If f: A ⟶ B is a bijective function and if n(B) = 7, then n(A) is equal to

(a)

7

(b)

49

(c)

1

(d)

14

The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

(a)

37

(b)

39

(c)

35

(d)

36

If A = 2⁶⁵ and B = 2⁶⁴ + 2⁶³ + 2⁶² +...+ 2⁰ Which of the following is true?

(a)

B is 2⁶⁴ more than A

(b)

A and B are equal

(c)

B is larger than A by 1

(d)

A is larger than B by 1

If 3 is the least prime factor of number 'a' and 7 is least prime factor of number 'b', then the least prime factor of a + b is ____________

(a)

a + b

(b)

2

(c)

5

(d)

10

A boy saves Rs. 1 on the first day Rs. 2 on the second day, Rs. 4 on the third day and so on. How much did the boy will save upto 20 days?

(a)

2¹⁹ + 1

(b)

2¹⁹- 1

(c)

2²⁰- 1

(d)

2²¹- 1

The values of a and b if 4x⁴ - 24x³ + 76x² + ax + b is a perfect square are

(a)

100, 120

(b)

10, 12

(c)

-120, 100

(d)

12, 10

The product of the sum and product of roots of equation (a²-b²)x²-(a+b)²x+(a³-b³) = 0 is ___________

(a)

\(\frac { { a }^{ 2 }+ab+{ b }^{ 2 } }{ (a-b) } \)

(b)

\(\frac { a-b }{ a+b } \)

(c)

\(\frac { a-b }{ a+b } \)

(d)

\(\frac { a-b }{ { a }^{ 2 }+ab+{ b }^{ 2 } } \)

If P and Q are matrices, then which of the following is true?

(a)

PQ ≠ QP

(b)

(P^T)^T ≠ P

(c)

P + Q ≠ Q + P

(d)

All are true

The two tangents from an external points P to a circle with centre at O are PA and PB. If \(\angle APB\) = 70^o then the value of \(\angle AOB\) is

(a)

100°

(b)

110°

(c)

120°

(d)

130°

If ABC is a triangle and AD bisects A, AB = 4cm, BD = 6cm, DC = 8cm then the value of AC is ____________

(a)

\(\frac { 16 }{ 3 } cm\)

(b)

\(\frac { 32 }{ 3 } cm\)

(c)

\(\frac { 3 }{ 16 } cm\)

(d)

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

If slope of the line PQ is \(\frac { 1 }{ \sqrt { 3 } } \) then slope of the perpendicular bisector of PQ is

(a)

\(\sqrt { 3 } \)

(b)

\(-\sqrt { 3 } \)

(c)

\(\frac { 1 }{ \sqrt { 3 } } \)

(d)

0

The area of triangle formed by the points (a, b+c), (b, c+a) and (c, a+b) is ____________

(a)

a+b+c

(b)

abc

(c)

(a+b+c)²

(d)

0

The lines y = 5x - 3, y = 2x + 9 intersect at A. The coordinates of A are ___________

(a)

(2, 7)

(b)

(2, 3)

(c)

(4, 17)

(d)

(-4, 23)

If 5x = sec\(\theta \) and \(\frac { 5 }{ x } \) = tan\(\theta \), then x² - \(\frac { 1 }{ { x }^{ 2 } } \) is equal to 

(a)

25

(b)

\(\frac { 1 }{ 25 } \)

(c)

5

(d)

1

If sin A + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is ___________

(a)

1

(b)

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

(c)

2

(d)

3

(cosec²θ - cot²θ) (1 - cos²θ) is equal to ___________

(a)

cosec θ

(b)

cos²θ

(c)

sec²θ

(d)

sin²θ

If tan θ + cot θ = 3 then tan²θ + cot²θ is equal to ___________

(a)

4

(b)

7

(c)

6

(d)

9

A ladder of length 14m just reaches the top of a wall. If the ladder makes an angle of 60^o with the horizontal, then the height of the wall is ____________

(a)

\(14\sqrt { 3 } \)

(b)

\(28\sqrt { 3 } \)

(c)

\(7\sqrt { 3 } \)

(d)

\(35\sqrt { 3 } \)

If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

(a)

4\(\pi\)r² sq.units

(b)

6\(\pi\)r² sq.units

(c)

3\(\pi\)r² sq.units

(d)

8\(\pi\)r² sq.units

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

The height of a cone is 60 cm. A small cone is cut off at the top by plane parallel to the base and its volume is \(\left[ \frac { 1 }{ 64 } \right] ^{ th }\) the volume of the original cone. Then the height of the smaller cone is ___________

(a)

45 cm

(b)

30 cm

(c)

15 cm

(d)

20 cm

A cylinder having radius 1 m and height 5 m is completely filled with milk. In how many conical flasks can this milk be filled if the radius and height is 50 cm each?

(a)

50

(b)

500

(c)

120

(d)

160

A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is

(a)

\(\frac{3}{10}\)

(b)

\(\frac{7}{10}\)

(c)

\(\frac{3}{9}\)

(d)

\(\frac{7}{9}\)

The mean of first first 10 odd natural number is ___________

(a)

5

(b)

10

(c)

20

(d)

19

If an event occurs surely, then its probability is _________.

(a)

1

(b)

0

(c)

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

(d)

\(\frac { 3 }{ 4 } \)