COMEDK 2022

Which of the following show both Frenkel and Schottky defect?

How many atoms are present in hcp per unit cell?

What is the molecular mass of X if the rate of diffusion of methane is twice that of X.

What will be the density of N\(_2\) gas at 230\(^\circ\)C and 3 atm pressure? (R = 0.082 L atm K\(^{-1}\) mol\(^{-1}\))

The process of aggregation of colloidal particles into an insoluble precipitate by the addition of suitable electrolyte is called

The correct condition for physical adsorption is

Which of the following are not path functions?
I. H \(-\) TS
II. W
III. q
IV. q + W

The relation between work done in reversible and irreversible process is

In which of the following changes, entropy decreases?

The difference between heat capacity at constant pressure and heat capacity at constant volume is

If the tangent to the curve \(xy + ax + by = 0\) at (1, 1) is inclined at an angle \({\tan ^{ - 1}}2\) with X-axis, then

Let \(f(x) = a - {(x - 3)^{8/9}}\), then maxima of \(f(x)\) is

If \(U_{n+1}=3 U_n-2 U_{n-1}\) and \(U_0=2, U_1=3\), then \(U_n\) is equal to

If \(4^n+15n+P\) is divisible by 9 for all \(n\in N\), then the least negative integral value of P is

The total number of terms in the expansion of \({(x + y)^{100}} + {(x - y)^{100}}\) is

The coefficient of \({x^{20}}\) in the expansion of \({(1 + 3x + 3{x^2} + {x^3})^{20}}\) is

In the expansion of \({(1 - 3x + 3{x^2} - {x^3})^{2n}}\), the middle term is

If two circles \({(x - 1)^2} + {(y - 3)^2} = {r^2}\) and \({x^2} + {y^2} - 8x + 2y + 8 = 0\) intersect in two distinct points, then

the circle \({x^2} + {y^2} + 4x - 7y + 12 = 0\) cuts an intercept on Y-axis of length

\(S\equiv x^2+y^2+2x+3y+1=0\) and \(S'\equiv x^2+y^2+4x+3y+2=0\) are two circles. The point \((-3,-2)\) lies

The argument of \({{1 - i\sqrt 3 } \over {1 + i\sqrt 3 }}\) is

Evaluate \({\left[ {{i^{22}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}\)

\({(i + \sqrt 3 )^{100}} + {(i - \sqrt 3 )^{100}} + {2^{100}}\) is equal to

\(\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {\cos x\,dx}\)

The solution of the differential equation \({{{d^2}y} \over {d{x^2}}} = 0\) represents

The solution of the differential equation \(\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0\) is

The solution of the differential equation \(x \frac{d y}{d x}=\cot y\) is

The approximate value of \((0.007)^{1/3}\) is

If \(f(x)+2f(1-x)=x^2+5,\forall\) real values of \(x\), then \(f(x)\) is given by

\(\int \frac{1}{x \sqrt{a x-x^2}} d x\) is

\(\int \frac{3^x}{\sqrt{1-9^x}} d x\) is equal to

If \(\mathop {\lim }\limits_{x \to 0} {{(1 + {a^3}) + 8{e^{1/x}}} \over {1 + (1 - {b^3}){e^{1/x}}}} = 2\), then

If the derivative of the function \(f(x) = \left\{ {\matrix{ {b{x^2} + ax + 4;} & {x \ge - 1} \cr {a{x^2} + b;} & {x < - 1} \cr } } \right.\) is everywhere continuous, then

If \(\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}\), then

Shade the feasible region for the inequations \(6x+4y\le120, 3x+10y\le180,x,y\ge0\) in a rough figure.

The maximum of Z is where, \(Z=4x+2y\) subject to constraints \(4x+2y\ge46,x+3y\le24\) and \(x,y\ge0\) is

Maximum value of \(z=12x+3y\), subject to constraints \(x\ge0,y\ge0,x+y\ge5\) and \(3x+y\le9\) is

The value of \({3^{{{\log }_4}5}} - {5^{{{\log }_4}3}}\) is

If for any 2 \(\times\) 2 square matrix A,
A (adj A) = \(\left[ {\matrix{ 8 & 0 \cr 0 & 8 \cr } } \right]\), then find the value of det (A).

If \(A = \left[ {\matrix{ a & 0 & 0 \cr 0 & a & 0 \cr 0 & 0 & a \cr } } \right]\), then \(|A||adj\,A|\) is equal to

If \(A = \left[ {\matrix{ {2 - k} & 2 \cr 1 & {3 - k} \cr } } \right]\) is a singular matrix, then the value of \(5k - {k^2}\) is

\((2^{3n}-1)\) is divisible by

\(\sum\limits_{n = 1}^m {n\,.\,n!}\) is equal to

If nC3 = 220, then n = ?

There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?

A regular polygon of n sides has 170 diagonals, then n is equal to

How many 5-digit numbers greater than 50,000 can be formed using the digits 1, 2, 3, 4, 5 without repetition?

The probability of choosing randomly a number c from the set {1, 2, 3, ... 9} such that the quadratic equation \(x^2+4x+c=0\) has real roots, is

Five persons A, B, C, D and E are in queue of a shop. The probability that A and B are always together is

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fail is