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 the ordered pairs (a + 2, 4) and (5, 2a + b) are equal then (a, b) is

(a)

(2,-2)

(b)

(5,1)

(c)

(2,3)

(d)

(3,-2)

Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

(a)

4x

(b)

2-2x

(c)

2-4x

(d)

4x-2

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

(a)

2025

(b)

5220

(c)

5025

(d)

2520

7^4k \(\equiv \) ________ (mod 100)

(a)

1

(b)

2

(c)

3

(d)

4

If m and n are the two positive integers then m² and n² are ____________

(a)

Co-prime

(b)

Not co-prime

(c)

Even

(d)

odd

y² + \(\frac {1}{y^{2}}\) is not equal to

(a)

\(\frac {y^{2} + 1}{y^{2}}\)

(b)

\({ \left( y+\frac { 1 }{ y } \right) }^{ 2 }\)

(c)

\({ \left( y-\frac { 1 }{ y } \right) }^{ 2 }+2\)

(d)

\({ \left( y+\frac { 1 }{ y } \right) }^{ 2 }-2\)

\(\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 } \) gives

(a)

\(\frac { { x }^{ 2 }-7x+40 }{ \left( x-5 \right) \left( x+5 \right) } \)

(b)

\(\frac { { x }^{ 2 }+7x+40 }{ \left( x-5 \right) \left( x+5 \right) \left( x+1 \right) } \)

(c)

\(\frac { { x }^{ 2 }-7x+40 }{ \left( { x }^{ 2 }-25 \right) \left( x+1 \right) } \)

(d)

\(\frac { { x }^{ 2 }+10 }{ \left( { x }^{ 2 }-25 \right) \left( x+1 \right) } \)

Which of the following is correct
(i) Every polynomial has finite number of multiples
(ii) LCM of two polynomials of degree 2 may be a constant
(iii) HCF of 2 polynomials may be constant
(iv) Degree of HCF of two polynomials is always less then degree of LCM

(a)

(i) and (ii)

(b)

(iii) and (iv)

(c)

(iii) only

(d)

(iv) only

The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then the length of AB is

(a)

\(6\frac { 2 }{ 3 } cm\)

(b)

\(\frac { 10\sqrt { 6 } }{ 3 } cm\)

(c)

\(66\frac { 2 }{ 3 } cm\)

(d)

15 cm

If in \(\triangle\)ABC, DE || BC, AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is

(a)

1.4 cm

(b)

1.8 cm

(c)

1.2 cm

(d)

1.05 cm

S and T are points on sides PQ and PR respectively of \(\Delta PQR\) If PS = 3cm, AQ = 6 cm, PT = 5 cm, and TR = 10 cm and then QR

(a)

4 ST

(b)

5 ST

(c)

3 ST

(d)

3 QR

The point of intersection of 3x − y = 4 and x + y = 8 is

(a)

(5, 3)

(b)

(2, 4)

(c)

(3, 5)

(d)

(4, 4)

The slope of the line joining (12, 3), (4, a) is \(\frac 18\). The value of ‘a’ is

(a)

1

(b)

4

(c)

-5

(d)

2

If the mid-point of the line segment joining \(A\left( \frac { x }{ 2 } ,\frac { y+1 }{ 2 } \right) \) and B(x + 1, y-3) is C(5, -2) then find the values of x, y ____________

(a)

(6, -1)

(b)

(-6, 1)

(c)

(-2, 1)

(d)

(3, 5)

If sin \(\theta \) = cos \(\theta \), then 2 tan² \(\theta \) + sin² \(\theta \) -1 is equal to 

(a)

\(\frac { -3 }{ 2 } \)

(b)

\(\frac { 3 }{ 2 } \)

(c)

\(\frac { 2 }{ 3 } \)

(d)

\(\frac { -2 }{ 3 } \)

If x = a tan\(\theta \) and y = b sec\(\theta \) then

(a)

\(\frac { { y }^{ 2 } }{ { b }^{ 2 } } -\frac { { x }^{ 2 } }{ { a }^{ 2 } } =1\)

(b)

\(\frac { x^{ 2 } }{ a^{ 2 } } -\frac { y^{ 2 } }{ b^{ 2 } } =1\)

(c)

\(\frac { x^{ 2 } }{ a^{ 2 } } +\frac { y^{ 2 } }{ b^{ 2 } } =1\)

(d)

\(\frac { x^{ 2 } }{ a^{ 2 } } -\frac { y^{ 2 } }{ b^{ 2 } } =0\)

The value of the expression [cosec (75^o + θ) - sec (15^o - θ) - tan (55^o + θ) + cot(35^o - θ] is ___________

(a)

-1

(b)

0

(c)

1

(d)

\(\frac{3}{2}\)

The top of two poles of height 18.5m and 7m are connected by a wire. If the wire makes an angle of measures 360^o with horizontal, then the length of the wire is ____________

(a)

23m

(b)

18m

(c)

28m

(d)

25.5m

The blanks of river are parallel. A swimmer starts from a point on one of the banks and swims in a straight line to the bank at 45^o and reaches the opposite bank at a point 20 m, from the point opposite to the straight point. The breadth of the river is equal to ____________

(a)

12.12m

(b)

14.14m

(c)

1016.16m

(d)

18.18m

The total surface area of a cylinder whose radius is \(\frac{1}{3}\)of its height is

(a)

\(\frac { 9\pi { h }^{ 2 } }{ 8 } \) sq.units

(b)

24\(\pi\)h² sq.units

(c)

\(\frac { 8\pi { h }^{ 2 } }{ 9 } \) sq.units

(d)

\(\frac { 56\pi { h }^{ 2 } }{ 9 } \) sq.units

In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is

(a)

5600\(\pi\) cm³

(b)

1120\(\pi\) cm³

(c)

56\(\pi\) cm³

(d)

3600\(\pi\) cm³

Variance of first 20 natural numbers is

(a)

32.25

(b)

44.25

(c)

33.25

(d)

30

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 observations 1, 2, 3, ... 50 have the variance V₁ and the observations 51, 52, 53, ... 100 have the variance V₂ then \(\frac { { V }_{ 1 } }{ { V }_{ 2 } } \) is ___________

(a)

2

(b)

1

(c)

3

(d)

0