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Let \(A = \{3, 5\}\). Then number of reflexive relations on \(A\) is
(a) 2
(b) 4
(c) 0
(d) 8
(2023) Ans
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If \(\vec{\alpha}\) and \(\vec{\beta}\) are position vectors of two points P and Q respectively, then find the position vector of a point R in QP produced such that \(QR=\frac{3}{2}QP\).
(AI 2016) An
- If \(\vec{\alpha}\) and \(\vec{\beta}\) are position vectors of two points P and Q respectively, then find the position vector of a point R in QP produced such that \(QR=\frac{3}{2}QP\).
(AI 2016) An
Find a vector $\vec{a}$ of magnitude $5\sqrt{2}$, making an angle
of $\frac{\pi}{4}$ with x-axis, $\frac{\pi}{2}$ with y-axis and an acute angle $\theta$
with z-axis.
(AI-2014) Ans
Find the position vector of a point which divides the join of points with position vectors $\vec{a}-2\vec{b}$ and $2\vec{a}+\vec{b}$ externally in the ratio $2:1$.
(Delhi 2016) An
Write the position vector of the point which divides the join of points with position vectors $3\vec{a}-2\vec{b}$ and $2\vec{a}+3\vec{b}$ in the ratio $2:1$.
(AI 2016) An
Find the unit vector in the direction of the sum of the vectors $2\hat{i}+3\hat{j}-\hat{k}$ and $4\hat{i}-3\hat{j}+2\hat{k}$.
(Foreign 2015)
Find a vector in the direction of $\vec{a}=\hat{i}-2\hat{j}$ that has magnitude 7 units.
(Delhi 2015C)
Write the direction ratios of the vector $3\vec{a}+2\vec{b}$ where $\vec{a}=\hat{i}+\hat{j}-2\hat{k}$ and $\vec{b}=2\hat{i}-4\hat{j}+5\hat{k}$.
(AI 2015C) An
Write a unit vector in the direction of the sum of the vectors $\vec{a}=2\hat{i}+2\hat{j}-5\hat{k}$ and $\vec{b}=2\hat{i}+\hat{j}-7\hat{k}$.
(Delhi 2014)
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Using integration, find the area of the region \(\{(x, y): 4x^2 + 9y^2 \le 36, 2x + 3y \ge 6\}\).
(2024) Ans
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Using integration, find the area of the region \(\{(x, y): 4x^2 + 9y^2 \le 36, 2x + 3y \ge 6\}\).
(2024) Ans