The range of the relation R = {(x, x²) |x is a prime number less than 13} is

(a)

{2,3,5,7}

(b)

{2,3,5,7,11}

(c)

{4,9,25,49,121}

(d)

{1,4,9,25,49,121}

If function f : N⟶N, f(x) = 2x then the function is, then the function is ___________

(a)

Not one - one and not onto

(b)

one-one and onto

(c)

Not one -one but not onto

(d)

one - one but not onto

If f is identify function, then the value of f(1) - 2f(2) + f(3) is: 

(a)

-1

(b)

-3

(c)

1

(d)

0

The sum of the exponents of the prime factors in the prime factorization of 1729 is

(a)

1

(b)

2

(c)

3

(d)

4

The value of (1³ + 2³ + 3³ +...+15³) - (1 + 2 + 3 +...+ 15)is 

(a)

14400

(b)

14200

(c)

14280

(d)

14520

The first term of an A.P. whose 8^th and 12^th terms are 39 and 59 respectively is ____________

(a)

5

(b)

6

(c)

4

(d)

3

Sum of first n terms of the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +...\) is ____________

(a)

\(\frac { n(n+1) }{ 2 } \)

(b)

\(\sqrt { n } \)

(c)

\(\frac { n\left( n+1 \right) }{ \sqrt { 2 } } \)

(d)

1

Which of the following should be added to make x⁴ + 64 a perfect square

(a)

4x²

(b)

16x²

(c)

8x²

(d)

-8x²

Transpose of a column matrix is

(a)

unit matrix

(b)

diagonal matrix

(c)

column matrix

(d)

row matrix

The HCF of two polynomials p(x) and q(x) is 2x(x + 2) and LCM is 24x(x + 2)² (x - 2) if p(x) = 8x³ + 32x² + 32x, then q(x) ___________

(a)

4x³-16x

(b)

6x³-24x

(c)

12x³+24x

(d)

12x³-24x

The real roots of the quadratic equation x²-x-1 are ___________

(a)

1, 1

(b)

-1, 1

(c)

\(\frac { 1+\sqrt { 5 } }{ 2 } ,\frac { 1-\sqrt { 5 } }{ 2 } \)

(d)

None

If in triangles ABC and EDF,\(\cfrac { AB }{ DE } =\cfrac { BC }{ FD } \) then they will be similar, when

(a)

\(\angle B=\angle E\)

(b)

\(\angle A=\angle D\)

(c)

\(\angle B=\angle D\)

(d)

\(\angle A=\angle F\)

In a \(\triangle\)ABC, AD is the bisector \(\angle\)BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. The length of the side AC is

(a)

6 cm

(b)

4 cm

(c)

3 cm

(d)

8 cm

In figure if PR is tangent to the circle at P and O is the centre of the circle, then \(\angle PQR\) is

(a)

120^o

(b)

100°

(c)

110°

(d)

90°

The ratio of the areas of two similar triangles is equal to ____________

(a)

The ratio of their corresponding sides

(b)

The cube of the ratio of their corresponding sides

(c)

The ratio of their corresponding attitudes

(d)

The square of the ratio of their corresponding sides

The equation of a line passing through the origin and perpendicular to the line 7x - 3y + 4 = 0 is

(a)

7x - 3y + 4 = 0

(b)

3x - 7y + 4 = 0

(c)

3x + 7y = 0

(d)

7x - 3y = 0

Find the slope of the line 2y = x + 8 ____________

(a)

\(\frac { 1 }{ 2 } \)

(b)

1

(c)

8

(d)

2

If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a² - 1) is equal to 

(a)

2a

(b)

3a

(c)

0

(d)

2ab

Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

(a)

\(\sqrt { 2 } \) x

(b)

\(\frac { x }{ 2\sqrt { 2 } } \)

(c)

\(\frac { x }{ \sqrt { 2 } } \)

(d)

2x

The value of (tan1^o tan2^o tan3^o..... tan89^o) is ___________

(a)

0

(b)

1

(c)

2

(d)

\(\frac{1}{2}\)

The angle of depression of a boat from a \(50\sqrt { 3 } \) m high bridge is 30^o. The horizontal distance of the boat from the bridge is ___________

(a)

150 m

(b)

\(150\sqrt { 3 } \)

(c)

60m

(d)

\(60\sqrt { 3 } \)

A spherical ball of radius r₁ units is melted to make 8 new identical balls each of radius r₂ units. Then r₁:r₂ is

(a)

2:1

(b)

1:2

(c)

4:1

(d)

1:4

A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is

(a)

45%

(b)

56%

(c)

67%

(d)

75%

The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is

(a)

3

(b)

15

(c)

5

(d)

225

If the data is multiplied by 4, then the corresponding variances is get multiplied by ___________

(a)

4

(b)

16

(c)

2

(d)

None