The solution of the differential equation $\dfrac{dy}{dx} = e^{x - y} + x^2 e^{-y}$ is:
Previous 10 Questions — JAMIA MILLIA ISLAMIA MCA 2021
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he degree of the differential equation
$\left[1 + \left(\dfrac{dy}{dx}\right)^2\right]^{3/2} = \dfrac{d^2y}{dx^2}$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2021
$\displaystyle \int \dfrac{\cos 2x - \cos 2\theta}{\cos x - \cos \theta}\, dx$ is equal to:
Topic: JAMIA MILLIA ISLAMIA MCA 2021
Maximum value of $\left(\dfrac{1}{x}\right)^x$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2021
If $f(x)=x^{2}\sin\frac{1}{x}$ for $x\neq0$, then the value of the function $f$ at $x=0$,
so that $f$ is continuous at …
Topic: JAMIA MILLIA ISLAMIA MCA 2021
If $x, y, z$ are all different from zero and
$\begin{vmatrix}
1 + x & 1 & 1 \\
1 & 1 + y & 1 \\
1 & 1 & 1 + z
\end{…
Topic: JAMIA MILLIA ISLAMIA MCA 2021
Let $f(t) =
\begin{vmatrix}
\cos t & 1 & 1 \\
2\sin t & 2t & 1 \\
\sin t & t & t
\end{vmatrix}$,
then $\displaystyle…
Topic: JAMIA MILLIA ISLAMIA MCA 2021
If A is a square matrix such that $A^2 = I$, then
$(A - I)^3 + (A - I)^3 - 7A$ is equal to:
Topic: JAMIA MILLIA ISLAMIA MCA 2021
If $\cos\alpha + \cos\beta + \cos\gamma = 3\pi$, then
$\alpha((\beta + \gamma) + \beta(\gamma + \alpha) + \gamma(\alp…
Topic: JAMIA MILLIA ISLAMIA MCA 2021
If the set A contains 5 elements and the set B contains 6 elements, then
the number of one-one and onto mappings from…
Topic: JAMIA MILLIA ISLAMIA MCA 2021
The maximum number of equivalence relations on the set $A = \{1,2,3\}$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2021
Next 10 Questions — JAMIA MILLIA ISLAMIA MCA 2021
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For any vector $\vec{a}$, the value of
$(\vec{a} \times \hat{i})^2 + (\vec{a} \times \hat{j})^2 + (\vec{a} \times \ha…
Topic: JAMIA MILLIA ISLAMIA MCA 2021
Number of vectors of unit length perpendicular to
$\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}$
and $\vec{b} = \hat{j} …
Topic: JAMIA MILLIA ISLAMIA MCA 2021
The reflection of the point $(\alpha, \beta, \gamma)$ in the xy-plane is:
Topic: JAMIA MILLIA ISLAMIA MCA 2021
The locus represented by $xy + yz = 0$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2021
Three persons A, B, and C fire at a target in turn, starting with A.
Their probabilities of hitting the target are $0.4…
Topic: JAMIA MILLIA ISLAMIA MCA 2021
A and B are two students. Their chances of solving a problem correctly are
$\dfrac{1}{3}$ and $\dfrac{1}{4}$ respecti…
Topic: JAMIA MILLIA ISLAMIA MCA 2021
If $a_n = \alpha^n - \beta^n$ and $\alpha, \beta$ are the roots of the equation
$x^2 - 6x - 2 = 0$, then find the val…
Topic: JAMIA MILLIA ISLAMIA MCA 2021
Let the quadratic equation $ax^2 + bx + c = 0$
where $a, b, c$ are obtained by rolling a dice thrice.
What is the proba…
Topic: JAMIA MILLIA ISLAMIA MCA 2021
Find the value of
$I = \displaystyle\int_{-1}^{1} x^2 e^{[x]} dx$,
where $[\,]$ denotes the greatest integer functi…
Topic: JAMIA MILLIA ISLAMIA MCA 2021
. Find the number of points where
$f(x) = |2x + 1| - 3|x + 2| + |x^2 + x - 2|$
is non-differentiable.
Topic: JAMIA MILLIA ISLAMIA MCA 2021
