List of practice Questions

Solve the following riddle:
I am a number, Tell my identity!
Take me seven times over, And add a fifty!
To reach a triple century, You still need forty!

If $f(a) = a^2 , \phi (a) = b^2 $ and $f'(a) = 3 \phi '(a)$ then $Lt_{x \to a} \frac{\sqrt{ f(x)} - a}{ \sqrt{\phi (x)} - b}$ is

Solution set of the inequality $\frac{1}{2^{x}-1} > \frac{1}{1-2^{x-1}}$ is

A student is to answer $10$ out of $13$ questions in an examination such that the he must choose at least $4$ from the first five questions. The number of choices available to him is :

The following Table shows the total power shortage in India from 1991–1997. Show the data in the form of a graph. Plot shortage percentage for the years on the Y-axis and the year on the X-axis.

S. No.	Year	Shortage (%)
1	1991	7.9
2	1992	7.8
3	1993	8.3
4	1994	7.4
5	1995	7.1
6	1996	9.2
7	1997	11.5

If 400 pollen grains are produced from a single monothecous anther from its components equally, what is the number of pollen grain mother cells in each of the sporangia ?

Which one of the following oxyacids of chlorine is the least oxidizing in nature ?

Position of particle located on x-axis changes with time (t) as x = 2.5t2.
Speed of the particle at t = 5 seconds is equal to?

Find the principal value of cot^-1$\sqrt3$

Find the degree measure corresponding to $\frac{\pi}{32} rad$.

The value of $tan1^{\circ}\, tan2^{\circ}\, tan3^{\circ} \ldots \, tan89^{\circ}$ is

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is

μ

. The standard deviation for this distribution is given by ______.

Find the angle between two vectors

(\vec{a} = 2 \hat{i} + \hat{j} - 3 \hat{k})

and

(\vec{b} = 3 \hat{i} - 2 \hat{j} - \hat{k})

.

Find the area bounded between the curve

y = x^{2}

and

y = x^{3}

.

How much work must be done by a force on 50 kg body in order to accelerate it from rest to 20 $ms^{-1}$ in 10 s

A horizontal underground stem is a

A gymnosperm with furcate venation which is grown in Budhist temples

A gymnosperm where fertilization occurs by both siphonogamy and zoidiogamy is

The reason for the stability of $Gd^{3+}$ ion is

Among [Ni(CO)₄], [Ni(CN)₄] ^2–, [NiCl₄] ^2– species, the hybridization states at the Ni atom are, respectively(At. No. of Ni = 28)

Name the members of the lanthanoid series which exhibit +4 oxidation state and those which exhibit +2 oxidation state. Try to correlate this type of behavior with the electronic configurations of these elements.