List of top Mathematics Questions asked in KCET

If the middle term of the $A.P$ is $300$ then the sum of its first $51$ terms is

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

If the area of the Ellipse is $\frac{x^{2}}{25}+\frac{y^{2}}{\lambda^{2}}=1$ is $20 \pi$ square units, then $\lambda$ is

For constant a, \(\frac{d}{dx}\)(x^x + x^a+ a^x + a^a) is

A vector $\vec{a}$ makes equal acute angles on the coordinate axis. Then the projection of vector $\vec{ b }=5 \hat{ i }+7 \hat{ j }-\hat{ k }$ on $\vec{ a }$ is

A and B are non-singleton sets and n(A × B) = 35. If B ⊂ A then ^n(A)C_n(B) =

If y = (cosx²)², then \(\frac{dy}{dx}\) is equal to

The mid points of the sides of triangle are (1, 5, -1) (0, 4, -2) and (2, 3, 4) then centroid of the triangle

A student has to answer 10 questions, choosing at least 4 from each of the parts A and B. If there are 6 questions in part A and 7 in part B, then the number of ways can the student choose 10 questions is

If the middle term of the A.P is 300 then the sum of its first 51 terms is

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) =

The function f(x) = x² - 2x is strictly decreasing in the interval

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

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

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 maximum slope of the curve y = -x³ + 3x² + 2x -27 is

If A and B are matrices of order 3 and |A| = 5, |B| = 3 then |3AB| is

The area of the region bounded by \(y=\sqrt{16-x^2}\) and x-axis 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 \((\frac{1+i}{1-i})^x=1\) then

The value of \(\int\frac{xe^x dx}{(1+x)^2}\) is equal to

The shaded region is the solution set of the inequalities

The area of the quadrilateral ABCD, when A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to