List of top Questions asked in KCET

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
If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\) then
The degree of the differential equation
\(1+(\frac{dy}{dx})^2+(\frac{d^2y}{dx^2})^2= \sqrt[3]{\frac{d^2y}{dx^2}+1}\) is
If a curve passes through the point (1, 1) at any point (x, y) on the curve, the product of the slope of its tangent and x co-ordinate of the point is equal to the y co-ordinate of the point, then the curve also passes through the point
The area of the region bounded by the line y = x +1, and the lines x = 3 and x = 5 is
\(\int\sqrt{5-2x+x^2}\ dx=\)
\(\int\limits^{\pi}_{0}\frac{x\tan x}{\sec x.\cosec x}\ dx=\)
\(\int\limits_{-2}^{0}(x^3+3x^2+3x+3+(x+1)\cos(x+1))\ dx=\)
\(\int\frac{1}{1+3\sin^2 x+8 \cos^2 x}\ dx=\)
If f(x) and g(x) are two functions with g(x) = \(x-\frac{1}{x}\) and fog(x) = \(x^3-\frac{1}{x^3}\) then f'(x) =
\(\int\limits_{2}^{8}\frac{5^{\sqrt{10-x}}}{5^{\sqrt{x}}+5^{\sqrt{10-x}}}\ dx=\)
A circular plate of radius 5 cm is heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. The rate at which its area is increasing when the radius is 5.2 cm is
If A = \(\begin{bmatrix}     1 & \tan\ \alpha/2 \\     -\tan\ \alpha/2 & 1 \end{bmatrix}\) and AB=I then B =
If f(x) = 1 + nx + \(\frac{n(n-1)}{2}x^2+\frac{n(n-1)(n-2)}{6}x^3+...+x^n\) then f"(1) =