List of practice Questions

The coefficient of \(x^4\) in the expansion of \((1 + x + x^2 + x^3)^{11}\) is:
If the \((2p)^{\text{th}}\) term of a H.P. is \(q\) and the \((2q)^{\text{th}}\) term is \(p\), then the \(2(p+q)^{\text{th}}\) term is:
\(\displaystyle \lim_{x \to 0} \left(\csc x\right)^{\frac{1}{\log x}}\) is equal to:
Let \( R = \{(3,3), (6,6), (9,9), (12,12), (6,12), (3,9), (3,12), (3,6)\} \) be a relation on the set \( A = \{3,6,9,12\} \). Then, the relation is:
In a face centered cubic lattice atoms $A$ are at the corner points and atoms $B$ at the face centered points. If atom $B$ is missing from one of the face centered points, the formula of the ionic compound is :
In a large building, there are 15 bulbs of 40\, W, 5 bulbs of 100 W, 5 fans of $80\, W$ and 1 heater of $1\, kW$. The voltage of the electric mains is $220 \,V$. The minimum capacity of the main fuse of the building will be :
In a monoclinic unit cell, the relation of sides and angles are respectively :
In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is :
In S$_N$2 reactions, the correct order of reactivity for the following compounds $CH_3Cl,CH_3CH_2Cl, (CH_3 )_2CHCl$ and (CH$_3 )_3CCl$ is
In the circuit shown, current (in A) through the 50 V and 30 V batteries are, respectively :
In the presence of peroxide, $HCl$ and $HI$ do not give anti-Markownikoff' s addition to alkenes because :
In the Victor-Meyer's test, the colour given by $1^{\circ}$, $2^{\circ}$and $3^{\circ}$ alcohols are respectively :
Let $f\left(n\right) = \left[\frac{1}{3} + \frac{3n}{100}\right]{n},$ where $\left[n\right]$ denotes the greatest integer less than or equal to n. Then $\sum\limits^{56}_{n = 1} \Delta_{r} f\left(n\right)$ is equal to :
Let $z\ne-i$ be any complex number such that $\frac{z-i}{z+i}$ is a purely imaginary number. Then $z+\frac{1}{z}$ is :
The conjugate base of hydrazoic acid is :
The correct order of bond dissociation energy among $N_2, O_2, O_2^-$ is shown in which of the following arrangements ?
The integral $\int x \,cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \,dx\, \left(x > 0\right)$ is equal to :
The minimum area of a triangle formed by any tangent to the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$ and the co-ordinate axes is :
The most suitable reagent for the conversion of $RCH_2OH \to RCHO$ is
The number of terms in an $A.P$. is even; the sum of the odd terms in it is $24$ and that the even terms is $30$. If the last term exceeds the first term by $10 \frac{1}{2},$ then the number of terms in the $A.P$. is :
The octahedral complex of a metal ion $M^{3+} $ with four monodentate ligands $L_1,L_2,L_3 \, and \, L_4 $ absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four ligands is
The variance of first $50$ even natural numbers is
Two soap bubbles coalesce to form a single bubble. If $V$ is the subsequent change in volume of contained air and $S$ the change in total surface area, $T$ is the surface tension and $P$ atmospheric pressure, which of the following relation is correct ?
Van der Waal's equation for a gas is stated as, $p = \frac{nRT}{V-nb}-a\left(\frac{n}{V}\right)^{2}.$ This equation reduces to the perfect gas equation, $p = \frac{nRT}{V}$ when ,
What happens when an inert gas is added to an equilibrium keeping volume unchanged ?