In a box, there are 8 alphabets cards with the letters: S,S,A,A,A,H,H,H. Find the probability that the word ASH will form if three cards are drawn simultaneously.

1) $$\dfrac{9}{28}$$
2) $$\dfrac{19}{28}$$
3) $$\dfrac{9}{14}$$
4) $$\dfrac{5}{14}$$

Slope of normal to the curve y = x² - 1/x²  at (-1,  0) is

1) -1/4
2) -4
3) 1/4
4) 4

If S₁ and S₂ are respectively the sets of local minimum and local maximum points of the function,
f(x) = 9x⁴+12x³ -36x² +25, x Î R , then :

1) S₁ = {-2,1}; S₂ ={0}
2) S₁ = {-2}; S₂ ={0, 1}
3) S₁ = {-2,1}; S₂ ={1}
4) S₁ = {-1}; S₂ ={0, 2}

If a is a complex number satisfying the equation α² + α + 1= 0, then α³¹ is equal to

1) α
2) α²
3) 1
4) i

In a class, there are 18 girls and 16 boys. The class teacher wants to choose one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that:

The name written on the card is the name of a boy.

1) $$\dfrac{8}{17}$$
2) $$\dfrac{5}{6}$$
3) $$\dfrac{15}{16}$$
4) None of these

?ABC is right angled at B. BD is an altitude. AD=3cm and DC=9cm. What is the value of AB (in cm)?

1) 6

2) 5

3) 4.5

4) 5.5

If g(x) = 2f (2x³ -3x²) + f (6x² -4x³ -3 ),  " x ΠR and f " (x) > 0,  " x ΠR, then g(x) is increasing on the interval

1) (-∞ , -1/2) È (0,1) 
2) (-1/2 , 0) È (1,∞ )
3) (0,∞)
4) (-∞ , 1)

If $$A=\begin{bmatrix} 2 & 1 \\ 4 & 1 \end{bmatrix}$$, $$B=\begin{bmatrix} 3 & 4 \\ 2 & 3 \end{bmatrix}$$and $$C=\begin{bmatrix} 3 & -4 \\ -2 & 3 \end{bmatrix}$$, then $$\displaystyle tr(A)+tr\left(\frac{ABC}{2}  \right) +tr\left(\frac{A{(BC)}^{2}}{4}  \right)+tr\left(\frac{A{(BC)}^{3}}{8}  \right)  +........+\infty =$$

1) 6
2) 9
3) 12
4) 15

The converse of "if x∈A∩B then x∈A and x∈B", is

1) If x∈A and x∈B, then x∈A∩B

2) If x∉A∩B, then x∉A or x∉B

3) If x∉A or x∉B, then x∉A∩B

4) If x∉A or x∉B, then x∈A∩B

Which one of the following is not correct ?

1) If f(x) is not continuous at x = a, then it is not differentiable at x = a
2) If f(x) is continuous at x = a, then it is differentiable at x = a
3) If f(x) and g(x) are differentiable at x = a, then f(x) + g(x) is also differentiable at x = a
4) If f(x) is continuous at x = a, then  exists