List of top Mathematics Questions asked in KCET

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

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

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

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

Solution of Differential Equating xdy – ydx = 0 represents

The equation of the line joining the points (-3, 4, 11) and (1, -2, 7) is

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

The area of the region bounded by \(y=\sqrt{16-x^2}\) and x-axis is

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

The shaded region is the solution set of the inequalities

The value of \(\int\limits_0^{4042}\frac{\sqrt{x}\ dx}{\sqrt{x}+\sqrt{4042-x}}\) is equal to

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

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

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) =

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 the area of the Ellipse is \(\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1\) is 20π square units, then λ 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 \(\vec{a}.\vec{b}=0\) and \(\vec{a}+\vec{b}\) makes an angle 60° with \(\vec{a}\) then

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 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