There are 10 different objects 1,  2,  3,  ... 10 arranged at random in 10 places marked 1,  2,  3,  ... , 10. The probability that exactly five of these objects occupy places corresponding to their number is

1) 13/ 3600
2) 11/ 3600
3) 17/ 3600
4) none

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) $$\displaystyle\frac{21}{220}$$

$$\dfrac{dy}{dx}=e^{-2y},x=5\Rightarrow y=0,$$ then  $$y=3,find\ the\ value\ of\ 2x$$.

1) e⁵ + 9
2) e⁶ + 9
3) e⁸ + 9
4) e⁴ + 9
.

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) $$\dfrac {27}{51}$$

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  x = cos α  + cos β  – cos( α  + β ) and y =  , then (x – y) equals

1) 0
2) 1
3) – 1
4) – 2

Given z²+z|z|+|z²| = 0 the locus of z is

1) A straight line
2) A circle
3) A pair of straight line
4) none

If A=$$\begin{bmatrix}11&1\\0&11\end{bmatrix}$$, B=$$\begin{bmatrix}0&-2\\-3&4\end{bmatrix}$$, I=$$\begin{bmatrix}1&0\\0&1\end{bmatrix}$$. Find $$A+3B+4I.$$

1) $$\begin{bmatrix}0&2\\-3&0\end{bmatrix}$$
2) $$\begin{bmatrix}15&2\\-13&-16\end{bmatrix}$$
3) $$\begin{bmatrix}15&-5\\-9&27\end{bmatrix}$$
4) $$\begin{bmatrix}11&2\\-4&-5\end{bmatrix}$$

The value of 'a' in order f(x)= √ 3?sinx−cosx−2ax+b decrease for all real values of x, is given by

1) a > 1
2) a ≥ 1
3) a ≥ 2
4) a < 2

If linear function f(x) and g(x) satisfy

1) f(x) = 3(x - 1)
2) f(x) = 3x – 5
3) g(x) = 3(x - 1)
4) g(x) = 3x  +  1