KCET 2020

If the side of a cube is increased by \(5 \%\), then the surface area of a cube is increased by

The maximum value of \(\frac{\log _e x}{x}\), if \(x>0\) is

If the curves \(2 x=y^2\) and \(2 x y=K\) intersect perpendicularly, then the value of \(K^2\) is

The area of the region bounded by the curve \(y^2=8 x\) and the line \(y=2 x\) is

The area of the region bounded by the line \(y=2 x+1, X\)-axis and the ordinates \(x=-1\) and \(x=1\) is

The number of terms in the expansion of \((x+y+z)^{10}\) is

If \(z=x+i y\), then the equation \(|z+1|=|z-1|\) represents

Find the value of \(\int_0^1 \frac{\log (1+x)}{1+x^2} d x\) is

The value of \(\int_{-1 / 2}^{1 / 2} \cos ^{-1} x d x\) is

The value of \(\int_{-\pi / 2}^{\pi / 2} \frac{\cos x}{1+e^x} d x\) is

The general solution of the differential equation \(x^2 d y-2 x y d x=x^4 \cos x d x\) is

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves \(c_1 y=\left(c_2+c_3\right) e^{x+c_4}\) is

The curve passing through the point \((1,2)\) given that the slope of the tangent at any point \((x, y)\) is \(\frac{3 x}{y}\) represents

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

If \(y=2 x^{n+1}+\frac{3}{x^n}\), then \(x^2 \frac{d^{2 y}}{d x^2}\) is

If \((x e)^y=e^y\), then \(\frac{d y}{d x}\) is

Let \(f:[2, \infty) \rightarrow R\) be the function defined \(f(x)=x^2-4 x+5\), then the ranges of \(f\) is

The value of \(\int \frac{1+x^4}{1+x^6} d x\) is

If \(\int \frac{3 x+1}{(x-1)(x-2)(x-3)} d x A \log |x-1| B \log |x-2|+C \log |x-3|+C\), then the values of \(A, B\) and \(C\) are respectively

The value of \(\int e^{\sin x} \sin 2 x d x\) is

The domain of the function defined by \(f(x)=\cos ^{-1} \sqrt{x-1}\) is

The value of \(\cos \left(\sin ^{-1} \frac{\pi}{3}+\cos ^{-1} \frac{\pi}{3}\right)\) is
Does not exist

If \(f(x)=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)\), then \(f^{\prime}(\sqrt{3})\) is

If $$f(x)=\left\{\begin{array}{cc}\frac{1-\cos K x}{x \sin x}, & \text { if } x \neq 0 \\ \frac{1}{2}, & \text { if } x=0\end{array}\right.$$ is continuous at \(x=0\), then the value of \(K\) is

The right hand and left hand limit of the function are respectively.
$$f(x)=\left\{\begin{array}{cc} \frac{e^{1 / x}-1}{e^{1 / x}+1}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0 \end{array}\right.$$

\(\lim _\limits{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right) \text { is equal to }\)

Corner points of the feasible region determined by the system of linear constraints are \((0,3),(1,1)\) and \((3,0)\). Let \(z=p x=q y\), where, \(p, q>0\). Condition on \(p\) and \(q\), so that the minimum of \(z\) occurs at \((3,0)\) and ...

The feasible region of an LPP is shown in the figure. If \(z=11 x+7 y\), then the maximum value of \(Z\) occurs at

The negation of the statement "For all real numbers \(x\) and \(y, x+y=y+x^{\prime \prime}\) is

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

If $$\left(\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right) A=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$$ then the matrix \(a\) is

If \(a_1 a_2 a_3 \ldots a_9\) are in AP, then the value of $$\left|\begin{array}{lll}a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9\end{array}\right|$$ is

If \(A\) and \(B\) are square matrices of same order and \(B\) is a skew symmetric matrix, then \(A^{\prime} B A\) is

If $$A=\left(\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right)$$ then \(A^4\) is equal to

If $$f(x)=\left|\begin{array}{ccc}x^3-x & a+x & b+x \\ x-a & x^2-x & c+x \\ x-b & x-c & 0\end{array}\right|$$, then

If \(A\) is a square matrix of order 3 and \(|A|=5\), then \(\mid A\) adj. \(A \mid\) is

If the parabola \(x^2=4\) ay passes through the point \((2,1)\), then the length of the latus rectum is

The value of \({ }^{16} C_9+{ }^{16} C_{10}-{ }^{16} C_6-{ }^{16} C_7\) is

The probability of solving a problem by three persons \(A, B\) and \(C\) independently is \(\frac{1}{2}, \frac{1}{4}\) and \(\frac{1}{3}\) respectively. Then the probability of the problem is solved by any two of them is

Events \(E_1\) and \(E_2\) from a partition of the sample space \(S\). \(A\) is any event such that \(P\left(E_1\right)=P\left(\dot{E}_2\right)=\frac{1}{2}, P\left(E_2 / A\right)=\frac{1}{2}\) and \(P\left(A / E_2\right)=\frac{2}{3}\), then...

If \(A, B, C\) are three mutually exclusive and exhaustive events of an experiment such that \(P(A)=2 P(B)=3 P(C)\), then \(P(B)\) is equal to

A die is thrown 10 times, the probability that an odd number will come up at least one time is

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{3}, P(B)=\frac{1}{2}\) and \(P(A \cap B)=\frac{1}{6}\), then \(P\left(A^{\prime} / B\right)\) is

If the sum of \(n\) terms of an AP is given by \(S_n=n^2+n\), then the common difference of the \(\mathrm{AP}\) is

If \(n(A)=2\) and total number of possible relations from Set A to set B is 1024, then \(n(B)\) is

If \(A=\{a, b, c\}\), then the number of binary operations on \(A\) is

If a relation \(R\) on the set \(\{1,2,3\}\) be defined by \(R=\{(1,1)\}\), then \(R\) is

If \(A=\{1,2,3,4,5,6\}\), then the number of subsets of A which contain at least two elements is

The standard deviation of the data 6, 7, 8, 9, 10 is

The two lines \(l x+m y=n\) and \(l^{\prime} x+m^{\prime} y=n^{\prime}\) are perpendicular if