List of top Mathematics Questions asked in KCET

The distance ‘s’ in meters travelled by a particle in ‘t’ seconds is given by s = \(\frac{2t^3}{3}-18t+\frac{5}{3}.\) The acceleration when the particle comes to rest is
If y = a sin x + b cos x, then y2 + \((\frac{dy}{dx})^2\) is a
The value of \(\begin{vmatrix}     \sin^2 14 \degree & \sin^2 66\degree & \tan 135\degree \\     \sin^2 66\degree & \tan 135\degree &     \sin^2 14 \degree \\     \tan 135\degree & \sin^2 14 \degree & \sin^2 66\degree \end{vmatrix}\)
An enemy fighter jet is flying along the curve given by y = x2 + 2. A soldier is placed at (3, 2) wants to shoot down the jet when it is nearest to him. Then the nearest distance is
nth term of the series
\(1+\frac{3}{7}+\frac{5}{7^2}+\frac{1}{7^2}+...\) is
If A and B are events such that P(A)=\(\frac{1}{4}\), P(A/B)=\(\frac{1}{2}\) and P(B/A)=\(\frac{2}{3}\) then P(B) is
\(\int\sqrt{\cosec x-\sin x}\ dx=\)
The equation of the plane through the points (2, 1, 0), (3, 2, -2) and (3, 1, 7) is
Let A = {x, y, z, u} and B = {a, b}. A function f : A → B is selected randomly. The probability that the function is an onto function is
If \(\sin^{-1}(\frac{2a}{1+a^2})+\cos^{-1}(\frac{1-a^2}{1+a^2})=\tan^{-1}(\frac{2x}{1-x^2})\) where a, x ∈ (0, 1) then the value of x is
Which of the following is an empty set ?
Ten chairs are numbered as 1 to 10. Three women and two men wish to occupy one chair each. First the women choose the chairs marked 1 to 6, then the men choose the chairs from the remaining. The number of possible ways is
Given that a,b and x are real numbers and a< b, x < 0 then
The value of \(e^{\log_{10}\tan 1°+\log_{10}\tan 2°+\log_{10}\tan 3°+...+\log_{10}\tan89°}\) is
If f(x) = ax + b, where a and b are integers, f(-1) = -5 and f(3) = 3 then a and b are respectively
The shaded region in the figure given is the solution of which of the inequations?
Shaded region of the figure
A bag contains 2n + 1 coins. It is known that n of these coins have head on both sides whereas the other n + 1 coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is \(\frac{31}{42}\), then the value of n is
\(|\vec{a}\times\vec{b}|^2+|\vec{a}.\vec{b}|^2=144\) and \(|\vec{a}|=4\) then \(|\vec{b}|\) is equal to
If (2, 3, -1) is the foot of the perpendicular from (4, 2, 1) to a plane, then the equation of the plane is
The point of intersection of the line x + 1 = \(\frac{y+3}{3}=\frac{-z+2}{2}\) with the plane 3x + 4y + 5z = 10 is
The length of perpendicular drawn from the point (3, -1, 11) to the line \(\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) is
If a lines makes an angle of \(\frac{\pi}{3}\) with each X and Y axis then the acute angle made by Z-axis is
If \(\vec{a}+2\vec{b}+3\vec{c}=\vec{0}\) and
\((\vec{a}\times\vec{b})+(\vec{b}\times\vec{c})+(\vec{c}\times\vec{a})=\lambda(\vec{b}\times\vec{c})\)
then the value of λ is equal to
In the interval (0, π/2), area lying between the curves y = tan x and y = cot x and the X-axis is
The component of \(\hat{i}\) in the direction of the vector \(\hat{i}+\hat{j}+2\hat{k}\) is