Differential Equations PYQs - Last 5 Years
WB JEE / Mathematics / Calculus / 12 recent questions
MathematicsCalculus2022-2026
Practice 12 WB JEE Mathematics questions from Differential Equations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
12
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Mathematics / Calculus
2022-2026
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12
Last 5 Years
2022-2026
12
Last 10 Years
2017-2026
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12PYQs
MCQ91.7%
MCQM8.3%
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#1 Unknown12
12 in last 5 years12 in last 10 years
Last 5 Years Differential Equations Questions
Showing 12 of 12 filtered questions.
1Differential Equations
Let $f:(0,1) \rightarrow(0,1)$ be a differentiable function such that $f^{\prime}(x) \neq 0 \forall x \in(0,1)$ and $f\left(\frac{1}{2}\right)=\frac{\sqrt{3}}{2}$. Suppose for all $x$, $\mathop {\lim }\limits_{t \to x} \frac{\int_0^t \sqrt...
MCQ+1 / -0.252026
2Differential Equations
The solution of the differential equation $2 x^2 y \frac{d y}{d x}=\tan \left(x^2 y^2\right)-2 x y^2$, given $y(1)=\sqrt{\frac{\pi}{2}}$ is
MCQ+1 / -0.252026
3Differential Equations
The population $p(t)$ at time $t$ of a certain mouse species follows the differential equation
\(\frac{d p(t)}{d t}=0.5 p(t)-450\)
If $p(0)=850$, then the time at which the population becomes zero is
\(\frac{d p(t)}{d t}=0.5 p(t)-450\)
If $p(0)=850$, then the time at which the population becomes zero is
MCQM+2 / -02025
4Differential Equations
If $x=\int\limits_0^y \frac{1}{\sqrt{1+9 t^2}} d t$ and $\frac{d^2 y}{d x^2}=a y$, then $a$ is equal to
MCQ+1 / -0.252025
5Differential Equations
If \(x y^{\prime}+y-e^x=0, y(a)=b\), then \(\lim _\limits{x \rightarrow 1} y(x)\) is
MCQ+1 / -0.252024
6Differential Equations
Let \(\mathrm{f}\) be a differential function with \(\lim _\limits{x \rightarrow \infty} \mathrm{f}(x)=0\). If \(\mathrm{y}^{\prime}+\mathrm{yf}^{\prime}(x)-\mathrm{f}(x) \mathrm{f}^{\prime}(x)=0\), $$\lim _\limits{x \rightarrow \infty} y(x...
MCQ+1 / -0.252024
7Differential Equations
The family of curves \(y = {e^{a\sin x}}\), where 'a' is arbitrary constant, is represented by the differential equation
MCQ+2 / -0.52023
8Differential Equations
Given \({{{d^2}y} \over {d{x^2}}} + \cot x{{dy} \over {dx}} + 4y\cos e{c^2}x = 0\). Changing the independent variable x to z by the substitution \(z = \log \tan {x \over 2}\), the equation is changed to
MCQ+1 / -0.252023
9Differential Equations
If \(y = {x \over {{{\log }_e}|cx|}}\) is the solution of the differential equation \({{dy} \over {dx}} = {y \over x} + \phi \left( {{x \over y}} \right)\), then \(\phi \left( {{x \over y}} \right)\) is given by
MCQ+1 / -0.252023
10Differential Equations
If the transformation \(z = \log \tan {x \over 2}\) reduces the differential equation \({{{d^2}y} \over {d{x^2}}} + \cot x{{dy} \over {dx}} + 4y\cos e{c^2}x = 0\) into the form \({{{d^2}y} \over {d{z^2}}} + ky = 0\) then k is equal to
MCQ+2 / -0.52022
11Differential Equations
The solution of \(\cos y{{dy} \over {dx}} = {e^{x + \sin y}} + {x^2}{e^{\sin y}}\) is \(f(x) + {e^{ - \sin y}} = C\) (C is arbitrary real constant) where f(x) is equal to
MCQ+1 / -0.252022
12Differential Equations
If \(x{{dy} \over {dx}} + y = x{{f(xy)} \over {f'(xy)}}\), then \(|f(xy)|\) is equal to
MCQ+1 / -0.252022