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CUET Mathematics 2025 Mathematics Mock Tests & Questions

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CUET Mathematics 2025

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59 min · 49 questions · 245 marks

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CUET Mathematics 2025 1 section

Mathematics

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59 min · 49 questions · 245 marks

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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(A\) and \(B\) are symmetric matrices of the same order, then which of the following are true? (A) \(AB-BA\) is a skew symmetric matrix (B) \(AB\) is a symmetric matrix (C) \(AB\) is a scalar matrix (D) \(AB+BA\) is…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Let \(A=[a_{ij}]\) be given by \(A=\begin{bmatrix}1&-1&2\\3&4&-5\\2&-1&3\end{bmatrix}\). Then the matrix \(B=[b_{ij}]\), where \(b_{ij}=\) Minor of \(a_{ij}\), is:
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(f(x)=\begin{vmatrix}0&x-1&x-2\\x+1&0&x-3\\x+2&x+3&0\end{vmatrix}\), then the value of \(f(0)\) is equal to:
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The interval on which the function \(f(x)=x^3+2x^2-1\) is decreasing, is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
For the function \(f(x)=e^{-2x}(2-x)^2\), the point of local maxima is:
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The particular solution of the differential equation \(\frac{dy}{dx}+\frac{3y}{x}=0,\ y(1)=1\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Two cards are drawn simultaneously at random from a well shuffled pack of 52 Cards. Let \(X\) be the random variable which denotes number of kings in the draw. Then the probability distribution of \(X\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(y=(x+1)(x^2+1)(x^4+1)(x^8+1)\) then \(\frac{dy}{dx}\) at \(x=-1\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The value of \(\int \frac{x^5}{\sqrt{1+x^3}}\,dx\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The corner points of the bounded feasible region determined by the system of linear constraints are \((15,0),(40,0),(4,18)\) and \((6,12)\). If objective function is \(Z=30x+20y\), then the sum of the maximum and the min…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The value of \(\int_{-1}^{1}|x^3-x|\,dx\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(A\) and \(B\) are invertible matrices of the same order, then \((AB)^{-1}\) is equal to
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The area of the region bounded by the parabola \(y^2=x\) and the straight line \(2y=x\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The feasible region represented by the constraints: \(x+2y\ge100,\ 2x-y\le0,\ 2x+y\le200,\ x\ge0,\ y\ge0\) of an LPP is: [Figure: graph with x and y axes (ticks at 50, 100, 150, 200) showing the lines x + 2y = 100, 2x -…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Which one of the following equations is a homogeneous differential equation?
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If A and B are independent events, then which of the following is/are true? (A) \(\overline{A}\) and B are independent events (B) \(P(A\cap B)=0\) (C) \(\overline{A}\) and \(\overline{B}\) are independent events (D)…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Let box I contains 3 black and 4 white balls, box II contains 2 black and 2 white balls, box III contains 4 black and 3 white balls. A box is selected at random and then a ball is randomly drawn from the selected box. If…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Cosine of the acute angle between the lines \(\frac{x-3}{2}=\frac{y-2}{1}=\frac{z-5}{2}\) and \(\frac{x-1}{6}=\frac{y-3}{-3}=\frac{z+6}{2}\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
\(\int \frac{dx}{e^x+e^{-x}}\) is equal to
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(P(A)=\frac{3}{5}\), \(P(B)=\frac{1}{2}\) and \(P(A\cap B)=\frac{1}{4}\), then \(P(\overline{A}\,|\,\overline{B})\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The area (in sq.units) of the region enclosed by the curve \(y=\cos x,\ \frac{-\pi}{2}\le x\le\frac{\pi}{2}\) and the \(x\)-axis is:
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Match List-I with List-II List-I | List-II (A) If vector \(\vec a\) and \(\vec b\) are such that \(\vec a=\lambda\vec b\) and \(|\vec a|=|\vec b|\), then | (I) \(\vec a\) and \(\vec b\) are orthogonal (B) Projection vect…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Match List-I with List-II List-I | List-II (A) The degree of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^2+\left(\frac{dy}{dx}\right)^2=x\sin\left(\frac{dy}{dx}\right)\) | (I) 4 (B) The degree of the diffe…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(\vec a\) is a unit vector and \((\vec x-\vec a)\cdot(\vec x+\vec a)=15\), then the value of \(|\vec x|\) is:
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The function \(f:\mathbb{R}\to[-1,1]\) defined by \(f(x)=\cos x\) is:
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots+\infty}}}\) then \(\frac{dy}{dx}\) equals to
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(A\) and \(B\) square matrices of order 3 such that \(|A|=-1\), \(|B|=5\), then the value of \(|2AB|\) is :
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
For the LPP: minimize \(z=6x+3y\) subject to the constraints \(4x+y\ge80\) \(x+5y\ge115\) \(3x+2y\le150\) \(x\ge0,\ y\ge0\) then the minimum value of z is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Let \(L_1\) and \(L_2\) be two lines, represented as, \(L_1: \vec r=\hat i+\hat j+\lambda(2\hat i-\hat j+\hat k)\) and \(L_2: \vec r=2\hat i+\hat j-\hat k+\mu(4\hat i-2\hat j+2\hat k)\), where \(\lambda\) and \(\mu\) are…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Which of the following statements are true? (A) The vector joining the points P(2,3,0) and Q(-1,-2,-4) directed from P to Q is \(\overrightarrow{PQ}=-3\hat i-5\hat j-4\hat k\) (B) Projection of a vector \(\vec a\) on oth…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(c_{ij}\) denotes the cofactor of element \(a_{ij}\) of the matrix \(A=\begin{bmatrix}1&2&-1\\0&-3&2\\4&2&3\end{bmatrix}\), then the value of \(c_{21}\cdot c_{33}\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The solution of the differential equation \((x^2+xy)dy=(x^2+y^2)dx\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The following system of equations: \(x+y-z=7\) \(4x+\lambda y-\lambda z=3\) \(3x+2y-4z=5\) does not possess a solution if the value of \(\lambda\) is:
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Match List-I with List-II List-I | List-II (A) Line : \(x=2y+1=z-1\) | (I) Crosses xz plane at (1, 0, 1) (B) Line : \(x+1=2y+1=z\) | (II) Crosses xz plane at (0, 0, 1) (C) Line : \(x-1=2y=z+1\) | (III) Crosses xz plane a…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
\(\int \frac{e^{2x}-1}{e^{2x}+1}\,dx=\)
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(\begin{vmatrix}p-a&0&c-r\\0&q-b&c-r\\a&b&r\end{vmatrix}=0\) then the value of \(\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
\(\int e^{-x}(\cot x+\operatorname{cosec}^2x)\,dx=\)
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The area of the region bounded by the curves \(y=x\) and \(y=x^3\) is:
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The corner points of the bounded feasible region determined by a set of constraints in an LPP are P(0, 5) Q(3, 5), R(5, 0) and S(4,1). If the objective function is \(z=ax+2by\), where, \(a,b>0\), then the condition on…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The projection of the vector \(5\hat i+\hat j-3\hat k\) on the vector \(\hat i+2\hat j-3\hat k\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
A coin is tossed and a die is thrown. The probability that the outcome will be a tail on the coin or a number greater than 3 on the die is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Match List-I with List-II List-I | List-II (A) \(\tan^{-1}\frac{2}{11}+\tan^{-1}\frac{7}{24}\) | (I) \(\frac{3\pi}{4}\) (B) \(\tan^{-1}2+\tan^{-1}3\) | (II) \(\pi\) (C) \(\tan^{-1}1+\tan^{-1}2+\tan^{-1}3\) | (III)…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
Match List-I with List-II List-I | List-II (A) The number of possible matrices of order \(3\times3\) with each entry 1 or 0 | (I) \(2^4\) (B) The number of possible matrices of order \(2\times3\) with each entry 1 or 0 |…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
A balloon which always remains spherical, has a variable diameter \(\frac{3}{2}(5x+7)\). Then the rate of change of its volume with respect to \(x\) is
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
The domain of the function \(y=\sin^{-1}(x-1)+\cos^{-1}\sqrt{x-1}\) is:
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
For \(x\in\mathbb{R}\), if \(f(x)=-(x-1)^2+2\), then (A) \(f\) is an increasing function on \((-\infty,1]\) (B) \(f\) has no critical points (C) \(f\) has a maximum value at \(x=1\) (D) \(f\) has a minimum value at…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(f(x)=\sin x-\cos x,\ x\in[0,2\pi]\) then (A) \(f(x)\) is increasing in \(\left(0,\frac{3\pi}{4}\right)\) (B) \(f(x)\) is decreasing in \(\left(0,\frac{3\pi}{4}\right)\) (C) \(f(x)\) is decreasing in…
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CUET UG CUET Mathematics 2025 Mathematics Medium MCQ (Single Correct)
If \(x=a\sec^3\theta,\ y=a\tan^3\theta\), then \(\frac{d^2y}{dx^2}\) equals.
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