Question # 1

A tower subtends an angleαat a point on the same level as the root of the tower and at a second point, b meters above the first, the angle of depression of the foot of the tower isβ. The height of the tower is

Choose an answer

b cotαtanβ

b tanαtanβ

b tanαcotβ

None of these

√11 is

Choose an answer

an irrational number

Rational number

odd number

Negative number

Choose an answer

Tan 180° = ______

Choose an answer

-1

0

1

Undefined

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

Choose an answer

The surface generated by lines, consists of two parts, called:

Choose an answer

vertex

apex

nappes

axis

A committee consists of 9 experts taken from three institutions A, B, and C, of which 2 are from, A, 3 form B and 4 from C. If three experts resign, then the probability that they belong to different institutions is

Choose an answer

1 / 729

1 / 24

1 / 21

2 / 7

If 3x4 +4x3+x5is divided by x+1 , which of the following is the remainder

Choose an answer

7

-2

6

1

The ortho center of triangle whose vertices are (0,0)(3,0)(0,4) is

Choose an answer

(0,0)

(1,1)

(2,2)

(3,3)

Choose an answer

A complex number

A rational number

A natural number

An irrational number

If (x₁, y₁) and (x₂,y₂) are the end points of a diameter then the centre of the circle is

Choose an answer

3 x 1

1 x 3

3 x 3

1 x 1

A ________ divides the plane into left and right half planes.

Choose an answer

Vertical line

Horizontal line

Non vertical line

Inequality

sin 2 α=

Choose an answer

If a parabola opens down, then its vertex is at the

Choose an answer

Right of the parabola

Left of parabola

Lowest point on the parabola

Highest point on the parabola

Choose an answer

A diagonal matrix is always

Choose an answer

Identity

Triangular

Scalar

Non-singular

Choose an answer

2

4

8

12

Choose an answer

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

Choose an answer

8

4

16

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

Choose an answer

2

-2

3

1

The probability that a slip of number divisible by 4 is picked from the slips bearing numbers 1, 2, 3, ...10 is

Choose an answer

1/5

1/4

1/3

1/2

(x + 2)²= x²+ 4x + 4 is

Choose an answer

A linear equation

A cubic equation

A quadratic equation

None

If x⁴- 10x²- 2x + 4 is divided by x + 3, then the reminder is

Choose an answer

1

0

4

None of these

3.5+5.4=5.4+3.5 =8.9 this property of addition is called

Choose an answer

additive identity

assoclative property

commulative property

closure property

A number A is said to be the A.M between the two numbers a and b if a, A, b are in

Choose an answer

A.M

A.P

G.P

G.M

A function whose range is just one element is called

Choose an answer

One-one function

Constant function

Onto function

Identity function

Second derivative of y = x⁹+ 10x²+ 2x - 1 at x = 0 is

Choose an answer

10

20

12

1

The behavior of trigonometric function is called

Choose an answer

Continuity

Discontinuity

Periodicity

Smoothness

Choose an answer

If the domain of sequence is finite set then the sequence is called

Choose an answer

geometric sequence

infinite sequence

finite sequence

arithmetic sequence

2/9,5/7∈ R,(2│9)(5│7)=10/63∈R this property is called

Choose an answer

Associative property

Identity property

Commutative property

Closure property w.r.t multiplication

Choose an answer

The period of 2 cos x is

Choose an answer

30π

7π

5π

2π

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

Choose an answer

π/2

-π/2

π

-π

Choose an answer

The points of intersection of the line y = 2x -3 and the circle x²+ y² - 3x =2y -3 = 0 are:

Choose an answer

two

three

less thean two

not intersect

∀x,y,z ∈ R and z 0,then

Choose an answer

x > y ⇒ xz > yz

x<y ⇒ xz < yz

x < y ⇒ xz > yz

None of these

Choose an answer

By expressing cos 113° in terms of trigonometrical ratios, answer will be

Choose an answer

− cos 76° = -0.7093

− cos 65° = -0.4258

− cos 67° = -0.3907

− cos 62° = -0.8520

The decimal fraction in which we have finite number of digits in its decimal part is called.

Choose an answer

recurring decimal fraction

Non terminating faction

Non recurring fraction

terminating decimal fraction

Choose an answer

0

20

90

80

Any point, where f is neither increasing nor decreasing and f(x) = 0 at that point, is called a

Choose an answer

Minimum

Maximum

Stationary point

Constant point

Choose an answer

y/x

x/y

y/z

None

Choose an answer

r + 3 >5 then which is true

Choose an answer

r + 2 > 4

r + 2 < 4

r + 2 = 4

None

Cos-1(x)=

Choose an answer

cos x

x

tan-1(-x)

Sec-1 (1/x)

H.M. between 3 and 7 is

Choose an answer

The multiplicative inverse of 4 is

Choose an answer

-4

-1/4

1/4

1

Choose an answer

0

1

undefined

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

Choose an answer

(0, -2)

(1, -3)

(2, 2)

(3, 0)

The different of tan x is

Choose an answer

sec2 x

ln |sec x|

sec2 xdx

-cos ec2 x

The value of sin-1 24/25 is equal to

Choose an answer

csc-1 25/24

sec-1 24/25

2 tan-1 4/5

2cos-1 24/25

If the 4th term in the expansion of (px + x^-1)^mis 2.5 for all x∈ R, then

Choose an answer

If (2, 3) and (2, 5) are end points of a diameter of a circle, then the centre of the circle is

Choose an answer

(2, 4)

(4, 8)

(0, 2)

(0, -2)

The graph of the linear equation of the form ax =by = c is a line which divided the plane into:

Choose an answer

Two similar regions

Two disjoint regions

Four equal parts

One region

0! = ______

Choose an answer

0

1

2

Not defined

The number of permutations of n objects of which there are n₁like of one kind, n₂like of the second kind and n₃like objects of third kind are

Choose an answer

The foot of perpendicular from (α,β,γ) only y-axis is

Choose an answer

(α, 0, 0)

(0,β, 0)

(0, 0, γ)

(0, 0, 0)

Choose an answer

1

2

0

4

The length of perpendicular from (3,1) to 4x +3y +20 =0 is

Choose an answer

6

7

3

8

4/√49 is a

Choose an answer

Irrational Number

Prime Number

Rational number

Whole number

The liner equation ax + by = c is called _________ of the inequality ax +by > c.

Choose an answer

Associated equation

Non-associated equation

disjoint equation

Feasible equation

Choose an answer

An upper triangular matrix

A lower triangular matrix

A diagonal matrix

A null matrix

Associative law of multiplication

Choose an answer

ab - ba

a(bc) = (ab) c

a(b + c) = ab +ac

(a +b)c = ac + bc

The equation of the chord of the circle x²+ y²- 4x = 0 whose mid-point is (1, 0) is

Choose an answer

y = 2

y = 1

x = 2

x = 1

The middle term of the expansion (1 + 2x)⁶is ______

Choose an answer

1st term

4th term

2nd term

5th term

The principal value of sin^-1(-1/2)

Choose an answer

π/3

π/4

π/6

-π/6

Choose an answer

k3

0

3k

k6

In triangle ABC, in which b=95, c=34, a =52^𝜊then the value of a=

Choose an answer

18 cm

18.027 cm

20.7 cm

19 cm

The slope of x-axis is

Choose an answer

0

undefined

1

Range of 2 tan x is ______

Choose an answer

[-2, 2]

-1 < x < 1

R

None of these

Sum of two quantities is at least 20 is denoted by

Choose an answer

x +y =20

x +y≥ 20

x +y≠ 20

x +y≤20

The area between the x-axis the curve y =4x-x2 is :

Choose an answer

32/2

15

18

21

The magnitude of a vector can never be

Choose an answer

Zero

Negative

Positive

None of these

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.