Continuity and differentiability 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 Continuity and differentiability with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Continuity and differentiability questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.
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MHT CET PYQs for Continuity and differentiability with Solutions
1.
It is known from past experience that in a certain plant there are on the average industrial accidents per month. Find the probability that there will be less than accidents in a given month. Given:- (A)
- (B)
- (C)
- (D)
2.
If y = sec–1\((\frac {x + x^{-1}}{x - x^{-1}})\), then \(\frac {dy}{dx}\) =?
\(-\frac {2}{(1+x^2)}\)
\(-\frac {1}{(1+x^2)}\)
\(\frac {2}{(1-x^2)}\)
\(\frac {1}{(1+x^2)}\)
3.
Given that: \[ x = a \sin(2t) (1 + \cos(2t)), \quad y = a \cos(2t) (1 - \cos(2t)) \] Find \(\frac{dy}{dx}\).- \( \frac{a \tan(t)}{b} \)
- \( \frac{a \tan(t)}{b} \)
- \( \frac{b \tan(t)}{a} \)
- \( \frac{b}{a \tan(t)} \)
4.
Give that f(x) =\(\frac {1-cos4x}{x^2}\) if x < 0 ,f(x) = a if x = 0 , f(x) =\(\frac {\sqrt {x}}{\sqrt {16 + \sqrt {x} }- 4}\) if x > 0, is continuous at x = 0, then a will be
- 16
- 2
- 4
- 8
5.
The second derivative of a sin 3t w.r.t. a cos 3t at t =π/4 is
\(- \frac {4√2}{3a}\)
\(\frac {4√2}{3a}\)
\(\frac {4√3}{3a}\)
12a
6.
If xy = e(x – y) , then \(\frac {dy}{dx}\) =?
\(\frac {log \ x}{(1+ log x)^2}\)
\(\frac {log \ x}{(1+ log x)}\)
\(\frac {xlog \ x}{(1+ log x)^2}\)
\(\frac {log \ x}{x(1+ log x)^2}\)
7.
If and , then, what is the value of ?- (A)
- (B)
- (C)
- (D)
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