List of top Questions asked in KCET

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

If A and B are two matrices such that AB=B and BA=A then A² + B² =

If \(x\begin{bmatrix}     3 \\  2 \end{bmatrix}+y\begin{bmatrix}     1 \\     -1 \end{bmatrix}=\begin{bmatrix}     15 \\     5\end{bmatrix}\) then the value of x and y are

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 f(x) = sin 2x + cos 2x and g(x)=x²-1, then g(f(x)) is invertible in the domain

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 :

If A = {1,2,3........,10} then number of subsets of A containing only odd number is

A proton moves with a velocity of 5 x 10⁶ j m/s, through the uniform electric field E = 4 x 10⁶ (2i + 0.2j + 0.1k) Vm^-1and the uniform magnetic field B = 0.2( i + 0.2 j + k) T. The approximate net force acting on the proton is

The trigonometric function y = tan x in the II quadrant

A solenoid of length 50 cm having 100 turns carries a current of 2.5 A. The magnetic field at one end of solenoid is