KCET 2022

Vacant space in body centered cubic lattice unit cell is about

How many number of atoms are there in a cube based unit cell, having one atom on each corner and 2 atoms on each body diagonal of cube?

Which of the following is not true about the amorphous solids?

Alkali halides do not show dislocation defect because

An aqueous solution of alcohol contains \(18 \mathrm{~g}\) of water and \(414 \mathrm{~g}\) of ethyl alcohol. The mole fraction of water is

Which property of \(\mathrm{CO}_2\) makes it biologically and geo-chemically important?

The volume of \(2.8 \mathrm{~g}\) of \(\mathrm{CO}\) at \(27^{\circ} \mathrm{C}\) and 0.821 atm pressure is
(\(R=0.08210 \text { L. atm K} \mathrm{~mol}^{-1}\))

Colloidal solution commonly used in the treatment of skin disease is

Which can adsorb larger volume of hydrogen gas?

The work done when 2 moles of an ideal gas expands rèversibly and isothermally from a volume of \(1 \mathrm{~L}\) to \(10 \mathrm{~L}\) at \(300 \mathrm{~K}\) is
(\(R=0.0083 \mathrm{~kJ} \mathrm{~K} \mathrm{~mol}^{-1}\))

The function \(f(x)=\log (1+x)-\frac{2 x}{2+x}\) is increasing on

The coordinates of the point on the \(\sqrt{x}+\sqrt{y}=6\) at which the tangent is equally inclined to the axes is

The function \(f(x)=4 \sin ^3 x-6 \sin ^2 x +12 \sin x+100\) is strictly

Area of the region bounded by the curve \(y=\tan x\), the \(X\)-axis and line \(x=\frac{\pi}{3}\) is

If \(3 x+i(4 x-y)=6-i\) where \(x\) and \(y\) are real numbers, then the values of \(x\) and \(y\) are respectively,

If \([x]\) is the greatest integer function not greater than \(x\), then \(\int_\limits0^8[x] d x\) is equal to

\(\int_0^{\pi / 2} \sqrt{\sin \theta} \cos ^3 \theta d \theta\) is equal to

\(\int_0^1 \frac{x e^x}{(2+x)^3} d x\) is equal to

Evaluate \(\int_\limits2^3 x^2 d x\) as the limit of a sum

\(\int_0^{\pi / 2} \frac{\cos x \sin x}{1+\sin x} d x\) is equal to

If \(\frac{d y}{d x}+\frac{y}{x}=x^2\), then \(2 y(2)-y(1)=\)

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

If \(y(x)\) is the solution of differential equation \(x \log x \frac{d y}{d x}+y=2 x \log x, y(e)\) is equal to

The sum of the degree and order of the differential equation \(\left(l+y_1^2\right)^{2 / 3}=y_2\) is

If \(y=\left(1+x^2\right) \tan ^{-1} x-x\), then \(\frac{d y}{d x}\) is

If \(x=e^\theta \sin \theta, y=e^\theta \cos \theta\) where \(\theta\) is a parameter, then \(\frac{d y}{d x}\) at \((1,1)\) is equal to

If \(y=e^{\sqrt{x \sqrt{x} \sqrt{x}}...,} x >1\), then \(\frac{d^2 y}{d x^2}\) at \(x=\log _e 3\) is

If \(f(1)=1, f^{\prime}(l)=3\), then the derivative of \(f(f(f(x)))+(f(x))^2\) at \(x=1\) is

If \(y=x^{\sin x}+(\sin x)^x\), then \(\frac{d y}{d x}\) at \(x=\frac{\pi}{2}\) is

If \(e^y+x y=e\) the ordered pair \(\left(\frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)\) at \(x=0\) is equal to

The domain of the function \(f(x)=\frac{1}{\log _{10}(1-x)}+\sqrt{x+2}\) is

If \(f: R \rightarrow R\) be defined by
$$f(x)=\left\{\begin{array}{llc} 2 x: & x>3 \\ x^2: & 1< x \leq 3 \\ 3 x: & x \leq 1 \end{array}\right.$$
then \(f(-1)+f(2)+f(4)\) is

\(\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x\) is equal to

If \(\int \frac{d x}{(x+2)\left(x^2+1\right)}=a \log \left|1+x^2\right|+b \tan ^{-1} x +\frac{1}{5} \log |x+2|+c,\) then

Domain \(\cos ^{-1}[x]\) is, where [ ] denotes a greatest integer function

If $$f(x)=\left\{\begin{array}{cc}x^2-1, & 0< x<2 \\ 2 x+3, & 2 \leq x<3\end{array}\right.$$,
the quadratic equation whose roots are \(\lim _\limits{x \rightarrow 2^{-}} f(x)\) and \(\lim _\limits{x \rightarrow 2^{+}} f(x)\) is

\(\lim _\limits{y \rightarrow 0} \frac{\sqrt{3+y^3}-\sqrt{3}}{y^3}=\)

The corner points of the feasible region of an LPP are \((0,2),(3,0),(6,0),(6,8)\) and \((0,5)\), then the minimum value of \(z=4 x+6 y\) occurs at

A dietician has to develop a special diet using two foods \(X\) and \(Y\). Each packet (containing \(30 \mathrm{~g}\) ) of food. \(X\) contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each pack...

If \(A\) is a matrix of order \(3 \times 3\), then \(\left(A^2\right)^{-1}\) is equal to

If $$A=\left[\begin{array}{ll}2 & -1 \\ 3 & -2\end{array}\right]$$, then the inverse of the matrix \(A^3\) is

If \(A\) is a skew symmetric matrix, then A\(^{2021}\) is

If $$A=\left[\begin{array}{ll}0 & 1 \\ 0 & 0\end{array}\right]$$, then \((a I+b A)^n\) is (where \(I\) is the identify matrix of order 2)

If \(A\) is a \(3 \times 3\) matrix such that \(|5 \cdot \operatorname{adj} A|=5\), then \(|A|\) is equal to

If there are two values of '\(a\)' which makes determinant
$$\Delta=\left|\begin{array}{ccc} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2 a \end{array}\right|=86$$
Then, the sum of these number is

If $$A_n=\left[\begin{array}{cc}1-n & n \\ n & 1-n\end{array}\right]$$, then
\(\left|A_1\right|+\left|A_2\right|+\ldots .\left|A_{2021}\right|=\)

If all permutations of the letters of the word MASK are arranged in the order as in dictionary with or without meaning, which one of the following is 19th word?

Find the mean number of heads in three tosses of a fair coin.

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{2}, P(B)=\frac{1}{2}\) and \(P(A \mid B)=\frac{1}{4}\), then \(P\left(A^{\prime} \cap B^{\prime}\right)\) is

A pandemic has been spreading all over the world. The probabilities are 0.7 that there will be a lockdown, 0.8 that the pandemic is controlled in one month if there is a lockdown and 0.3 that it is controlled in one month if there is no loc...