MHT CET PYQs for Vectors with Solutions: Practice MHT CET Previous Year Questions

Educational Content Expert | Updated on - Nov 26, 2025

Vectors 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 Vectors with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Vectors questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.

MHT CET PYQs for Vectors with Solutions

1.
If $\vec{a} , \vec{b} , \vec{c}$ are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then $[\vec{a} + \vec{b} + \vec{c} \, \, \vec{b} - \vec{a} - \vec{c}] = ?$
- 0
- 6
- 12
- 18
View Solution
2.
Evaluate $ \sin \left( \tan^{-1}\frac{4}{5} + \tan^{-1}\frac{4}{3} + \tan^{-1}\frac{1}{9} - \tan^{-1}\frac{1}{7} \right) $:
- $ \frac{1}{2} $
- $ \frac{1}{\sqrt{2}} $
- $ \frac{\sqrt{3}}{2} $
- $ 1 $
View Solution
3.
Let $ \mathbf{a} $, $ \mathbf{b} $, and $ \mathbf{c} $ be vectors of magnitude 2, 3, and 4 respectively. If: - $ \mathbf{a} $ is perpendicular to $ (\mathbf{b} + \mathbf{c}) $, - $ \mathbf{b} $ is perpendicular to $ (\mathbf{c} + \mathbf{a}) $, - $ \mathbf{c} $ is perpendicular to $ (\mathbf{a} + \mathbf{b}) $, then the magnitude of $ \mathbf{a} + \mathbf{b} + \mathbf{c} $ is equal to:
- 29
- $ \sqrt{29} $
- 26
- $ \sqrt{26} $
View Solution
4.
If $f (x)$ and $g (x)$ are two probability density functions, $f (x) = {\begin{array}{cc} \frac{x}{a} + 1 & : - a \leq x < 0 \\ - \frac{x}{a} + 1 & 0 \leq x \leq a \\ 0 & otherwise \end{array}$ $g (x) = {\begin{array}{cc} - \frac{x}{a} & : - a \leq x \leq 0 \\ \frac{x}{a} & : 0 \leq x \leq a \\ 0 & : otherewise \end{array}$ Which one of the following statements is true?
- (A) Mean of $f (x)$ and $g (x)$ are same; Variance of $f (x)$ and $g (x)$ are same
- (B) Mean of $f (x)$ and $g (x)$ are same; Variance of $f (x)$ and $g (x)$ are different
- (C) Mean of $f (x)$ and $g (x)$ are different; Variance of $f (x)$ and $g (x)$ are same
- (D) Mean of $f (x)$ and $g (x)$ are different; Variance of $f (x)$ and $g (x)$ are different
View Solution
5.
If $ \sqrt{\frac{y}{x}} + 4\sqrt{\frac{x}{y}} = 4 $, then $ \frac{dy}{dx} $:
- $ xy $
- $ \frac{x}{y} $
- $ -4 $
- $ 4 $
View Solution
6.
Given the vectors: \[ \mathbf{a} = i + 3j - k, \quad \mathbf{b} = 3i - j + 2k, \quad \mathbf{c} = i + 2j - 2k \] and the following information: \[ \frac{\mathbf{a} \cdot \mathbf{c}}{|\mathbf{c}|} = \frac{10}{3} \] Find the value of $ \alpha + \beta $ and the projection of $ \mathbf{a} $ on $ \mathbf{c} $.
- $ \alpha + \beta = 30^\circ $, Projection of $ \mathbf{a} $ on $ \mathbf{c} = 5 $
- $ \alpha + \beta = 45^\circ $, Projection of $ \mathbf{a} $ on $ \mathbf{c} = 4 $
- $ \alpha + \beta = 60^\circ $, Projection of $ \mathbf{a} $ on $ \mathbf{c} = 6 $
- $ \alpha + \beta = 90^\circ $, Projection of $ \mathbf{a} $ on $ \mathbf{c} = 7 $
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MHT CET PYQs for Vectors with Solutions: Practice MHT CET Previous Year Questions

MHT CET PYQs for Vectors with Solutions

1.
If $\vec{a} , \vec{b} , \vec{c}$ are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then $[\vec{a} + \vec{b} + \vec{c} \, \, \vec{b} - \vec{a} - \vec{c}] = ?$

2.
Evaluate \( \sin \left( \tan^{-1}\frac{4}{5} + \tan^{-1}\frac{4}{3} + \tan^{-1}\frac{1}{9} - \tan^{-1}\frac{1}{7} \right) \):

5.
If \( \sqrt{\frac{y}{x}} + 4\sqrt{\frac{x}{y}} = 4 \), then \( \frac{dy}{dx} \):

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MHT CET PYQs for Vectors with Solutions

1.If $\vec{a} , \vec{b} , \vec{c}$ are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then $[\vec{a} + \vec{b} + \vec{c} \, \, \vec{b} - \vec{a} - \vec{c}] = ?$

2.Evaluate \( \sin \left( \tan^{-1}\frac{4}{5} + \tan^{-1}\frac{4}{3} + \tan^{-1}\frac{1}{9} - \tan^{-1}\frac{1}{7} \right) \):

4.If f(x) and g(x) are two probability density functions,f(x)={xa+1:−a≤x<0−xa+10≤x≤a0 otherwise g(x)={−xa:−a≤x≤0xa:0≤x≤a0: otherewise Which one of the following statements is true?

5.If \( \sqrt{\frac{y}{x}} + 4\sqrt{\frac{x}{y}} = 4 \), then \( \frac{dy}{dx} \):

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1.
If $\vec{a} , \vec{b} , \vec{c}$ are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then $[\vec{a} + \vec{b} + \vec{c} \, \, \vec{b} - \vec{a} - \vec{c}] = ?$

2.
Evaluate \( \sin \left( \tan^{-1}\frac{4}{5} + \tan^{-1}\frac{4}{3} + \tan^{-1}\frac{1}{9} - \tan^{-1}\frac{1}{7} \right) \):

5.
If \( \sqrt{\frac{y}{x}} + 4\sqrt{\frac{x}{y}} = 4 \), then \( \frac{dy}{dx} \):