MHT CET PYQs for Quadratic Equations with Solutions: Practice MHT CET Previous Year Questions

Educational Content Expert | Updated on - Nov 26, 2025

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

MHT CET PYQs for Quadratic Equations with Solutions

1.
Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.
- 2 and 3
- 3 and -2
- -2 and -3
- 1 and 6
View Solution
2.
Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.
- $ x = 2, 3 $
- $ x = 1, 6 $
- $ x = -2, 3 $
- $ x = -1, -6 $
View Solution
3.
If the roots of the quadratic equation $ x^2 - 7x + 12 = 0 $ are $ \alpha $ and $ \beta $, then the value of $ \alpha + \beta $ is:
- $ 7 $
- $ 12 $
- $ 5 $
- $ 6 $
View Solution
4.
If $\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}$ , $\vec{b} = 3 \hat{i} - \hat{j} + 2 \hat{k}$ then the angle between $\vec{a} + \vec{b}, \vec{a} - \vec{b}$ is:
- (A) $0^{\circ}$
- (B) $180^{\circ}$
- (C) $90^{\circ}$
- (D) $- 180^{\circ}$
View Solution
5.
The equation $ (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 $, where $ x $ is a variable with real roots. Then the interval of $ p $ may be any one of the following:
- $ (0, 2\pi) $
- $ (-\pi, 0) $
- $ (-\frac{\pi}{2}, \frac{\pi}{2}) $
- $ (0, \pi) $
View Solution
6.
Find the position vector of the midpoint of the vector joining the points $P (2, 3, 4)$ and $Q (4, 1, - 2)$ .
- (A) $3 \hat{i} + 2 \hat{j} + \hat{k}$
- (B) $- 3 \hat{i} - 2 \hat{j} - \hat{k}$
- (C) $- 5 \hat{i} - 3 \hat{j} - 8 \hat{k}$
- (D) $5 \hat{i} - 3 \hat{j} + 8 \hat{k}$
View Solution
7.
The point which does not belong to the feasible region of the LPP:Minimize: $Z = 60 x + 10 y$ subject to $3 x + y \geq 18$ $2 x + 2 y \geq 12$ $x + 2 y \geq 10$ $x, y \geq 0$ is:
- (A) $(0, 8)$
- (B) $(4, 2)$
- (C) $(6, 2)$
- (D) $(10, 0)$
View Solution
8.
Find the sum of the roots of the quadratic equation $ 2x^2 - 5x + 3 = 0 $.
- $ \frac{5}{2} $
- $ \frac{3}{2} $
- $ \frac{7}{2} $
- $ \frac{1}{2} $
View Solution
9.
Consider the following statements:1. If $y = \ln (\sec x + \tan x)$ , then $\frac{d y}{d x} = \sec x$ .2. If $y = \ln (cosec x - \cot x)$ , then $\frac{d y}{d x} = cosec x$ .Which of the above is / are correct?
- (A) 1 only
- (B) 2 only
- (C) Both 1 and 2
- (D) Neither 1 nor 2
View Solution
10.
If $\cos^{- 1} (\frac{p}{a}) + \cos^{- 1} (\frac{q}{b}) = α$ , then $\frac{p^{2}}{a^{2}} + k \cos α + \frac{q^{2}}{b^{2}} = \sin^{2} α$ where $k$ is equal to:
- (A) $- \frac{2 p q}{a b}$
- (B) $\frac{2 p q}{a b}$
- (C) $- \frac{p q}{a b}$
- (D) $\frac{p q}{a b}$
View Solution

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MHT CET PYQs for Quadratic Equations with Solutions: Practice MHT CET Previous Year Questions

MHT CET PYQs for Quadratic Equations with Solutions

1.
Find the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).

2.
Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.

3.
If the roots of the quadratic equation \( x^2 - 7x + 12 = 0 \) are \( \alpha \) and \( \beta \), then the value of \( \alpha + \beta \) is:

4.
If $\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}$ , $\vec{b} = 3 \hat{i} - \hat{j} + 2 \hat{k}$ then the angle between $\vec{a} + \vec{b}, \vec{a} - \vec{b}$ is:

5.
The equation \( (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 \), where \( x \) is a variable with real roots. Then the interval of \( p \) may be any one of the following:

6.
Find the position vector of the midpoint of the vector joining the points $P (2, 3, 4)$ and $Q (4, 1, - 2)$ .

7.
The point which does not belong to the feasible region of the LPP:Minimize: $Z = 60 x + 10 y$ subject to $3 x + y \geq 18$ $2 x + 2 y \geq 12$ $x + 2 y \geq 10$ $x, y \geq 0$ is:

8.
Find the sum of the roots of the quadratic equation $ 2x^2 - 5x + 3 = 0 $.

9.
Consider the following statements:1. If $y = \ln (\sec x + \tan x)$ , then $\frac{d y}{d x} = \sec x$ .2. If $y = \ln (cosec x - \cot x)$ , then $\frac{d y}{d x} = cosec x$ .Which of the above is / are correct?

10.
If $\cos^{- 1} (\frac{p}{a}) + \cos^{- 1} (\frac{q}{b}) = α$ , then $\frac{p^{2}}{a^{2}} + k \cos α + \frac{q^{2}}{b^{2}} = \sin^{2} α$ where $k$ is equal to:

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MHT CET PYQs for Quadratic Equations with Solutions

1.Find the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).

2.Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.

3.If the roots of the quadratic equation \( x^2 - 7x + 12 = 0 \) are \( \alpha \) and \( \beta \), then the value of \( \alpha + \beta \) is:

4.If a→=i^+2j^−3k^, b→=3i^−j^+2k^ then the angle between a→+b→,a→−b→ is:

5.The equation \( (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 \), where \( x \) is a variable with real roots. Then the interval of \( p \) may be any one of the following:

6.Find the position vector of the midpoint of the vector joining the points P(2,3,4) and Q(4,1,−2).

7.The point which does not belong to the feasible region of the LPP:Minimize: Z=60x+10ysubject to 3x+y≥182x+2y≥12x+2y≥10x,y≥0 is:

8.Find the sum of the roots of the quadratic equation $ 2x^2 - 5x + 3 = 0 $.

9.Consider the following statements:1. If y=ln⁡(sec⁡x+tan⁡x), then dydx=sec⁡x.2. If y=ln⁡(cosecx−cot⁡x), then dydx=cosecx.Which of the above is / are correct?

10.If cos−1⁡(pa)+cos−1⁡(qb)=α, then p2a2+kcos⁡α+q2b2=sin2⁡α where k is equal to:

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1.
Find the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).

2.
Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.

3.
If the roots of the quadratic equation \( x^2 - 7x + 12 = 0 \) are \( \alpha \) and \( \beta \), then the value of \( \alpha + \beta \) is:

4.
If $\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}$ , $\vec{b} = 3 \hat{i} - \hat{j} + 2 \hat{k}$ then the angle between $\vec{a} + \vec{b}, \vec{a} - \vec{b}$ is:

5.
The equation \( (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 \), where \( x \) is a variable with real roots. Then the interval of \( p \) may be any one of the following:

6.
Find the position vector of the midpoint of the vector joining the points $P (2, 3, 4)$ and $Q (4, 1, - 2)$ .

7.
The point which does not belong to the feasible region of the LPP:Minimize: $Z = 60 x + 10 y$ subject to $3 x + y \geq 18$ $2 x + 2 y \geq 12$ $x + 2 y \geq 10$ $x, y \geq 0$ is:

8.
Find the sum of the roots of the quadratic equation $ 2x^2 - 5x + 3 = 0 $.

9.
Consider the following statements:1. If $y = \ln (\sec x + \tan x)$ , then $\frac{d y}{d x} = \sec x$ .2. If $y = \ln (cosec x - \cot x)$ , then $\frac{d y}{d x} = cosec x$ .Which of the above is / are correct?

10.
If $\cos^{- 1} (\frac{p}{a}) + \cos^{- 1} (\frac{q}{b}) = α$ , then $\frac{p^{2}}{a^{2}} + k \cos α + \frac{q^{2}}{b^{2}} = \sin^{2} α$ where $k$ is equal to: