KCET 2021

The third ionisation enthalpy is highest in

Which of the following is not true for oxidation?

The property of the alkaline earth metals that increases with their atomic number is

The correct statement regarding defects in solid is

A metal crystallises in bcc lattice with unit cell edge length of \(300 \mathrm{~pm}\) and density \(615 \mathrm{~g~cm}^{-3}\). The molar mass of the metal is

In chrysoberyl, a compound containing beryllium, aluminium and oxygen, oxide ions form cubic close packed structure. Aluminium ions occupy \(\frac{1}{4}\)th of octahedral voids. The formula of the compound is

A pure compound contains \(2.4 \mathrm{~g}\) of \(\mathrm{C}, 1.2 \times 10^{23}\) atoms of \(\mathrm{H}, 0.2\) moles of oxygen atoms. Its empirical formula is

When the absolute temperature of ideal gas is doubled and pressure is halved, the volume of gas

Zeta potential is

A colloidal solution is subjected to an electric field than colloidal particles more towards anode. The amount of electrolytes of \(\mathrm{BaCl}_2, \mathrm{AlCl}_3\) and \(\mathrm{NaCl}\) required to coagulate the given colloid is in the o...

The maximum slope of the curve \(y=-x^3+3 x^2+2 x-27\) is

A particle starts form rest and its angular displacement (in radians) is given by \(\theta=\frac{t^2}{20}+\frac{t}{5}\). If the angular velocity at the end of \(t=4\) is \(k\), then the value of \(5 k\) is

The cost and revenue functions of a product are given by \(c(x)=20 x+4000\) and \(R(x)=60 x+2000\) respectively, where \(\mathrm{x}\) is the number of items produced and sold. The value of \(x\) to earn profit is

The function \(f(x)=x^2-2 x\) is strictly decreasing in the interval

The area of the region bounded by \(y=-\sqrt{16-x^2}\) and \(X\)-axis is

If \(\left(\frac{1+i}{1-i}\right)^x=1\), then

The value of \(\int_0^{4042} \frac{\sqrt{x} d x}{\sqrt{x}+\sqrt{4042-x}}\) is equal to

If \(I_n=\int_0^{\frac{\pi}{4}} \tan ^n x d x\), where \(n\) is positive integer, then \(I_{10}+I_8\) is equal to

The number of solutions of \(\frac{d y}{d x}=\frac{y+1}{x-1}\), when \(y(\mathrm{l})=2\) is

Solution of differential equating \(x d y-y d x=0\) represents

If \(y=\left(\cos x^2\right)^2\), then \(\frac{d y}{d x}\) is equal to

Consider the following statements
Statement 1 : If \(y=\log _{10} x+\log _e x\), then \(\frac{d y}{d x}=\frac{\log _{10} e}{x}+\frac{1}{x}\)
Statement 2 : If \(\frac{d}{d x}\left(\log _{10} x\right)=\frac{\log x}{\log 10}\) and $$\frac{d}{d...

For constant \(a, \frac{d}{d x}\left(x^x+x^a+a^x+a^a\right)\) is

If the parametric equation of curve is given by \(x=\cos \theta+\log \tan \frac{\theta}{2}\) and \(y=\sin \theta\), then the points for which \(\frac{d y}{d x}=0\) are given by

If \(a\) and \(b\) are fixed non-zero constants, then the derivative of \(\frac{a}{x^4}-\frac{b}{x^2}+\cos x\) is \(m a+n b-p\), where

If \(y=(x-1)^2(x-2)^3(x-3)^5\), then \(\frac{d y}{d x}\) at \(x=4\) is equal to

If the area of the ellipse is \(\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1\) is \(20 \pi\) sq units, then \(\lambda\) is

\(f: R \rightarrow R\) defined by \(f(x)\) is equal to $$\left\{\begin{array}{l}2 x, x> 3 \\ x^2, 1< x \leq 3, \text { then } f(-2)+f(3)+f(4) \text { is } \\ 3 x, x \leq 1\end{array}\right.$$

The function \(f(x)=\sqrt{3} \sin 2 x-\cos 2 x+4\) is one-one in the interval

Domain of the function
\(f(x)=\frac{1}{\sqrt{\left[x^2\right]-[x]-6}},\)
where \([x]\) is greatest integer \(\leq x\) is

Domain of \(f(x)=\frac{x}{1-|x|}\) is

Let \(A=\{x: x \in R, x\) is not a positive integer) Define \(f: A \rightarrow R\) as \(f(x)=\frac{2 x}{x-1}\), then \(f\) is

The value of \(\int \frac{x e^x d x}{(1+x)^2}\) is equal to

The value of \(\int e^x\left[\frac{1+\sin x}{1+\cos x}\right] d x\) is equal to

\(\int \frac{x^3 \sin \left(\tan ^{-1}\left(x^4\right)\right)}{1+x^8} d x\) is equal to

The value of \(\int \frac{x^2 d x}{\sqrt{x^6+a^6}}\) is equal to

\(\tan ^{-1}\left[\frac{1}{\sqrt{3}} \sin \frac{5 \pi}{2}\right] \sin ^{-1}\left[\cos \left(\sin ^{-} \frac{\sqrt{3}}{2}\right)\right]\) is equal to

\(\cos \left[\cot ^{-1}(-\sqrt{3})+\frac{\pi}{6}\right]\) is equal to

If $$f(x)=\left|\begin{array}{ccc}\cos x & 1 & 0 \\ 0 & 2 \cos x & 3 \\ 0 & 1 & 2 \cos x\end{array}\right|$$, then \(\lim _\limits{x \rightarrow \pi} f(x)\) is equal to

Consider the following statements
Statement 1 : \(\lim _\limits{x \rightarrow 1} \frac{a x^2+b x+c}{x^2+b x+a}\) is 1
(where \(a+b+c \neq 0\)).
Statement 2 : \(\lim _\limits{x \rightarrow -2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2}\) is $$\frac...

At \(x=1\), the function
$$f(x)=\left\{\begin{array}{cc} x^3-1, & 1< x < \infty \\ x-1, & -\infty< x \leq 1 \end{array}\right. \text { is }$$

The shaded region is the solution set of the inequalities

If $$A=\left[\begin{array}{ccc}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right]$$
$$ B=\left[\begin{array}{ll}2 & 1 \\ 3 & 2 \\ 1 & 1\end{array}\right]$$, then \((A B)^{\prime}\) is equal to

Let \(M\) be \(2 \times 2\) symmetric matrix with integer entries, then \(M\) is invertible if

If \(A\) and \(B\) are invertible matrices then which of the following is not correct?

If \(A\) and \(B\) are matrices of order 3 and \(|A|=5,|B|=3\), then \(|3 A B|\) is

If \(x^3-2 x^2-9 x+18=0\) and $$A=\left|\begin{array}{lll}1 & 2 & 3 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|$$ then the maximum value of \(A\) is

If the parabola \(y=\alpha x^2-6 x+\beta\) passes through the point \((0,2)\) and has its tangent at \(x=\frac{3}{2}\) parallel to \(X\)-axis, then

\(A\) and \(B\) are non-singleton sets and \(n(A \times B)=35\). If \(B \subset A\), then \({ }^{n(A)} C_{n(B)}\) is equal to

A student has to answer 10 questions, choosing at least 4 from each of the parts \(A\) and \(B\). If there are 6 questions in part \(A\) and 7 in part \(B\), then the number of ways can the student choose 10 questions is