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.
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
2.
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
3.
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:- \( \frac{\pi}{4} \)
- \( \frac{\pi}{3} \)
- \( \frac{\pi}{2} \)
- \( \frac{\pi}{6} \)
4.
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
5.
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
6.
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
- \( \frac{5}{3} \)
- \( 1 \)
- \( 0 \)
- \( \frac{3}{5} \)
7.
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
\(\frac {2π}{3}\)
\(\frac {5π}{6}\)
\(\frac {5π}{9}\)
\(\frac {3π}{4}\)
8.
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:- \( p \land q \)
- \( \sim (p \land q) \)
- \( \sim p \land \sim q \)
- \( \sim p \land q \)
9.
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.
10.
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- \(\frac {3(3\hat i + 2\hat j + 5\hat k)}{\sqrt {38}}\)
- \(\frac {9\hat i + 6\hat j + 15\hat k}{19}\)
- \(\frac {3(3\hat i + 2\hat j + 5\hat k)}{38}\)
- \(\frac {6(3\hat i + 2\hat j + 5\hat k)}{\sqrt {38}}\)
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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