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CUET Mathematics 2024 Mathematics Mock Tests & Questions

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CUET Mathematics 2024

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61 min · 50 questions · 250 marks

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CUET Mathematics 2024 1 section

Mathematics

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61 min · 50 questions · 250 marks

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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If A and B are symmetric matrices of the same order, then AB-BA is a :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \(A\) is a square matrix of order 4 and \(|A| = 4\), then \(|2A|\) will be :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \([A]_{3\times 2}[B]_{x\times y} = [C]_{3\times 1}\), then :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If a function \(f(x) = x^2 + bx + 1\) is increasing in the interval \([1,2]\), then the least value of b is :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
Two dice are thrown simultaneously. If \(X\) denotes the number of fours, then the expectation of X will be:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
For the function \(f(x) = 2x^3 - 9x^2 + 12x - 5, x \in [0,3]\), match List-I with List-II: List-I | List-II (A) Absolute maximum value | (I) -1 (B) Absolute minimum value | (II) 0 (C) Point of maxima | (III) -5 (D) Point…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
An objective function \(Z = ax + by\) is maximum at points (8,2) and (4,6). If \(x \ge 0\) and \(y \ge 0\) and \(ab = 25\), then the maximum value of the function is equal to:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The area of the region bounded by the lines \(x + 2y = 12\), \(x = 2\), \(x = 6\) and \(x\)-axis is:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
A die is rolled thrice. What is the probability of getting more than 4 in the first and the second throw of dice and a number less than 4 in the third throw?
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The corner points of the feasible region determined by - \(x + y \le 8, 2x + y \ge 8, x \ge 0, y \ge 0\) are A(0,8), B(4,0). If the objective function \(Z = ax + by\) has its maximum value on the line segment AB, then th…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \(t = e^{2x}\) and \(y = \log_e t^2\), then \(\frac{d^2y}{dx^2}\) is :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
\(\int \frac{\pi}{x^{n+1} - x}\,dx =\)
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The value of \(\int_0^1 \frac{a - bx^2}{(a + bx^2)^2}\,dx\) is:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The second order derivative of which of the following functions is \(5^x\) ?
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The degree of the differential equation \(\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = \left(k\frac{d^2y}{dx^2}\right)\) is :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
Let R be the relation over the set A of all straight lines in a plane such that \(l_1 R l_2 \Leftrightarrow l_1\) is parallel to \(l_2\). Then R is:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The probability of not getting 53 Tuesdays in a leap year is:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The angle between two lines whose direction ratios are proportional to \(1, 1, -2\) and \((\sqrt{3} - 1), (-\sqrt{3} - 1), -4\) is:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \((\vec{a} - \vec{b}) \cdot (\vec{a} + \vec{b}) = 27\) and \(|\vec{a}| = 2|\vec{b}|\), then \(|\vec{b}|\) is:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \(\tan^{-1}\left(\frac{2}{3^{-x}+1}\right) = \cot^{-1}\left(\frac{3}{3^{x}+1}\right)\), then which one of the following is true?
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \(A, B\) and \(C\) are three singular matrices given by \(A = \begin{bmatrix} 1 & 4 \\ 3 & 2a \end{bmatrix}\), \(B = \begin{bmatrix} 3b & 5 \\ 4 & 2 \end{bmatrix}\) and…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The value of the integral \(\int_{\log_e 2}^{\log_e 3} \frac{e^{2x} - 1}{e^{2x} + 1}\,dx\) is :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three vectors such that \(\vec{a} + \vec{b} + \vec{c} = \vec{0}\), where \(\vec{a}\) and \(\vec{b}\) are unit vectors and \(|\vec{c}| = 2\), then the angle between the vectors…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
Let \([x]\) denote the greatest integer function. Then match List-I with List-II : List-I | List-II (A) |x-1|+|x-2| | (I) is differentiable everywhere except at x = 0 (B) x-|x| | (II) is continuous everywhere (C) x-[x] |…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The rate of change (in cm\(^2\)/s) of the total surface area of a hemisphere with respect to radius r at \(r = \sqrt[3]{1.331}\) cm is :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The area of the region bounded by the lines \(\frac{x}{7\sqrt{3}a} + \frac{y}{b} = 4\), \(x = 0\) and \(y = 0\) is :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \(A\) is a square matrix and \(I\) is an identity matrix such that \(A^2 = A\), then \(A(I - 2A)^3 + 2A^3\) is equal to:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
Match List-I with List-II List-I | List-II (A) Integrating factor of \(x\,dy - (y + 2x^2)dx = 0\) | (I) \(\frac{1}{x}\) (B) Integrating factor of \((2x^2 - 3y)dx = x\,dy\) | (II) \(x\) (C) Integrating factor of…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If the function \(f: \mathbb{N} \to \mathbb{N}\) is defined as \(f(n) = n - 1\) if \(n\) is even, and \(f(n) = n + 1\) if \(n\) is odd, then (A) f is injective (B) \(f\) is into (C) \(f\) is surjective (D) f is invertibl…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
\(\int_0^{\pi/2} \frac{1 - \cot x}{\operatorname{cosec} x + \cos x}\,dx =\)
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If the random variable X has the following distribution : X | 0 | 1 | 2 | otherwise P(X) | k | 2k | 3k | 0 Match List-I with List-II : List-I | List-II (A) k | (I) \(\frac{5}{6}\) (B) P(X < 2) | (II) \(\frac{4}{3}\) (C)…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
For a square matrix \(A_{n\times n}\) (A) \(|\operatorname{adj} A| = |A|^{n-1}\) (B) \(|A| = |\operatorname{adj} A|^{n-1}\) (C) \(A(\operatorname{adj} A) = |A|\) (D) \(|A^{-1}| = \frac{1}{|A|}\) Choose the correct answer…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The matrix \(\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\) is a : (A) scalar matrix (B) diagonal matrix (C) skew-symmetric matrix (D) symmetric matrix
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The feasible region represented by the constraints \(4x + y \ge 80, x + 5y \ge 115, 3x + 2y \le 150, x, y \ge 0\) of an LPP is [Figure: graph with x and y axes showing the three lines. Marked points: (0,80), (0,75), (2,7…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The area of the region enclosed between the curves \(4x^2 = y\) and \(y = 4\) is:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
\(\int e^x \left(\frac{2x+1}{2\sqrt{x}}\right) dx =\)
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \(f(x)\), defined by \(f(x) = kx + 1\) if \(x \le \pi\) and \(f(x) = \cos x\) if \(x > \pi\), is continuous at \(x = \pi\), then the value of \(k\) is :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \(P = \begin{bmatrix} -1 \\ 2 \\ 1 \end{bmatrix}\) and \(Q = \begin{bmatrix} 2 & -4 & 1 \end{bmatrix}\) are two matrices, then \((PQ)'\) will be :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
\(\Delta = \begin{vmatrix} 1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1 \end{vmatrix}\) (A) \(\Delta = 2(2 - \cos^2 x)\) (B) \(\Delta = 2(2 - \sin^2 x)\) (C) Minimum value of \(\Delta\) is 2 (D) Maximum val…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
\(f(x) = \sin x + \frac{1}{2}\cos 2x\) in \([0, \frac{\pi}{2}]\) (A) \(f'(x) = \cos x - \sin 2x\) (B) The critical points of the function are \(x = \frac{\pi}{6}\) and \(x = \frac{\pi}{2}\) (C) The minimum value of the f…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The direction cosines of the line which is perpendicular to the lines with direction ratios \(1, -2, -2\) and \(0, 2, 1\) are:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
Let \(X\) denote the number of hours you play during a randomly selected day. The probability that \(X\) can take values \(x\) has the following form, where \(c\) is some constant. \(P(X = x) = 0.1\) if \(x = 0\); \(cx\)…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
\(\sin y = x\sin(a + y)\), then \(\frac{dy}{dx}\) is :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The unit vector perpendicular to each of the vectors \(\vec{a} + \vec{b}\) and \(\vec{a} - \vec{b}\), where \(\vec{a} = \hat{i} + \hat{j} + \hat{k}\) and \(\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}\), is:
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
The distance between the lines \(\vec{r} = \hat{i} - 2\hat{j} + 3\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k})\) and \(\vec{r} = 3\hat{i} - 2\hat{j} + 1\hat{k} + \mu(4\hat{i} + 6\hat{j} + 12\hat{k})\) is :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
If \(f(x) = 2\left(\tan^{-1}(e^x) - \frac{\pi}{4}\right)\), then \(f(x)\) is :
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
For the differential equation \((x\log_e x)dy = (\log_e x - y)dx\) (A) Degree of the given differential equation is 1. (B) It is a homogeneous differential equation. (C) Solution is \(2y\log_e x + A = (\log_e x)^2\), whe…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
There are two bags. Bag-1 contains 4 white and 6 black balls and Bag-2 contains 5 white and 5 black balls. A die is rolled, if it shows a number divisible by 3, a ball is drawn from Bag-1, else a ball is drawn from Bag-2…
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
Which of the following cannot be the direction ratios of the straight line \(\frac{x-3}{2} = \frac{2-y}{3} = \frac{z+4}{-1}\) ?
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CUET UG CUET Mathematics 2024 Mathematics Medium MCQ (Single Correct)
Which one of the following represents the correct feasible region determined by the following constrains of an LPP? \(x + y \ge 10, 2x + 2y \le 25, x \ge 0, y \ge 0\)
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