List of practice Questions

The standard deviation of n observations $x_1,x_2,\dots x_n$ is 2 If $\sum _{i=1}^n{x}_i=20$ and $\sum _{i=1}^n{x}_i^2=100,$ then $n$ is equal to

The number of real solutions of the equation |x|² + 5|x| + 4 = 0 is

The coordinates of a moving point p are (2t² + 4, 4t + 6). Then  its locus will be a

The sum of n terms of two AP's are in the ratio of $(3n+8):(7n+15)$. Find the ratio of their ${12}^{\text{th }}$ terms.

If in a triangle ABC, sin A, sin B, sin C are in A.P., then 

The shortest distance from the point (1, 2, -1) to the surface of the sphere x² + y² + z² = 54 is

If a point P is equidistant from A(1, 3), B(-3, 5) and C(5, -1), then PA is equal to

If $\sin \theta =\frac{2t}{1+t^2}$ and $\theta$ lies in the second quadrant, then $\cos \theta$ is equal to

Evaluate the integral: ${\int }_1^2\log xdx$

A coin is biased so that the head is 3 times as likely to occur as tail.If the coin is tossed twice,find the probability distribution of number of tails.

Consider the following species $(\mathrm{I}){\mathrm{S}}_4{\mathrm{O}}_6^{2-}$$(\mathrm{II}){\mathrm{S}}_3{\mathrm{O}}_9$$(\mathrm{III}){\mathrm{S}}_2{\mathrm{O}}_5^{2-}$$(\mathrm{IV}){\mathrm{P}}_3{\mathrm{O}}_9^{3-}$Which of the above species have same number of $X-0-X$ linkages? $(X=P\text{ or }S)$

Q in the above sequence of reactions is

The correct statement(s) about following sugars (X) and (Y) is/are:

Blackened oil painting can be restored into original form by the action of:

The addition of HBr to 2-pentene gives

Which one of the following observations is not true when a mixture of KCl, K2Cr2O7 and conc. H2SO4 is warmed carefully?

Consider the following diagram and mark the correct answer.

Polysaccharides are formed by _______.

Which of the following is a reason for the addition of spice oils to certain foods for the reason of preservation?

Which of the following groups of organisms does not belong to indicator species?

Whose work is to protect the land from floods, remove sediments and other pollutants and recharge groundwater?

Soil around the stem of a potato plant is constantly removed from a very young stage so that only roots remain in the soil. Potato  tubers in the plant will