CUET UG 2025 — Mathematics Geometry
Consider the lines l1:0x−1=1y−1=12−z and l2:2x=0y=42z−1, then which of the following are correct?
(A) Direction Ratio's of l1=<0,1,1>
(B) Direction Ratio's of l2=<2,0,2>
(C) Angle between l1 and l2= 3π
(D) Angle between l1 and l2= 32π
Choose the correct answer from the options given below:
Held on 15 May 2025 · Verified 13 Jul 2026.
(B) and (D) only
(A) and (C) only
(A), (B) and (C) only
(D) only
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
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
Work through every CUET UG Geometry PYQ, year by year.