List of top Questions asked in KCET

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) =

If the function of f(x) = \(\frac{1}{x+2}\), then the point of discontinuity of the composite function y = f(f(x)) is

The function f(x) = cot x is discontiuous on every point of the set

If \(u=\sin^{-1}(\frac{2x}{1+x^2})\) and \(v=\tan^{-1}(\frac{2x}{1-x^2})\) then \(\frac{du}{dv}\) is

If \(\Delta=\begin{vmatrix}     1 & a & a^2 \\     1 & b & b^2 \\     1 & c & c^2 \end{vmatrix}\) and \(\Delta_1=\begin{vmatrix}     1 & 1 & 1 \\     bc & ca & ab \\     a & b & c \end{vmatrix}\) then

The area of a triangle with vertices(-3,0),(3, 0) and (0, k) is 9 sq.units, the value of k is

If A =\(\begin{bmatrix}   2-k & 2 \\     1 & 3-k \end{bmatrix}\) is a singular matrix, then the value of 5k - k² is equal to

The value of
\(\cot^{-1}[\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}]\) where x ∈ \((0,\frac{\pi}{4})\) is

The contrapositive of the statement
“If two lines do not intersect in the same plane then they are parallel.” is

Let the relation R be defined in N by aRb if 3a + 2b = 27 then R is

Let f : R→R be defined by f(x)= 3x²-5 and g : R→R by g(x)=\(\frac{x}{x^2+1}\) then gof is

f : R → R and g : [0, ∞) → R are defined by f(x) = x² and g(x)=\(\sqrt{x}\). Which one of the following is not true ?

The mean of 100 observations is 50 and their standard deviation is 5. Then the sum of squares of all observations is

If n is even and the middle term in the expansion of \((x^2+\frac{1}{x})^n\) is 924 x⁶, then n is equal to

If \(\lim\limits_{x \rightarrow 0} \frac{\sin(2+x)-\sin(2-x)}{x}\)= A cos B, then the values of A and B respectively are

The distance between the foci of a hyperbola is 16 and its eccentricity is \(\sqrt2\). Its equation is

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is

Identify A, B and C in the sequence :

The refracting angle of prism is A and refractive index of material of prism is $\cot \frac{A}{2}$ The angle of minimum deviation is

Identify A and B in the reaction

Element X, Y and Z have atomic number 19, 37 and 55 respectively. Which of the following statements is true about them

The property of halogens which is not correctly matched is

Which noble gas has least tendency to form compounds ?