List of top Mathematics Questions asked in KCET

Given that A and B are two events such that P(B) = \(\frac{3}{5}\) P(A/B) = \(\frac{1}{2}\) and P(A ∪ B) = \(\frac{4}{5}\) then P(A) =
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is
If the middle term of the A.P is 300 then the sum of its first 51 terms is
Solution of Differential Equating xdy – ydx = 0 represents
The shaded region is the solution set of the inequalities
Shaded Region
The equation of the line joining the points (-3, 4, 11) and (1, -2, 7) is
The value of \(\int\frac{x^2dx}{\sqrt{x^6+a^6}}\) is equal to
A car manufacturing factory has two plants X and Y. Plant X manufactures 70% of cars and plant Y manufactures 30% of cars. 80% of cars at plant X and 90% of cars at plant Y are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant X is
Let A = { x : x ∈ R; x is not a positive integer } Define f : A → R as f(x) = \(\frac{2x}{x-1}\), then f is
Consider the following statements :
Statement 1 : \(\lim\limits_{x\rightarrow1}\frac{ax^2+bx+c}{cx^2+bx+a}\) is 1 (where a + b + c ≠ 0)
Statement 2 : \(\lim\limits_{x\rightarrow-2}\frac{\frac{1}{x}+\frac{1}{2}}{x+2}\) is \(\frac{1}{4}\)
If the parametric equation of curve is given by x = cosθ + log tan \(\frac{θ}{2}\) and y = sinθ, then the points for which \(\frac{dy}{dx}=0\) are given by
The number of solutions of \(\frac{dy}{dx}=\frac{y+1}{x-1}\) when y(1) = 2 is
If A and B are matrices of order 3 and |A| = 5, |B| = 3 then |3AB| is
f : R → R defined by f(x) = \(\left\{ \begin{aligned}     & 2x;x>3 \\     &x^2;1<x≤3\\     & 3x;x≤1 \end{aligned} \right.\) then f(-2) + f(3) + f(4) is
The area of the region bounded by \(y=\sqrt{16-x^2}\) and x-axis is
The mid points of the sides of triangle are (1, 5, -1) (0, 4, -2) and (2, 3, 4) then centroid of the triangle
\(\tan^{-1}[\frac{1}{\sqrt3}\sin\frac{5\pi}{2}]\sin^{-1}[\cos(\sin^{-1}\frac{\sqrt3}{2})]=\)
\(\int\frac{x^3\sin(\tan^{-1}(x^4))}{1+x^8}dx\) is equal to
Domain of f(x) = \(\frac{x}{|-|x|}\) is
A particle starts form rest and its angular displacement (in radians) is given by \(\theta=\frac{t^2}{20}+\frac{t}{5}\). If the angular velocity at the end of t = 4 is k, then the value of 5k is
The function f(x) = \(\sqrt3\) sin2x - cos2x + 4 is one-one in the interval
If f(x) = \(\begin{vmatrix}     cosx & 1 & 0 \\     0 & 2cosx & 3 \\     0 & 1 & 2cosx \\ \end{vmatrix}\) then \(\lim\limits_{x\rightarrow\pi} f(x)=\)
The diagonals of a parallelogram are the vectors \(3\hat{i}+6\hat{j}-2\hat{k}\) and \(-\hat{i}-2\hat{j}-8\hat{k}\) then the length of the shorter side of parallelogram is
The value of \(\int\frac{xe^x dx}{(1+x)^2}\) is equal to
If \((\frac{1+i}{1-i})^x=1\) then