If arg (z - a) = π/4, where a ? R, then the loss of z ? C is a

1) hyperbola
2) parabola
3) ellipse
4) straight line

If $$\displaystyle AB^{T}=\begin{vmatrix} 1 & 2 &0  \\ 3 & 2 & 0  \end{vmatrix}$$ and A has only one column then B has ______ column(s)

1) 1 
2) 3
3) 2
4) can't say

Nine-fifth of the temperature in centrigrade (C) of a body plus 32^o is equal to the temperature of the same body in Fahrenheit (F). Find F, when C=55^o

1) 131^o

2) 1201^o

3) 140^o

4) 166^o

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative,  then the first term is

1) 12
2) 4
3) -4
4) -12

Order and degree of $$x^{3}\dfrac{d^{3}y}{dx^{3}}+2x^{2}\dfrac{d^{2}y}{dx^{2}}+6y=x^{4}$$ are:

1) 3, 1
2) 1, 3
3) 3, 2
4) 2, 2

If a_ij = 0(i≠j) and aij=2(i=j) then the matrix A=[aij]_n×n is a _______ matrix

1) unit
2) null
3) scalar
4) skew symmetric

One card is drawn from a well-shuffled deck of $$52$$ cards. Find the probability that the card drawn is a spade or a face card:

1) $$\displaystyle \frac{9}{26}$$
2) $$\displaystyle \frac{3}{26}$$
3) $$\displaystyle \frac{11}{26}$$
4) None of these

The coefficient of three consecutive of (1 + χ)ⁿ⁺⁵ are in the ratio 5 : 10 : 14. Then, n is equal to

1) 1
2) 3
3) 4
4) 6

The sum of infinity of the series 1 + 2/3 + 6/3² + 10/3³ + 14/3⁴ + ... is

1) 3
2) 4
3) 6
4) 2

An open cylinder has a round drain with radius $$r$$ in the bottom of tank. $$t\displaystyle =\frac{R^2}{r^2}\sqrt{\frac{2h}{g}}$$ governs the time required to empty the tank where $$R$$ is the radius of the tank and $$h$$ is the depth of water in cylinder and $$g=980\,cm/s^2$$ is the acceleration due to gravity. Find the time required to empty the tank if the radius of the tank is $$w$$ m and depth of water is $$4$$m and drain has a radius of  $$5 cm$$.

1) $$0.03w^2$$

2) $$0.05w^2$$

3) $$0.08w^2$$

4) $$0.1w^2$$.