List of practice Questions

Acetic acid on heating with $ {NH_3}$ forms $A$. When $A$ reacts with $ {LiAlH_4}$ followed by hydrolysis gives $B$. When $B$ is heated with chloroform in $KOH$ medium gives $C$. What are $B$ and $C$ respectively?

The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is

An organic compound $X\left( C _{7} H _{7} Cl \right)$ when reacted with $KCN / C _{2} H _{5} OH$ gave major product $Y . Z$ is formed when $Y$ is reduced with $LiAlH _{4}$. What are $Y$ and $Z$ ?

$\cos ^{2} 5^{\circ}-\cos ^{2} 15^{\circ}-\sin ^{2} 15^{\circ}+\sin ^{2} 35^{\circ}$ $+\cos 15^{\circ} \sin 15^{\circ}-\cos 5^{\circ} \sin 35^{\circ}=$

Identify the set of acidic oxides.

If $\begin{vmatrix}a+b+2c&a&b\\ c&2a+b+c&b\\ c&a&a+2b+c\end{vmatrix} = 2 $, then $a^3 + b^3 + c^3 - 3abc$ =

An $\alpha$-particle moves in a circular path of radius $1\, cm$ in a uniform magnetic field of $0.125\, T$. The de Broglie wavelength associated with the $\alpha$-particle is

For a particle executing simple harmonic motion, the displacement-time $(x - t)$ graph is as shown in the figure. The acceleration of the particle at $t = \frac{4}{3} s$ is

If $\cos \theta \neq 0$ and $\sec \theta - 1 = ( \sqrt{2} - 1 ) \tan \theta $ then $\theta $ =

The velocity of an object moving in a straight line path is given as a function of time by $v = 6t - 3t^2$. where $v$ is in $ms^{-1} , t $ is in $s$. The average velocity of the object between $t = 0$ and $t = 2s$ is

Which of the following reactions can be used to prepare diborane? I) $ {BF_3 + LiAlH_4 ->[ether]}$ II) $ {BF_3 + NaH ->[450 k]}$ III) $ {Na_2B_4O_7 + H_2O -> }$ IV) $ { NaBH_4 + I_2 ->}$

$CuSO_4$ solution is electrolysed for $15$ minutes to deposit $0.4725\, g$ of copper at the cathode. The current in amperes requited is (Faraday = $96.500 \,C\,mol^{-1}$. atomic weight of copper = $63$)

If $\sqrt{1-x^{6} }+ \sqrt{1-y^{6}} =a\left(x^{3} -y^{3}\right) , $ then $ y^{2} \frac{dy}{dx} = $

The molecule/ion having diamagnetic nature and a bond order of $1.0$ is

If $k$ is one of the roots of the equation $x^2 - 25x + 24 = 0 $ such that $A = \begin{bmatrix}1&2&1\\ 3&2&3\\ 1&1&k\end{bmatrix} $ is a non-singular matrix, then $A^{-1}$ =

$KMnO _{4}$ oxidises $S _{2} O _{3}^{2-}$ to $SO _{4}^{2-}$ in medium $x$ and $NO^{-}_2$ to $NO^{-}_3$ in medium $y, x$ and $y$ are respectively

If $y = \sin^2 (\cot^{-1} \sqrt{\frac{1+x}{1-x}} ) $, then $\frac{dy}{dx}$ =

In a nuclear reactor the activity of a radioactive substance is $2000 / s$. If the mean life of the products is $50$ minutes, then in the steady power generation, the number of radio nuclides is

Sodium nitrite is reacted with $H_2SO_4$ to form $NaHSO_4, HNO_3$, water and $X$. Gold is dissolved in aqua-regia to form water, $AuCl^{-}_4$ and $Y. X$ and $Y$ are respectively

If $\alpha$ and $\beta$ are the roots of $x^{2}+7 x+3=0$ and $\frac{2 \alpha}{3-4 \alpha}, \frac{2 \beta}{3-4 \beta}$ are the roots of $a x^{2}+b x+c=0$ and $GCD$ of $a, b, c$ is $1$ , then $a+b+c=$

If $\alpha , \beta , \gamma$ are the roots of $x^3 - 6x^2 + 11x - 6 = 0 $ , then the equation having the roots $\alpha^2 + \beta^2 + \gamma^2$ and $\gamma^2 + \alpha^2$ is

If $f(x)=(2k + 1)x - 3 - ke^{-x } + 2e^x$ is monotonically increasing for all $x \in R$, then the least value of $k$ is

If each line of a pair of lines passing through origin is at a perpendicular distance of $4$ units from the point $(3, 4)$, then the equation of the pair of lines is

If $x = \frac{3}{10} + \frac{3.7}{10.15} + \frac{3.7.9}{10.15.20} + $ ...., then $5x + 8$ =

If two unbiased six-faced dice are thrown simultaneously until a sum of either $7$ or $11$ occurs, then the probability that $7$ comes before $11$ is