CUET UG 2025 — Mathematics Geometry
Consider f(x)=sin(3x)+4,∀x∈R. Then
(A) Maximum value of f(x) is 5
(B) Minimum value of f(x) is 3
(C) Maximum value of f(x) is attained at x=6π
(D) Minimum value of f(x) is attained at x=0
Choose the correct answer from the options given below:
Held on 30 May 2025 · Verified 13 Jul 2026.
(A), (B) and (C) only
(A), (B) and (D) only
(C) and (D) only
(B) and (D) only
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Consider the line $\vec{r} = -2\hat{i} + 3\hat{j} + \hat{k} + \lambda(5\hat{i} - 3\hat{j} - \hat{k})$. Match List-I with List-II | List-I | List-II | |---|---| | (A) A point on the given line | (I) $\left(\frac{5}{\sqrt{35}}, \frac{-3}{\sqrt{35}}, \frac{-1}{\sqrt{35}}\right)$ | | (B) Direction ratios of the given line | (II) (2, 3, 1) | | (C) Direction cosines of the given line | (III) (5, -3, -1) | | (D) Direction ratios of a line perpendicular to given line | (IV) (-2, 3, 1) | Choose the correct answer from the options given below:
The value of $\cot\left(\cos^{-1}\frac{7}{25}\right)$ is
The angle between the pair of lines given by $\vec{r} = \hat{i} + 2\hat{j} - 3\hat{k} + \lambda (\hat{i} - 2\hat{j} + 2\hat{k})$ and $\vec{r} = 5\hat{i} + \hat{j} + \hat{k} + \mu (3\hat{i} - 2\hat{j} + 6\hat{k})$ is
The minimum value of the function $f(x) = 3\sin x - 4\cos x, x \in [-4\pi, 4\pi]$ is equal to
The coordinates of the image of the point P (5, 4, 2) in the line $\vec{r} = (-\hat{i} + 3\hat{j} + \hat{k}) + \mu(2\hat{i} + 3\hat{j} - \hat{k})$, where $\lambda$ is a parameter, is
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