List of practice Questions

If $\lambda_1 , \lambda_2$ and $\lambda_3$ are the eigen values (i.e. characteristic values) of the matrix $\begin{vmatrix}1&2&15\\ 3&4&11\\ 5&6&7\end{vmatrix}$ then $ \left(1 -\lambda_{1}\right)\left(1+\lambda _{2}\right)\left(1+\lambda _{3}\right)$ equals
If $p, q , r$ are the roots of the equation $\begin{vmatrix}x&1&2\\ 1&x&2\\ 1&2&x\end{vmatrix} = 0$ , then $\frac{p^{4} +q^{4}+r^{4}}{p^{2}+q^{2} +r^{2}}$ is equal to
Define $f (x) = min{x^2 + 1, x + 1]$ for.$x e\in R$. Then $ \int\limits_{-1}^1f (x)dx $ is
The value of the integral $\int\limits_{0}^{\pi/ 4} \frac{1+\sin^{2} }{ \cos^{3} x} dx $ is
With sodium hydroxide, silver nitrate forms a black precipitate of
Mass defect in a fusion reaction is 0.36%. Energy liberated when 1 gm of material undergoes fusion in kWh is
A particle is projected with a velocity so that height attained becomes equal to the radius of the earth. Then the velocity is
An example of a zero order reaction is
If $n$ is a positive integer which is relatively prime to $6,$ and if $n$ has $8$ divisors, then $12n$ has
If $A$ is a square matrix.such that $A^3 = 0$, then $(I + A)^{-1}$ is
When alcohol reacts with concentrated $H_{2}SO_{4},$ intermediate compound formed is :
In the manufacture of ordinary glass the substance used is
Which of the following reagents can be used to distinguish between phenol and benzyl alcohol ?
Magnetic moment of deuteron is
A step up transformer has turns ratio $10 : 1$. A source of emf 2 volts is fed to the primary. Secondary voltage developed is
Curie temperature is the temperature above which
If $\sin(\pi \cos \theta) = \cos(\pi \sin \theta),$ then $\sin 2 \theta$ equals
Acetophenone when nitrated, the major product obtained is
Power alcohol is
Smoke is an example of
Stainless steel is an alloy of
The number of integral values of k for which the equation $7 \cos x + 5 \sin x = 2k + 1$ has solution is
Tranquilisers
The minimum energy required to excite $H_2$ atom from its ground state is
Which of the following unicellular organisms has a macronucleus for trophic function and one or more micronuclei for reproduction?