If the line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ-plane at the point

1) a = 8, b = 2
2) a = 2, b = 8
3) a = 4, b = 6
4) a = 6, b = 4

p: I am topper.

q: I worked hard.

The symbolic form of the statement : "I am topper or I worked hard", formed from statements p,q can be

1) P↔Q

2) P∨Q

3) P∧Q

4) P→Q

Find the solution of  $$\displaystyle \frac{dy}{dx}= \frac{x+2y-2}{2x+y-3}.$$

1) $$\displaystyle \left ( x+y-2 \right )= k\left ( x-y \right )^{3}$$
2) $$\displaystyle \left ( x+y-2 \right )= k\left ( x+y \right )^{3}$$
3) $$\displaystyle \left ( x+y-2 \right )= k\left ( x+y \right )^{4}$$
4) $$\displaystyle \left ( x+y-2 \right )= k\left ( x-y \right )^{4}$$
.

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one women. Then the probability for these committees to have more women than men, is.

1) $$\displaystyle\frac{3}{11}$$
2) $$\displaystyle\frac{2}{23}$$
3) $$\displaystyle\frac{1}{11}$$
4) $$\displaystyle\frac{21}{220}$$

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 the two circles x² + 2y² - 2x + 22y + 5 = 0 and x² + y² + 14x + 6y + k = 0 intersect orthogonally, then k is equal to

1) -49
2) – 47
3) 49
4) 47

The derivative of

If $$ A = \begin{bmatrix} a & x \\ y & a \end{bmatrix} $$ and if $$xy=1$$ , then $$ \text{det} (AA^T) $$ is equal to :

1) $$ a^2 - 1$$
2) $$ (a^2+1)^2 $$
3) $$ 1 - a^2 $$
4) $$ (a^2 - 1)^2 $$

If ,  where  , then α -β is equal to :
 

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) $$\dfrac {27}{51}$$