List of top Mathematics Questions asked in KCET

If the eccentricity of the hyperbola $\frac {x^2}{a^2}-\frac {y^2}{b^2}=1$ is $\frac {5}{4}$ and $2x + 3y -6 = 0$ is a focal chord of the hyperbola, then the length of transverse axis is equal to

The inverse of the matrix $A =\begin{bmatrix} {2}&{0} &{0}\\ {0}&{3}& {0} \\ {0}&{0}&{4}\\ \end{bmatrix}$ is

If $A$ is a matrix of order $3$, such that $A (adj A) = 10\, I$, then $|adj A| $ =

Which of the following is not a correct statement ?

If $21^{st}$ and $22^{nd}$ terms in the expansion of $(1 + x)^{44}$ are equal, then $x$ is equal to

The domain of the function $f(x) = \sqrt {\cos x}$ is

In a class of $60$ students, $25$ students play cricket and $20$ students play tennis, and $10$ students play both the games. Then, the number of students who play neither is

Equation of the plane perpendicular to the line $\frac {x}{1} = \frac {y}{2} = \frac {z}{3}$ and Passing through the point $(2, 3, 4)$ is

A gardener is digging a plot of land. As he gets tired, he works more slowly. After $' t '$ minutes he is digging at a rate of $\frac {2} {\sqrt {t}} $square metres per minute. How long will it take him to dig an area of $40$ square metres ?

If $x+y\leq2,x \geq 0,y \geq 0$ the point at which maximum value of $3x + 2y$ attained will be

If the function $f(x)$ defined by $\frac {x^{100}}{100}+\frac {x^{99}}{100}+\dots \frac {x^2}{100}+x+1$ then $f'(0)$ is equal to

The general solution of the differential equation $\frac {dy}{dx}+\frac {y}{x}=3x$ is

Given $0 \leq x \leq \frac {1}{2}$ then the value of $\tan \left[\sin^{-1}\left\{\frac{x}{\sqrt {2}}+\frac {\sqrt {1-x^2}} {\sqrt {2}}\right\}-\sin^{-1}x\right]$ is

The area of the parallelogram whose adjacent sides are $\hat{i}+ \hat {k} $ and $2\hat {i}+\hat {j}+\hat {k}$ is

How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$, if each number starts with $67$ and no digit appears more than once ?

If $a, b$ and $c$ are in A.P., then the value of $\begin{vmatrix} {x+2}&{x+3} &{x+a}\\ {x+4}&{x+5}& {x+b} \\ {x+6}&{x+7} &{x+c}\\ \end{vmatrix}$ is

Area of the region bounded by two parabolas $y\, =\, x^2$ and $x \,= \, y^2 $ is

The order and degree of the differential equation $y=x\frac{dy}{dx}+\frac{2}{\frac{dy}{dx}}$ is

The value of $\sin (2\, \sin^{-1}\, 0.8)$ is equal to

The value of the integral $\int_\limits{-\pi/4}^{\pi/4} \log (\sec \theta-\tan \theta) d \theta$ is

A stone is dropped into a quiet lake and waves move in circles at the speed of $5\, cm/sec$. At that instant, when the radius of circular wave is $8 \,cm$, how fast is the enclosed area increasing ?

If $A$ is $3 \times 4$ matrix and $B$ is a matrix such that $A'B$ and $BA'$ are both defined. Then $B$ is of the type

The angle between two diagonals of a cube is

In a triangle $ABC, a[b \,cos \,C - c\, cos\, B]$ =

The symmetric part of the matrix $A =\begin{bmatrix} {1}&{2} &{4}\\ {6}&{8}& {2} \\ {2}&{-2}&{7}\\ \end{bmatrix} $ is