1) 2?₁  + ?₂  = 0   
2) ?₁  + 2?₂  = 0
3) ?₁  + 2?₂  = 0  
4) ?₁  = 2?₂

While shuffling a pack of 52 playing cards, 2 are accidentally dropped. The probability that the missing cards to be of different colours is

1) $$\dfrac {29}{52}$$
2) $$\dfrac {1}{2}$$
3) $$\dfrac {26}{51}$$
4) $$\dfrac {27}{51}$$

If y = k sin px, then the value of the determinant   is equal to  

1) 1
2) 0
3) -1
4) none

x (x^{n – 1} - n a^{n – 1} ) + aⁿ (n – 1) is divisible by (x – a)²  for

1) n > 1
2) n > 2
3) n ∈ N
4)  n > 2,  n ∈ N

$$(2x)^2 + 4(2x) + 7 = Mx^2 + 8x + 7$$, find value of M

1) 3

2) 5

3) 4

4) 6

The area (in sq units) of the region bounded by x = - 1, x = 2, y = x² + 1 and y = 2x - 2 is

1) 10
2) 7
3) 8
4) 9

The lines p(p²  + 1) x – y + q = 0 and (p²  + 1)2 x + (p²  + 1) y + 2q = 0 are perpendicular to a common line for

1) no value of p
2) exactly one value of p
3) exactly two values of p
4) more than two values of p 

If $$A = \begin{bmatrix}1 & -2 & 3 \\ -4 & 2 & 5\end{bmatrix}$$ and $$B = \begin{bmatrix}1 & 3 \\ -1 & 0 \\ 2 & 4\end{bmatrix}$$. Show that $$(AB)' = ?$$

1) B'A'
2) A'B'
3) AB'
4) A'B

Let O be centre, S, S' be foci of hyperbola. If tangent at any point P on hyperbola cuts asymptotes at M and N then OM + ON =

1)  |SP - S'P|
2)  SP + S'P
3) SS'
4) distance between vertices

Let f : R → R be given by f(x) = ax+b / cx +d,   a,  b,  c and d being non-zero real numbers. Its inverse  f ^-1 (x) will be the same as f(x) provided

1) a + b = 0
2) a + c = 0
3) a + d = 0
4) b + c = 0