List of top Mathematics Questions asked in KCET

If the area of the parallelogram with \(\vec{a}\) and \(\vec{b}\) as two adjacent sides is 15 sq.units then the area of the parallelogram having \(3\vec{a}+2\vec{b}\) and \(\vec{a}+3\vec{b}\) as two adjacent sides in sq.units is

If a and b are fixed non-zero constants, then the derivative of \(\frac{a}{x^4}-\frac{b}{x^2}\) + cos x is ma + nb - p where

The angle between the lines whose direction cosines are \((\frac{\sqrt3}{4},\frac{1}{4},\frac{\sqrt3}{2})\) and \((\frac{3}{4},\frac{1}{4},\frac{-\sqrt3}{2})\) is

If \(A=\begin{bmatrix}     1 & -2 & 1 \\     2 & 1 & 3 \\ \end{bmatrix}\ B=\begin{bmatrix}     2 & 1 \\     3 & 2 \\     1 & 1 \\ \end{bmatrix}\) then (AB)' is equal to

In a certain two 65% families own cell phones, 15000 families own scooter and 15% families own both. Taking into consideration that the families own at least one of the two, the total number of families in the town is

The equation of straight line which passes through the point (a cos³θ, a sin³θ) and perpendicular to x secθ+y cosecθ = a is

If A,B and C are three independent events such that P(A) = P(B) = P(C) = P then P(at least two of A, B, C occur) =

At x = 1, the function f(x) = \(\left\{ \begin{aligned}     & x^3-1\ \ \ \ \ \ 1<x<\infin \\     & x-1\ \ \ \ \ -\infin<x≤1 \\      \end{aligned} \right.\) is

The cost and revenue functions of a product are given by c(x) = 20x + 4000 and R(x) = 60x + 2000 respectively where x is the number of items produced and sold. The value of x to earn profit is

The number of solutions of $\frac{d y}{d x}=\frac{y+1}{x-1}$ when $y(1)=2$ is

Solution of Differential Equation $xdy - ydx = 0$ represents

If $\vec{a} \cdot \vec{b}=0$ and $\vec{a}+\vec{b}$ makes an angle $60^{\circ}$ with $\vec{a} $ then

If the area of the parallelogram with $\vec{a}$ and $\vec{b}$ as two adjacent sides is $15$ s units then the area of the parallelogram having $3 \vec{a}+2 \vec{b}$ and $\vec{a}+3 \vec{b}$ as two adjacent sides in s units is

If a plane meets the coordinate axes at $A, B$ and $C$ in such a way that the centroid of triangle $ABC$ is at the point $(1,2,3)$ then the equation of the plane is

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

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

If f(x) = \(\begin{vmatrix} x^3-x & a+x & b+x \\ x-a & x^2-x & c+x \\ x-b & x-c & 0 \\ \end{vmatrix}\) then

Rain is falling vertically with a speed of $12 \,ms^{-1}$. A woman rides a bicycles with a speed of $12 \,ms^{-1}$ in east to west direction. What is the direction in which she should hold her umbrella?

The negation of the statement "For all real numbers x and y, x + y = y + x" is

If the sum of n terms of an A.P is given by $S_n = n^2 + n$, then the common difference of the A.P is

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

If (xe)^y = e^x, then \(\frac{dy}{dx}\) is

If $|tan \,A + \cot \,A = 2$, then the value of $\tan^4 A + \cot^ 4 A = $

The right hand and left hand limit of the function are respectively