Question # 1

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none of these

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1

12

5

29

Two circle x² + y²+2x - 8 = 0 and x² + y² -6 + 6x -46 =0:

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touch internally

do not intersect

touch externally

None of these

For each even natural number n (n²-1) is divisible by

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6

3

4

8

π is the ration of

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Area of a circle to its diameter

Area of a circle to its radius

Circumference of a circle to its diameter

Circumference of circle to its radius

An unbiased die is thrown. Then the probability of getting a prime is

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1/2

2/3

3/4

None of these

The multiplicative inverse of 0 is

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1

-1

0

Does not exist

The parabola y²= x is symmetric about

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x-axis

y-axis

Both x and y-axis

The line y = x

The set of whole numbers is subset of

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The set on integers

The set of natural numbers

{1, 3, 5, 7, ....}

The set of prime numbers

The law of tangents is ______

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The tangents drawn from the point P to a circle are real and coincident if

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P is on the circle

P is inside the circle

P is outside the circle

none of these

w^-1= ______

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0

1

w

w²

The angle between the vectors 3i + j - k and 2i - j + k is

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The product of the four fourth roots of unity is

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0

1

-1

None of these

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

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Associative property

Identity property

Commutative property

Closure property w.r.t multiplication

The domain of the principle cos function is

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none of these

60° = ______

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If cosα= 4/5, then cosα/2

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If tan^-13 + tan^-1x = tan^-18, then x=

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5

1/5

5/14

14/5

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none of these

cos 315° = ______

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perpendicular vectors

parallel vectors

concurrent vectors

none of these

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0

1

2

4

The set of ordered pairs (x,y) such that ax+ by < c, and (x,y) such that ax + by>0, are called

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Linear Inequalities

Feasible regions

Half planes

Boundary

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

The consecutive terms of a progressions are 30, 24, 20. The next term of the progression is

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0

1

8

∞

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

Range of tanθis

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Set of complex numbers

Set of real numbers

Set of odd numbers

Set of positive integers only

The length of the tangent from (2, 1) to the circle x²+ y²+ 4y + 3 = 0 is

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The two lines y = 2x and x =2y are

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Parallel

Perpendicular

Equally inclined with axes

Congruent

For the equation |x²| + |x| -6 =0, the roots are

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One and only one real number

Real with sum one

Real with sum zero

Real with product zero

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

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1/5

2/5

1/10

3/10

If A and B are two matrices such that AB = B and BA = A then A2 + B2 =

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2 AB

2 BA

A + B

AB

The number of real tangents that can be drawn to the ellipse 3x²+ 5y²= 32 passing thro. (3, 5) is

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0

1

2

Infinite

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7

5

6

None of these

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4

3

2

1

I f the focus is F ( 0,-a) and directrix is the line v=a, then equation of the parabola is:

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x² = 4ay

y² = 4ax

y² = -4ax

x² = 4ax

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The law of consines

The law of sines

The law of tangents

None of these

Which of the following is not a solution of system of inequalities 2x- 3y ≤6,2x +y≥ 2,x +2y≤ 8, x≥ 0,y ≥ 0

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(1,0)

(0,4)

(3,0)

(8,0)

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The range of function f(x)=-x2+2x-1 is

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R

(-∞,0]

(-∞,1]

[0,∞)

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none of these

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

In the interval 0≤ x ≤ π, the sine is

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Not a function

Not defined

Infinity

Not one-to-one function

Cycle tyres are supplied in lots of 10 and there is a chance if 1 in 500 tyres to be defective. Using Poisson distribution, the approximate number of lots containing no defective tyre in a consignment of 10, 0000 lots is

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9028

9208

9802

9820

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-2x cos x²

-2x²sin x²

-x²sin x

-2x²sin x²

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30°

45°

60°

90°

The equation of the sphere passing thro' (0, 0, 0), (a, 0, 0), (0, b, 0), (9, 0, c) is

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x²+ y²+ z²+ 2 ax +2 by + 2cz = 0

x²+ y²+ z²- 2ax - 2 by - 2cz = 0

x²+ y²+ z²- ax - by - cz = 0

x²+ y²+ z²+ ax + by + cz = 0

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8

1/56

56

None of these

If the sum of even coefficients in the expansion of (1+x)n is 128 then

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n=7

n=9

n=8

None

The modulus of 12-5i is:

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7

13

√7

119

Some of two real numbers is also a real number , this property is called:

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Commutative property w.r.t addition

Closure property w.r.t. addition

Associative property w.r.t. addition

Distributive property w.r.t addition

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Which of the following has the same value as i113

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i

-1

-i

1

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Derivative of a w.r.t x is

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0

1

x

w^-12= ______

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0

1

w

w²

The synthetic division method is only used to divide a polynomial by

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quadratic equation

binomial

linear equation

monomial

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none of these

The equation x²+ y²= 0 represents

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A circle

A degenerate circle

An empty set

A st. line

An equation in which at least one term contains dy/dx, d² y /dx²etc, is called.

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Differential equation

Initial condition

General solution

Singular equation

What is the 26th term of the sequence, if its general term is a_{n = (-1)}ⁿ⁺¹

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2

26

27

1

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

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2

-2

3

1

The equation of the parabola with directirx x = 2 and the axis y = 0 is

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y²= 8x

y²= -8x

y²= 4x

y²= -4x

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all are correct

In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=

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12

n=14

17

n=15

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In one hour the minute hand of a clock turns through

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To express a single rational fraction as a sum of two or more single rational fractions which are called

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improper fractions

Partial fractions

mixed form

Polynomials

The property used in -3 <-2 ⇒0 <1

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Commutative property

Additive property of inequality

Additive inverse

Additive identity

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sin²αcos²α=

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-1

0

1

None of these

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The set {1,-1, i, -i} form a group under

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Addition

Multiplication

Subtraction

None

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cos 2x + c

- cos 2x + c

tan 2x + c

cot 2x + c

The first three terms in the expansion of (1 - x)^-2are

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1 - 2x + 3x²

1 - 2x - 3x²

1 + 2x + 3x²

-2 - 2x +3x²

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The angle of depression of the point at a distance 70 meters from the foot of the tower from the top of the tower is 45^𝜊.The height of the tower is

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37m

97m

101m

70m

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A positive integer

A negative integer

A natural number

An irrational number

For all points (x,y) in fourth quadrant

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x > 0 , y < 0

x > 0 , y > 0

x < 0 , y < 0

x < 0 , y > 0

x²+ x - 6 = 0 is

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An equation

An identity

A polynomial

None of these

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Two circles are said to be concentric if they have

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same radius

same chord

same centre

same diameter

If S and P are the sum and the product of roots of a quadratic equation, then the quadratic equation is

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x²+ Sx - P = 0

x²- Sx + P = 0

x²- Sx - P = 0

X²+ Sx + P = 0

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A circle is a limiting case of an ellipse whose eccentricity

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Tends to a

Tends to b

Tends to 0

Tends to a + b

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The sum of first 60 natural numbers is

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1830

3660

1640

1770

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1

2

3/2

5/2

Three integers are chosen at random from the first 20 integers. Then probability that their product is even, is

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2 / 19

3 / 29

17 / 19

4 / 19