List of practice Questions

If $A=\begin{bmatrix} {2}&{1} &{0}\\ {0}&{2}& {1} \\ {1}&{0}&{2}\\ \end{bmatrix}$ then $| adj A|$ =

Triangle $ABC$ has vertices $(0, 0), (11, 60)$ and $(91, 0)$. If the line $ y=kx $ cuts the triangle into $2$ two triangles of equal area, then $k$ is equal to

A metal wire of length $ l $ area of cross-section A and Young's modulus Y behaves as a spring of spring constant k given by

If $\alpha$ and $\beta$ are the roots of $x^2 + x + 1 = 0$ then $\alpha^{16}+\beta^{16}$=

If one side of a triangle is double the other and the angles opposite to these sides differ by $60^\circ$, then the triangle is

In the group $G= \{0, 1,2, 3,4, 5\}$ under addition modulo $6,(2 +_6 3^{-1} +_6 4)^{-1}$=

A bivalent metal has an equivalent mass of $32$. The molecular mass of the metal nitrate is

The smallest positive integral value of $'n'$ such that $\left[\frac {1+\sin \frac {\pi}{8}+\,i\,\cos \frac {\pi}{8}}{1+\sin \frac {\pi}{8}-\,i\,\cos \frac {\pi}{8}} \right]^n$ is purely imaginary is, $n$ =

If $\begin{vmatrix} {1+\sin^2}&{\cos^2 \theta } &{4\sin 2\theta}\\ {\sin^2}&{1+\cos^2}& {4\sin2\theta} \\ {\sin^2\theta}&{\cos^2\theta}&{4\sin2\theta-1}\\ \end{vmatrix} =0 $ and $ 0< \theta

If$\vec{a}.\vec{b}\, = \,- |\vec{a}| \, |\vec{b}|$ then the angle between $\vec{a}$ and $ \vec{b}$ is

If the volume of the parallelopiped with $ \vec{a},\vec{b} $ and $ \vec{c}$ as coterminous edges is $40 \,cubic$ units, then the volume of the parallelopiped having $ \vec{b}+\vec{c} , \vec{c}+ \vec{a} $ and $ \vec{a}+ \vec{b}$ as coterminous edges in cubic units is

How many ' $mL$' of perhydrol is required to produce sufficient oxygen which can be used to completely convert $2 \,L$ of $SO _{2}$ gas to $SO _{3}$ gas?

For the following cell reaction $Ag \left| Ag ^{+}\right| AgCl \left| Cl ^{\ominus}\right| Cl _{2}, Pt$ $\Delta G ^{\circ} f ( AgCl )=-109\, kJ / mol$ $\Delta G ^{\circ} f \left( Cl ^{-}\right)=-129\, kJ / mol$ $\Delta G ^{\circ} f \left( Ag ^{+}\right) 78 \,kJ / mol$ $E ^{\circ}$ of the cell is

$1^{st}$ polar body is formed at which stage of oogenesis?

A cell when kept in sugar solution, gets dehydrated/reduced in size. Then the solution is

If energy E, velocity v and time T are taken as fundamental quantities, the dimensional formula for surface tension is

In the case of peppered moth (Biston betularia) the black-coloured form became dominant over the light-coloured form in England during industrial revolution. This is an example of

A dominant gametophytic phase alternated by multicellular dependent sporophytic phase is represented by

Which is not part of glomerular ultrafiltrate ?

See the electrical circuit shown in this figure. Which of the following equations is a correct equation for it ?

Which of the following is a symbiotic nitrogen fixer?

In an experiment of Wheatstone bridge, a null point is obtained at the centre of the bridge wire. When a resistance of $10 \, \Omega $ is connected in one gap, the value of resistance in other gap is

If the acceleration-displacement graph of simple harmonic motion of a particle is given, then the time period of the particle will be

Among the following, the compound that contains ionic, covalent and coordinate linkage is