List of top Mathematics Questions asked in KCET

If \[ y = \frac{\cos x}{1 + \sin x} \] then:
If \(A\) is a square matrix such that \(A^2 = A\), then \((I - A)^3\) is:
General solution of the differential equation \[ \frac{dy}{dx} + y \tan x = \sec x \quad \text{is:} \]
If \( A \) is a square matrix of order \( 3 \times 3 \), \( \det A = 3 \), then the value of \( \det(3A^{-1}) \) is:
The number of four digit even numbers that can be formed using the digits 0, 1, 2 and 3 without repetition is:
Consider the following statements:
Statement-I: The set of all solutions of the linear inequalities 3x + 8 < 17 and 2x + 8 ≥ 12 are x < 3 and x ≥ 2 respectively.
Statement-II: The common set of solutions of the linear inequalities 3x + 8 < 17 and 2x + 8 ≥ 12 is (2,3).
Which of the following is true?
Which of the following statements is not correct?

The equation \[ 2 \cos^{-1} x = \sin^{-1} \left( 2 \sqrt{1 - x^2} \right) \] is valid for all values of \(x\) satisfying:

If the number of terms in the binomial expansion of \((2x + 3)^n\) is 22, then the value of \(n\) is:
If A and B are two matrices such that AB is an identity matrix and the order of matrix B is \(3 \times 4\), then the order of matrix A is:
If the 4th, 10th, and 16th terms of a G.P. are \(x\), \(y\), and \(z\) respectively, then
The number of diagonals that can be drawn in an octagon is:
If \( B = \begin{bmatrix} 1 & 3 \\ 2 & \alpha \end{bmatrix} \) is the adjoint of a matrix \( A \) and \( |A| = 2 \), then the value of \( \alpha \) is:

Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 

 Choose the correct answer from the options given below:

The function f(x) is given by:

For x < 0:
f(x) = ex + ax

For x ≥ 0:
f(x) = b(x - 1)2


The function is differentiable at x = 0. Then,
A function \( f(x) \) is given by:
\[ f(x) = \begin{cases} \frac{1}{e^x - 1}, & \text{if } x \neq 0 \\ \frac{1}{e^x + 1}, & \text{if } x = 0 \end{cases} \] Then, which of the following is true?
If \( Z_1 \) and \( Z_2 \) are two non-zero complex numbers, then which of the following is not true?
If a matrix \( A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} \) satisfies \( A^6 = kA' \), then the value of \( k \) is:
If \( A = \begin{bmatrix} k & 2 \\ 2 & k \end{bmatrix} \) and \( |A^3| = 125 \), then the value of \( k \) is:
If \( A \) and \( B \) are two non-mutually exclusive events such that \( P(A | B) = P(B | A) \), then:
Consider the following statements. Statement (I): If \( E \) and \( F \) are two independent events, then \( E' \) and \( F' \) are also independent. Statement (II): Two mutually exclusive events with non-zero probabilities of occurrence cannot be independent. Which of the following is correct?
If \( A \) and \( B \) are two events such that \( A \subseteq B \) and \( P(B) \neq 0 \), then which of the following is correct?
The maximum value of \( z = 3x + 4y \), subject to the constraints \( x + y \leq 40, x + 2y \geq 60 \) and \( x, y \geq 0 \) is:
Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is \( \frac{2}{5} \). If she visits temple A, the probability that she meets her friend is \( \frac{1}{3} \). The probability that she meets her friend, whereas it is \( \frac{2}{7} \) if she visits temple B. Meera met her friend at one of the two temples. The probability that she met her friend at temple B is:
Consider the following statements: Statement (I): In a LPP, the objective function is always linear. Statement (II): In a LPP, the linear inequalities on variables are called constraints. Which of the following is correct?