KCET 2018

$\mathrm{KMnO}_4$ acts as an oxidising agent in alkaline medium. When alkaline $\mathrm{KMnO}_4$ is treated with KI , iodide ion is oxidised to

Very pure $\mathrm{N}_2$ can be obtained by

Dead burnt plaster is

In FCC, the unit cell is shared equally by how many unit cells?

Edge length of a cube is 300 pm . Its body diagonal would be

1.0 g of Mg is burnt with 0.28 g of $\mathrm{O}_2$ in a closed vessel. Which reactant is left in excess and how much?

Dry ice is

For an ideal gas, compressibility factor is

Which of the following electrolytes will have maximum coagulating value for $\mathrm{AgI} / \mathrm{Ag}^{+}$ sol?

Gold sol is not a

Approximate change in the volume $V$ of a cube of side $x$ metres caused by increasing the side by $3 \%$ is

The maximum value of $\left(\frac{1}{x}\right)^x$ is

$f(x)=x^x$ has stationary point at

The area bounded by the line $y=x, X$-axis and ordinates $x=-1$ and $x=2$ is

The area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is

The constant term in the expansion of $\left(x^2-\frac{1}{x^2}\right)^{16}$ is

The maximum area of a rectangle inscribed in the circle $(x+1)^2+(y-3)^2=64$ is

If $\left(\frac{1-i}{1+i}\right)^{96}=a+i b$, then $(a, b)$ is

$\int_{-2}^2|x \cos \pi x| d x$ is equal to

$ \int_0^{1 / 2} \frac{d x}{\left(1+x^2\right) \sqrt{1-x^2}}$ is equal to

$\int_0^1 \frac{d x}{e^x+e^{-x}}$ is equal to

The integrating factor of $\frac{d y}{d x}+y=\frac{1+y}{x}$ is

The degree and the order of the differential equation $\frac{d^2 y}{d x^2}=\sqrt[3]{1+\left(\frac{d y}{d x}\right)^2}$ respectively are

The solution of the differential equation $x \frac{d y}{d x}-y=3$ represents a family of

If $f(x)=|\cos x-\sin x|$, then $f^{\prime}\left(\frac{\pi}{6}\right)$ is equal to

\(\text { If } y=\sqrt{x+\sqrt{x+\sqrt{x+\ldots \infty}}} \text {, then } \frac{d y}{d x} \text { is equal }\) to

If $\cos y=x \cos (a+y)$ with $\cos a \neq \pm 1$, then $\frac{d y}{d x}$ is equal to

If $|x+5| \geq 10$, then

Let $f(x)=x-\frac{1}{x}$, then $f(-1)$ is

Let $f, g: R \rightarrow R$ be two functions defined as $f(x)=|x|+x$ and $g(x)=|x|-x \forall x \in R$. Then $(f \circ g)(x)$ for $x<0$ is

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

A is a set having 6 distinct elements. The number of distinct functions from $A$ to $A$ which are not bijections is

The distance between the foci of a hyperbola is 16 and its eccentricity is $\sqrt{2}$. Its equation is

$\int \frac{1}{\sqrt{3-6 x-9 x^2}} d x$ is equal to

$\int e^{\sin x} \cdot\left(\frac{\sin x+1}{\sec x}\right) d x$ is equal to

$\int \frac{1}{1+e^x} d x$ is equal to

If $\sin ^{-1} x+\cos ^{-1} y=\frac{2 \pi}{5}$, then $\cos ^{-1} x+\sin ^{-1} y$ is

The value of the expression $\tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{5}}\right)$ is

If $f(x)=\left\{\begin{array}{cl}\frac{\log _e x}{x-1} & ; x \neq 1 \\ k & ; x=1\end{array}\right.$
is continuous at $x=1$, then the value of $k$ is

If $f(x)=\left\{\begin{array}{clc}\frac{\sqrt{1+k x}-\sqrt{1-k x}}{x} & \text { if }-1 \leq x<0 \\ \frac{2 x+1}{x-1} & \text { if } 0 \leq x \leq 1\end{array}\right.$
is continuous at $x=0$, then the value of $k$ is

The value of $\lim \limits_{x \rightarrow 0} \frac{[x]}{x}$ is :

The feasible region of an LPP is shown in the figure. If $z=3 x+9 y$, then the minimum value of $z$ occurs at

For the LPP, maximize $z=x+4 y$ subject to the constraints $x+2 y \leq 2, x+2 y \geq 8, x, y \geq 0$

$P  (n): 2^{2 n}-1$ is divisible by $k$ for all $n \in N^{\prime \prime}$ is true, then the value of ' $k$ ' is

The negation of the statement " 72 is divisible by 2 and $3^{\prime \prime}$ is

If $A=\left[\begin{array}{cc}2 & -2 \\ -2 & 2\end{array}\right]$, then $A^n=2^k A$, where $k$ is equal to

Let $A$ be a square matrix of order $3 \times 3$, then $|5 A|$ is equal to

If $x, y, z \in R$, then the value of determinant $\left|\begin{array}{lll}\left(5^x+5^{-x}\right)^2 & \left(5^x-5^{-x}\right)^2 & 1 \\ \left(6^x+6^{-x}\right)^2 & \left(6^x-6^{-x}\right)^2 & 1 \\ \left(7^x+7^{-x}\right)^2 & \left(7^x-7^{-x...

If $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right]$, then $A A^{\prime}$ is equal to

If $\left(x_1, y_1\right),\left(x_2, y_2\right)$ and $\left(x_3, y_3\right)$ are the vertices of a triangle whose are is ' $k$ ' square units, then $\left|\begin{array}{lll}x_1 & y_1 & 4 \\ x_2 & y_2 & 4 \\ x_3 & y_3 & 4\end{array}\right|^2...