Vector Algebra is an important topic in the Mathematics section in MHT CET exam. Practising this topic will increase your score overall and make your conceptual grip on MHT CET exam stronger.
This article gives you a full set of MHT CET PYQs for Vector Algebra with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Vector Algebra questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.
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MHT CET PYQs for Vector Algebra with Solutions
1.
Which of the following is correct?- \( B'AB \) is symmetric if \( A \) is symmetric.
- \( B'AB \) is skew-symmetric if \( A \) is symmetric.
- \( B'AB \) is symmetric if \( A \) is skew-symmetric.
- \( B'AB \) is skew-symmetric if \( A \) is skew-symmetric.
2.
If vector $\vec{r}$ with d.c.s. $l, m, n$ is equally inclined to the co-ordinate axes, then the total number of such vectors is- 4
- 6
- 8
- 2
3.
Let \( p: \) I am brave, \( q: \) I will climb the Mount Everest. The symbolic form of a statement, 'I am neither brave nor I will climb the Mount Everest' is:- \( p \land q \)
- \( \sim (p \land q) \)
- \( \sim p \land \sim q \)
- \( \sim p \land q \)
4.
The vector projection of b on a , where a = 3\(\hat {i}\) + 2\(\hat {j}\) + 5\(\hat {k}\) and b = 7\(\hat {i}\) - 5\(\hat {j}\) - \(\hat {k}\) is- \(\frac {3(3\hat i + 2\hat j + 5\hat k)}{\sqrt {38}}\)
- \(\frac {9\hat i + 6\hat j + 15\hat k}{19}\)
- \(\frac {3(3\hat i + 2\hat j + 5\hat k)}{38}\)
- \(\frac {6(3\hat i + 2\hat j + 5\hat k)}{\sqrt {38}}\)
5.
If \( \mathbf{a} = \frac{1}{\sqrt{10}} (4\hat{i} - 3\hat{j} + \hat{k}) \) and \( \mathbf{b} = \frac{1}{5} (\hat{i} + 2\hat{j} + 2\hat{k}) \), then the value of \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]- 5
- -3
- -5
- 3
6.
If $ \mathbf{a} $ and $ \mathbf{b} $ are non-coplanar unit vectors such that $ \mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \frac{\mathbf{b}}{2} $ then the angle between $ \mathbf{a} $ and $ \mathbf{b} $ is:- \( \frac{\pi}{4} \)
- \( \frac{\pi}{3} \)
- \( \frac{\pi}{2} \)
- \( \frac{\pi}{6} \)
7.
If \( X \) is a random variable such that \( P(X = -2) = P(X = -1) = P(X = 2) = P(X = 1) = \frac{1}{6} \), and \( P(X = 0) = \frac{1}{3} \), then the mean of \( X \) is
- \( \frac{5}{3} \)
- \( 1 \)
- \( 0 \)
- \( \frac{3}{5} \)
8.
If \( \mathbf{a} = 3\hat{i} + 4\hat{j} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} \), find \( \mathbf{a} \cdot \mathbf{b} \) (the dot product).2
- 4
- 10
- 12
9.
If a and b are two vectors such that I\(\vec {a}\)I + I\(\vec {b}\)I = \(\sqrt 2\) with \(\vec {a}\).\(\vec {b}\) = –1, then the angle between \(\vec {a}\) and \(\vec {b}\) is
\(\frac {2π}{3}\)
\(\frac {5π}{6}\)
\(\frac {5π}{9}\)
\(\frac {3π}{4}\)
10.
The ratio in which the plane r.(\(\hat i\) -2\(\hat j\) + 3\(\hat k\) ) =17 divides the line joining the points -2\(\hat i\)+4\(\hat j\)+7\(\hat k\) and 3\(\hat i\)-5\(\hat j\)+8\(\hat k\) is
- 5 : 3
4 : 5
3 : 10
10 : 3
11.
A vector parallel to the line of intersection of the planes \[ \overrightarrow{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 1 \quad \text{and} \quad \overrightarrow{r} \cdot (\hat{i} + 4\hat{j} - 2\hat{k}) = 2 \] is:- \( -2\hat{i} + 7\hat{j} + 13\hat{k} \)
- \( 2\hat{i} - 7\hat{j} + 13\hat{k} \)
- \( -\hat{i} + 4\hat{j} + 7\hat{k} \)
- \( \hat{i} - 4\hat{j} + 7\hat{k} \)
12.
If a, b, c are position vectors of points A, B, C respectively, with 2a + 3b -5c = 0 , then the ratio in which point C divides segment AB is
- 3:2 externally
- 2:3 externally
- 3:2 internally
- 2:3 internally
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