KCET 2018

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...

If $\left[\begin{array}{cc}1 & 1 \\ -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}2 \\ 4\end{array}\right]$, then the values of $x$ and $y$ respectively are

The value of determinant $\left|\begin{array}{lll}a-b & b+c & a \\ b-a & c+a & b \\ c-a & a+b & c\end{array}\right|$ is

The number of ways in which 5 girls and 3 boys can be seated in a row so that no two boys are together is

Everybody in a room shakes hands with everybody else. The total number of handshakes is 45 . The total number of persons in the room is

If $A$ and $B$ are mutually exclusive events, given that $P(A)=\frac{3}{5}, P(B)=\frac{1}{5}$, then $P(A$ or $B)$ is

The probability of happening of an event $A$ is 0.5 and that of $B$ is 0.3 . If $A$ and $B$ are mutually exclusive events, then the probability of neither $A$ nor $B$ is

In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is

A flashlight has 10 batteries out of which 4 are dead. If 3 batteries are selected without replacement and tested, then the probability that all 3 are dead is

A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn at random, then another ticket is drawn without replacing the first one. The probability that both the tickets may show even numbers is

If $a, b, c$ are three consecutive terms of an AP and $x, y, z$ are three consecutive terms of a GP, then the value of $x^{b-c} \cdot y^{c-a} \cdot z^{a-b}$ is