1:2

3:2

2:3

2:1

(n + 2) (n + 1)n in factorial form is

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16 / 7

6 / 17

7 / 16

None of these

The identity element with respect to subtraction is

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0

1

-1

Does not exist

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2x - 3x + c

x²- 3x + c

The number of combinations of 10 different objects taken 8 objects at a time is

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90

45

55

50

a + x is ______

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A trinomial

A binomial

A monomial

None of these

The general equation of circle x³ + y³ + 2gx + 2fy + c = 0 , contains:

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Three independent variables

Two independent conntants

Three indepentent parameters

Three independent constants

If p and q are two statements then their biconditional 'p if q' is denoted by

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The second degree equation 2x2 -xy+ 5x -2y +2 =0 represents

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Circle

Hyperbola

Ellipse

Pair of straight lines

The 5th term of (3a-2b)^-1is

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

a >b, b >c ⇒a >c is a

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Multiplicative property

Additive property

Trichotomy property

Transitive property of inequality

The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is

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x + y + z - 15 = 0

x - y + z - 15 = 0

x - y - z - 15 = 0

x + y + z + 15 = 0

The fifth term of (a+2x3)17 is

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

How many types of an equation

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1

3

2

None

Which of the following is factor of p(x) =2x3 +3x2+3x+2 ?

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x+1

2x+1

3x+1

2x-1

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The period of sin x/2 = Cos x/3 is

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2p

12p

13p

7p

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{x|x∈R∧x≠x} is a

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Infinite set

Null set

Finite set

None of these

Two cards are drawn at random without replacement. the probability that the first is a king and second is not a king is

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48 / 663

24 / 663

12 / 663

None of these

The set {Z\{0}} is group w.r.t

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Addition

Multiplication

Division

Subtraction

Three dice are thrown together. The probability of getting a total of at least 6 is

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103 / 108

10 / 216

93 / 108

None of these

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x³- x²+ x + c

6x - 2 + c

x³- 2x + c

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3K

K2

K3

K

The point ________ is in the solution of the inequality 4x - 3y < 2

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(0,1)

(2,1)

(2,2)

(3,3)