List of practice Questions

Two planets of radii $R_1$ and $R_2$ have the same density. The ratio of the acceleration due to gravity on these planets is

If $f\left(x\right) = \frac{x^{2} -1}{x^{2} +1} ,x\in R$ then the minimum value of $f$ is

The conjugate acid of $ {HCO_3^-}$ is

According to Lewis concept, an acid is a/an

The decarboxylating agent is

Methoxymethane and ethanol exhibit

Let $f (x)$ and $g(x)$ be differentiable functions on (0, 2] such that $f"(x) - g"(x) = 0, f'(1) = 2g'(1) = 4, f(2) = 3g(2) = 9.$ Then $f (x)- g(x)$ at $ x = 3/2$ is

If the area of a circle increases at a uniform rate, then its perimeter varies

The surface area of a ball is increasing at the rate of $2 \pi \, s cm/sec$. The rate at which the radius is increasing when the surface area is $16 \pi \, s cm$ is

If $A = \begin{bmatrix}3&2\\ 4&5\end{bmatrix} $ and $AC = \begin{bmatrix}19&24\\ 37&46\end{bmatrix}$ then $C= $

The area of the parallelogram with $\vec{a}$ and $\vec{b}$ as adjacent sides is $20\, s \,units$. Then the area of the parallelogram having $7\vec{a} + 5\vec{b}$ and $8\vec{a} + 11\vec{b}$ as adjacent sides is

The compound which gives hydrocarbon on distillation with zinc dust is

Two identical rods of length L, mass M are riveted at right angles at their mid points Moment of inertia of the system about the perpendicular axis passing through the centre is

Ratio of maximum to minimum intensities is

The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is

The point of contact of the tangent $x + 2y + 2 = 0$ with the parabola $x^2 = 16y$ is

Following is the substitution reaction in which \(-CN\) replaces \(-Cl\)
\(R - CI + KCN \overset{\Delta}{\rightarrow} R - CN + KCI\)
To obtain propane nitrile, \(R-Cl\) should be:

Which of the two ions from the list given below, have the geometry that is explained by the same hybridisation of orbitals $NO^- _ 2 ,NO_3^- , NH_2^- , NH_4^+,SCN ^- ?$