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Mathematics
List of top Mathematics Questions asked in KCET
If \( A \) and \( B \) are two non-mutually exclusive events such that \( P(A | B) = P(B | A) \), then:
KCET - 2025
KCET
Mathematics
Probability
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:
KCET - 2025
KCET
Mathematics
Probability
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?
KCET - 2025
KCET
Mathematics
Probability
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:
KCET - 2025
KCET
Mathematics
Linear Programming Problem
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?
KCET - 2025
KCET
Mathematics
Linear Programming Problem
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?
KCET - 2025
KCET
Mathematics
Relations and functions
Let \( A = \{a, b, c\} \), then the number of equivalence relations on \( A \) containing \( (b, c) \) is:
KCET - 2025
KCET
Mathematics
Set Theory
Find
\[ \sec^2 \left( \tan^{-1} 2 \right) + \csc^2 \left( \cot^{-1} 3 \right) = ? \]
KCET - 2025
KCET
Mathematics
Inverse Trigonometric Functions
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:
KCET - 2025
KCET
Mathematics
Probability
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?
KCET - 2025
KCET
Mathematics
Set Theory
The mean deviation about the mean for the data \( 4, 7, 8, 9, 10, 12, 13, 17 \) is:
KCET - 2025
KCET
Mathematics
measurement of angles
If \( \cos x + \cos^2 x = 1 \), then the value of \( \sin^2 x + \sin^4 x \) is:
KCET - 2025
KCET
Mathematics
Inverse Trigonometric Functions
If \( A = \{ x : x \text{ is an integer and } x^2 - 9 \geq 0 \} \),
\[ B = \{ x : x \text{ is a natural number and } 2 \leq x \leq 5 \}, \quad C = \{ x : x \text{ is a prime number} \leq 4 \} \]
Then \( (B - C) \cup A \) is:
KCET - 2025
KCET
Mathematics
Set Theory
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?
KCET - 2025
KCET
Mathematics
Inverse Trigonometric Functions
Domain of the function \( f(x) = \frac{1
{(x-2)(x-5)} \) is:}
KCET - 2025
KCET
Mathematics
types of functions
Which of the following is not correct?
KCET - 2025
KCET
Mathematics
Inverse Trigonometric Functions
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:
KCET - 2025
KCET
Mathematics
Area under Simple Curves
The area of the region bounded by the curve
\[ y = x^2 \quad \text{and the line} \quad y = 16 \quad \text{is:} \]
KCET - 2025
KCET
Mathematics
Area under Simple Curves
The distance of the point \( P(-3,4,5) \) from the yz-plane is:
KCET - 2025
KCET
Mathematics
Distance of a Point From a Line
The value of the integral
\[ \int_0^1 \log(1 - x) \, dx \]
is:
KCET - 2025
KCET
Mathematics
Integration
If 'a' and 'b' are the order and degree respectively of the differentiable equation
\[ \frac{d^2 y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + x^4 = 0, \quad \text{then} \, a - b = \, \_ \_ \]
KCET - 2025
KCET
Mathematics
Differential equations
The function \( f(x) = \tan x - x \)
KCET - 2025
KCET
Mathematics
Derivatives
The integral
\[ \int \frac{dx}{x^2 \left( x^4 + 1 \right)^{3/4}} \]
equals:
KCET - 2025
KCET
Mathematics
Integration
The value of
\( \int_{-1}^1 \sin^5 x \cos^4 x \, dx \)
is:
KCET - 2025
KCET
Mathematics
Integration
The value of
\( \int \frac{dx}{(x+1)(x+2)} \)
is:
KCET - 2025
KCET
Mathematics
Integration
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