If n((A \(\times\) B) ∩(A \(\times\) C)) = 8 and n(B ∩ C) = 2, then n(A) is

(a)

6

(b)

4

(c)

8

(d)

16

Domain of the function \(y={x-1\over x+1}\) is __________

(a)

1R

(b)

Q

(c)

R-(-1)

(d)

R-1

Which one of the following is false?

(a)

(A')' = A

(b)

AUA' = A

(c)

A⋂A' = Ø

(d)

AUA' = U

Find a so that the sum and product of the roots of the equation 2x²+ (a - 3) x + 3a - 5 = 0 are equal is

(a)

1

(b)

2

(c)

0

(d)

4

If \(\alpha\) and \(\beta\) are the roots of 2x² - 3x - 4 = 0 find the value of \(\alpha^2+\beta^2\)

(a)

\(\frac{41}{4}\)

(b)

\(\frac{\sqrt{14}}{2}\)

(c)

0

(d)

none of these

There is a letter lock with 3 rings each marked with 5 letters and do not know the keyword. The total number of attempts can be made to know the keyword is  _________

(a)

3⁵

(b)

5³

(c)

124

(d)

5

Assertion (A): Every body in a room shakes hands with everybody else. The total number of persons in the room is n. The number of hand shakes is \(\frac{n(n-1)}{2}\)
Reason (R): The number of handshakes is nC₂

(a)

Both A and R are true and R is the correct explanation of A

(b)

Both A and R are true but R is not the correct explantion of A

(c)

A is true R is false

(d)

is false R is true

The nth term of a G.P is 128 and the sum of its n terms is 225. If its common ratio is 2, then its first term is ______________

(a)

1

(b)

3

(c)

8

(d)

none of these 

The distance between the line 12x - 5y + 9 = 0 and the point (2, 1) is ______________

(a)

\(\pm\frac{28}{13}\)

(b)

\(\frac{28}{13}\)

(c)

\(-\frac{28}{13}\)

(d)

none of these

At x \(={3\over 2}\) the function \(f(x)={|2x-3|\over 2x-3}\) is

(a)

continuous

(b)

discontinuous

(c)

differentiable

(d)

non-zero