List of top Questions asked in KCET

If \( A = \begin{bmatrix} k & 2 \\ 2 & k \end{bmatrix} \) and \( |A^3| = 125 \), then the value of \( k \) is:
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 non-mutually exclusive events such that \( P(A | B) = P(B | A) \), then:
If \( A \) and \( B \) are two events such that \( A \subseteq B \) and \( P(B) \neq 0 \), then which of the following is correct?
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?
A die has two faces each with number '1', three faces each with number '2' and one face with number '3'. If the die is rolled once, then \(P(1 \text{ or } 3)\) is:
Let \( A = \{a, b, c\} \), then the number of equivalence relations on \( A \) containing \( (b, c) \) is:
Let the functions \( f \) and \( g \) be \[ f : [0, \frac{\pi}{2}] \to \mathbb{R} \text{ given by } f(x) = \sin x \text{ and } g(x) = \cos x, \text{ where } R \text{ is the set of real numbers}. \] Consider the following statements: Statement (I): \( f \) and \( g \) are one-to-one. Statement (II): \( f + g \) is one-to-one. Which of the following is correct?
Find \[ \sec^2 \left( \tan^{-1} 2 \right) + \csc^2 \left( \cot^{-1} 3 \right) = ? \]
A and B are two sets having 3 and 6 elements respectively. Consider the following statements: - Statement (I): Minimum number of elements in \( A \cup B \) is 3 - Statement (II): Maximum number of elements in \( A \cap B \) is 3 Which of the following is correct?
Domain of the function \( f(x) = \frac{1{(x-2)(x-5)} \) is:}
If \( f(x) = \sin[\lfloor x^2 \rfloor] - \sin[\lfloor -x^2 \rfloor] \), where \( \lfloor x \rfloor \) denotes the greatest integer less than or equal to \( x \), then which of the following is not true?
Which of the following is not correct?
If \( \cos x + \cos^2 x = 1 \), then the value of \( \sin^2 x + \sin^4 x \) is:
The value of the integral \[ \int_0^1 \log(1 - x) \, dx \] is:
The area bounded by the curve \[ y = \sin\left(\frac{x}{3}\right), \quad x \text{ axis}, \quad \text{the lines } x = 0 \text{ and } x = 3\pi \] is:
The area of the region bounded by the curve \[ y = x^2 \quad \text{and the line} \quad y = 16 \quad \text{is:} \]
The function \( f(x) = \tan x - x \)
The value of \( \int \frac{dx}{(x+1)(x+2)} \) is:
The value of \( \int_{-1}^1 \sin^5 x \cos^4 x \, dx \) is:
The value of \( \int_0^{\frac{2\pi}{0}} \left( 1 + \sin \left( \frac{x}{2} \right) \right) \, dx \) is:
The integral \[ \int \frac{dx}{x^2 \left( x^4 + 1 \right)^{3/4}} \] equals:
If \( y = a \sin^3 t \), \( x = a \cos^3 t \), then \( \frac{dy}{dx} \) at \( t = \frac{3\pi}{4} \) is:
Consider the following statements:
% Statement Statement (I): If either \( |\vec{a}| = 0 \) or \( |\vec{b}| = 0 \), then \( \vec{a} \cdot \vec{b} = 0 \).
% Statement Statement (II): If \( \vec{a} \times \vec{b} = 0 \), then \( \vec{a} \) is perpendicular to \( \vec{b} \).
Which of the following is correct?
If a line makes angles \( 90^\circ, 60^\circ \) and \( \theta \) with \( x, y \) and \( z \) axes respectively, where \( \theta \) is acute, then the value of \( \theta \) is: