# KCET 2020 Mathematics Questions with Answers Key Solutions

## $2^{y-x}$

## $-2^{y-x}$

## $2^{x-y}$

## $\frac {2^y-1}{2^x-1}$

## $-\frac {1}{2}$

## $\frac {1}{2}$

## $\frac {1}{\sqrt{3}}$

## $-\frac {1}{\sqrt{3}}$

## 1 and 1

## 1 and -1

## -1 and -1

## -1 and 1

## 6n(n+1)y

## n(n+1)y

## $x \frac{dy}{dx}+y$

## $y$

## $4$

## $2\sqrt{2}$

## $2$

## $8$

## $\frac {log x}{ (1+logx)^2}$

## $\frac {1}{ (1+logx)^2}$

## $\frac {log x}{ (1+logx)}$

## $\frac {e^x}{ x(y-1)}$

## 10%

## 60%

## 6%

## 20%

## $tan^{-1} x + tan^{-1}x^3+C$

## $tan^{-1} x +\frac {1}{3} tan^{-1}x^3+C$

## $tan^{-1} x - \frac {1}{3} tan^{-1}x^3+C$

## $tan^{-1} x +\frac {1}{3} tan^{-1}x^2+C$

## $2e^{sinx} (sin x - 1) +C$

## $2e^{sinx} (sin x + 1) +C$

## $2e^{sinx} (cos x + 1) +C$

## $2e^{sin x} (cos x - 1) +C$

## $\pi$

## $\frac {\pi}{2}$

## $1$

## $\frac {\pi^2}{2}$

## 5, -7, -5

## 2, -7, -5

## 5, -7, 5

## 2, -7, 5

## $\frac{\pi}{2} log2$

## $\frac{\pi}{4} log2$

## $\frac{1}{2} $

## $\frac{\pi}{8} log2$

## $\frac{16}{3} sq.units$

## $\frac{4}{3} sq.units$

## $\frac{3}{4} sq.units$

## $\frac{8}{3} sq.units$

## 2

## 0

## 1

## -2

## 1

## 2

## 3

## 4

## $y = x^2 sinx + cx^2$

## $y = x^2 sinx + c$

## $y = sinx + cx^2$

## $y = cos x + cx^2$

## $\frac{9}{4}$

## $2$

## $\frac{5}{2}$

## $5$

## $\frac{\sqrt{14}}{2}$

## $14$

## $7$

## $\sqrt{14}$

## $\left|\overrightarrow{a}+\overrightarrow{b}\right|$

## $\frac {\left|\overrightarrow{a}+\overrightarrow{b}\right|}{2}$

## $\frac {\left|\overrightarrow{a}-\overrightarrow{b}\right|}{2}$

## $\left|\overrightarrow{a}-\overrightarrow{b}\right|$

## Circle

## Parabola

## Ellipse

## Hyperbola

## 6

## -5

## -6

## 5

## $\frac {293}{7}$

## $\frac {\sqrt {293} } {7}$

## $\frac {293} {49}$

## $\frac {\sqrt {293} } {49}$

## $\frac {3}{\sqrt{30}}$

## $\frac {3}{50}$

## $\frac {4}{5\sqrt{2}}$

## $\frac {\sqrt{2}} {10}$

## $\frac{\pi}{4}$

## $\frac{\pi}{6}$

## $\frac{\pi}{3}$

## $\frac{\pi}{2}$

## $p = 2q$

## $p = \frac {q}{2}$

## $p = 3q$

## $p = q$

## (0,5)

## (3,3)

## (5,0)

## (3,2)

## $\frac{1}{1024}$

## $\frac{1023}{1024}$

## $\frac{11}{1024}$

## $\frac{1013}{1024}$

## $\frac{2}{3}$

## $\frac{1}{3}$

## $\frac{1}{2}$

## $\frac{1}{12}$

## $\frac{1}{2}$

## $\frac{2}{3}$

## 1

## $\frac{1}{4}$

## $\frac{1}{12}$

## $\frac{1}{4}$

## $\frac{1}{24}$

## $\frac{1}{8}$

## 512

## 20

## 10

## 5

## 64

## 63

## 57

## 58

## ll'+mm'=0

## lm'+ml'

## lm+l'm'=0

## lm'+ml'=0

## 1

## 4

## 2

## 8

## 4

## 1

## 2

## 6

## For all real numbers x and $y, x + y \ne y + x$

## For some real numbers x and y, x+y = y+x

## For some real number x and y, x + y $\ne$ y + x

## for some real numbers x and y, x-y=y-x

## 2

## 3

## 4

## 6

## Reflexive and symmetric

## Reflexive and transitive

## symmetric and transitive

## Only symmetric

## Q49. Let $f:[2,\infty) \to R$ be the function defined $f(x) = x^2 - 4x + 5$ , then the range of f is

## $(-\infty, \infty)$

## $[1, \infty)$

## $(1, \infty)$

## $[5, \infty)$

## $\frac{1}{11}$

## $\frac{2}{11}$

## $\frac{3}{11}$

## $\frac{4}{11}$

## [1, 2]

## [0, 2]

## [-1, 1]

## [0, 1]

## 0

## 1

## -0

## Does not exist

## A

## 2A

## I

## 4A

## $\begin{pmatrix}2&1\\ 3&2\end{pmatrix}$

## $\begin{pmatrix}2&-1\\ -3&2\end{pmatrix}$

## $\begin{pmatrix}-2&1\\ 3&-2\end{pmatrix}$

## $\begin{pmatrix}2&-1\\ 3&2\end{pmatrix}$

## f(1)=0

## f(2)=0

## f(0)=0

## f(-1)=0

## Symmetric matrix

## Null matrix

## Diagonal matrix

## Skew symmetric matrix

## $\pm \frac{1}{2}$

## 0

## $\pm 2$

## $\pm 1$

## $\frac{9}{2}(a_1+a_9)$

## $(a_1+a_9)$

## $log_e(log_e e)$

## 1

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