KCET 2019

In the reaction of gold with aquaregia, oxidation state of nitrogen changes from

Which cleansing agent gets precipitated in hard water?

Which of the following is a network crystalline solid?

The number of atoms in \(2.4 \mathrm{~g}\) of body centred cubic crystal with edge length \(200 \mathrm{pm}\) is (density \(=10 \mathrm{~g} \mathrm{~cm}^{-3}, \mathrm{~N}_A=6 \times 10^{23}\) atoms\(/ \mathrm{mol}\))

1 mole of \(\mathrm{NaCl}\) is doped with \(10^{-5}\) mole of \(\mathrm{SrCl}_2\). The number of cationic vacancies in the crystal lattice will be

The mass of \(\mathrm{AgCl}\) precipitated when a solution containing \(11.70 \mathrm{~g}\) of \(\mathrm{NaCl}\) is added to a solution containing \(3.4 \mathrm{~g}\) of \(\mathrm{AgNO}_3\) is [Atomic mass of \(\mathrm{Ag}=108\), Atomic mas...

Which of the following equations does not represent Charles's law for a given mass of gas at constant pressure?

Which of the following is an example of homogeneous catalysis?

Critical Micelle concentration for a soap solution is \(1.5 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}\). Micelle formation is possible only when the concentration of soap solution in \(\mathrm{mol} \mathrm{~L}^{-1}\) is

The reaction in which \(\Delta H=\Delta U\) is

The sides of an equilateral triangle are increasing at the rate of \(4 \mathrm{~cm} / \mathrm{sec}\). The rate at which its area is increasing, when the side is \(14 \mathrm{~cm}\)

The interval in which the function \(f(x)=x^3-6 x^2+9 x+10\) is increasing in

The area of the region above \(X\)-axis included between the parabola \(y^2=x\) and the circle \(x^2+y^2=2 x\) in square units is

The area of the region bounded by \(Y\)-axis, \(y=\cos x\) and \(y=\sin x, 0 \leq x \leq \frac{\pi}{2}\) is

The number of terms in the expansion of \(\left(x^2+y^2\right)^{25}-\left(x^2-y^2\right)^{25}\) after simplification is

\(\int_\limits{-3}^3 \cot ^{-1} x d x=\)

\(\int_\limits0^2\left[x^2\right] d x=\)

\(\int_\limits0^1 \sqrt{\frac{1+x}{1-x}} d x=\)

The integrating factor of the differential equation \(\left(2 x+3 y^2\right) d y=y d x(y>0)\) is

The equation of the curve passing through the point \((1,1)\) such that the slope of the tangent at any point \((x, y)\) is equal to the product of its co-ordinates is

The order of the differential equation \(y=C_1 e^{C_2+x}+C_3 e^{C_4+x}\) is

If \([x]\) represents the greatest integer function and \(f(x)=x-[x]-\cos x\), then \(f^{\prime}\left(\frac{\pi}{2}\right)=\)

If \(x=a \sec ^2 \theta\) & \(y=a \tan ^2 \theta\), then \(\frac{d^2 y}{d x^2}=\)

\(\sqrt[3]{y} \sqrt{x}=\sqrt[6]{(x+y)^5}\), then \(\frac{d y}{d x}=\)

The eccentricity of the ellipse \(9 x^2+25 y^2=225\) is

\(f: R \rightarrow R\) and \(g:[0, \infty) \rightarrow R\) is defined by \(f(x)=x^2\) and \(g(x)=\sqrt{x}\). Which one of the following is not true?

If \(|3 x-5| \leq 2\) then

The value of \(\sqrt{24.99}\) is

The domain of the function \(f: R \rightarrow R\) defined by \(f(x)=\sqrt{x^2-7 x+12}\) is

\(\int x^3 \sin 3 x d x=\)

\(\int \frac{1}{\sqrt{x}+x \sqrt{x}} d x=\)

$$\begin{aligned} & \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x \\ & \quad=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \end{aligned}$$
Then \(A, B, C\) are respectively

If \(f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right)\) then \(f^{\prime}(0)=\)

\(\cos \left[2 \sin ^{-1} \frac{3}{4}+\cos ^{-1} \frac{3}{4}\right]=\)

If \(a+\frac{\pi}{2}<2 \tan ^{-1} x+3 \cot ^{-1} x< b\) then '\(a\)' and '\(b\)' are respectively.

If $$f(x)=\left\{\begin{array}{cl}\frac{\sin 3 x}{e^{2 x}-1} ; & x \neq 0 \\ k-2 ; & x=0\end{array}\right.$$ is continuous at \(x=0\), then \(k=\)

\(\sum_\limits{r=1}^n(2 r-1)=x\) then, \(\lim _\limits{n \rightarrow \infty}\left[\frac{1^3}{x^2}+\frac{2^3}{x^2}+\frac{3^3}{x^2}+\ldots+\frac{n^3}{x^2}\right]=\)

Rolle's theorem is not applicable in which one of the following cases?

The shaded region in the figure is the solution set of the inequations.

The negative of the statement "All continuous functions are differentiable."

The inverse of the matrix $$\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]$$ is

If \(P\) and \(Q\) are symmetric matrices of the same order then \(P Q-Q P\) is

If $$3 A+4 B^{\prime}=\left[\begin{array}{ccc}7 & -10 & 17 \\ 0 & 6 & 31\end{array}\right]$$ and $$2 B+3 A^{\prime}\left[\begin{array}{cc}-1 & 18 \\ 4 & 0 \\ -5 & -7\end{array}\right]$$ then \(B=\)

If $$A=\left[\begin{array}{ll}1 & 3 \\ 4 & 2\end{array}\right], B=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right]$$, Then \(\left|A B B^{\prime}\right|=\)

If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is

The constant term in the expansion of $$\left|\begin{array}{ccc}3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 x+1 & 4 x-1\end{array}\right|$$ is

The number of 4 digit numbers without repetition that can be formed using the digits \(1,2,3,4,5,6,7\) in which each number has two odd digits and two even digits is

If \(P(n): 2^n< n !\) Then the smallest positive integer for which \(P(n)\) is true, is

Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is consonant is

A random variable '\(X\)' has the following probability distribution

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