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

(a)

4x

(b)

2-2x

(c)

2-4x

(d)

4x-2

If f(x) + f(1 - x) = 2 then \(f\left( \frac { 1 }{ 2 } \right) \) is ___________

(a)

5

(b)

-1

(c)

-9

(d)

1

The difference between the remainders when 6002 and 601 are divided by 6 is ____________

(a)

2

(b)

1

(c)

0

(d)

3

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 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 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

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

If the angle between two radio of a circle is ^o, the angle between the tangents at the end of the radii is ____________

(a)

50^o

(b)

90^o

(c)

40^o

(d)

70^o

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

A line passing through the point (2, 2) and the axes enclose an area ∝. The intercept on the axes made by the line are given by the roots of ____________

(a)

x²-2-∝x+∝ = 0

(b)

x²+2∝x+∝ = 0

(c)

x²-∝x+2∝ = 0

(d)

none of these

If sin A = \(\frac{1}{2}\), then the value of cot A is ___________

(a)

\(\sqrt{3}\)

(b)

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

(c)

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

(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

If A is an assets angle of Δ ABC, right angle at 3, then the value of sin A T cos A is ___________

(a)

=1

(b)

>1

(c)

<1

(d)

=2

(sec A + tan A)(1 - sin A) is equal to ___________

(a)

sec A

(b)

sin A

(c)

cosec A

(d)

cos A

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 ratio of the volumes of two spheres is 8 : 27. If r and R are the radii of sphere respectively, Then (R - r) : r is ___________

(a)

1:2

(b)

1:3

(c)

2:3

(d)

4:9

A semicircular thin sheet of a metal of diameter 28 cm is bent and an open conical cup. What is the capacity of the cup?

(a)

\(\left[ \frac { 1000 }{ 3 } \right] \sqrt { 3 } { cm }^{ 3 }\)

(b)

\(300\sqrt { 3 } { cm }^{ 3 }\)

(c)

\(\left[ \frac { 700 }{ 3 } \right] \sqrt { 3 } { cm }^{ 2 }\)

(d)

\(\left[ \frac { 1078 }{ 3 } \right] \sqrt { 3 } { cm }^{ 3 }\)

A girl calculates the probability of her winning in a match is 0.08 what is the probability of her losing the game ___________

(a)

91%

(b)

8%

(c)

92%

(d)

80%

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