Evaluate the following integral: $ \int_{-2}^{2} \frac{3x^3 + 2|x| + 1}{x^2 + |x| + 1}\,dx $
Previous 10 Questions — JAMIA MILLIA ISLAMIA MCA 2022
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If $
\begin{vmatrix}
x & 3 & 6 \\
3 & 6 & x \\
6 & x & 3
\end{vmatrix}
=
\begin{vmatrix}
2 & x & 7 \\
x & 7 & 2 \\
7 & …
Topic: JAMIA MILLIA ISLAMIA MCA 2022
If $
\begin{vmatrix}
a & p & x \\
b & q & y \\
c & r & z
\end{vmatrix}
= 16
$, then the value of
$
\begin{vmatrix}
p+q…
Topic: JAMIA MILLIA ISLAMIA MCA 2022
If $
\begin{vmatrix}
x & 3 & 6 \\
3 & 6 & x \\
6 & x & 3
\end{vmatrix}
=
\begin{vmatrix}
2 & x & 7 \\
x & 7 & 2 \\
7 & …
Topic: JAMIA MILLIA ISLAMIA MCA 2022
For two datasets each of size $5$, variances are $4$ and $5$ and means are $2$ and $4$ respectively.
The variance of th…
Topic: JAMIA MILLIA ISLAMIA MCA 2022
The numbers $3, 5, 7, 4$ have frequencies $x, x+4, x-3, x+8$.
If their arithmetic mean is $4$, then the value of $x$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2022
Marks obtained by $4$ students are: $25,35,45,55$. The average deviation from the mean is
Topic: JAMIA MILLIA ISLAMIA MCA 2022
$(p\wedge \neg q)\wedge(\neg p\wedge q)$ is
Topic: JAMIA MILLIA ISLAMIA MCA 2022
The variance of first $50$ even natural numbers is
Topic: JAMIA MILLIA ISLAMIA MCA 2022
The median of a set of $9$ distinctive observations is $20.5$. If each of the largest $4$ observations of the set is in…
Topic: JAMIA MILLIA ISLAMIA MCA 2022
Negation of $,q \vee \sim (p \wedge r),$ is
Topic: JAMIA MILLIA ISLAMIA MCA 2022
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If $A,B,C$ are angles of a triangle, then the value of
$
\begin{vmatrix}
\sin 2A & \sin C & \sin B \\
\sin C & \sin 2B…
Topic: JAMIA MILLIA ISLAMIA MCA 2022
Evaluate the following integral:
$
\int_{-\pi/2}^{\pi/2} \log\!\left(\frac{2-\sin x}{2+\sin x}\right)\,dx
$
Topic: JAMIA MILLIA ISLAMIA MCA 2022
Solve the differential equation: $x\,\dfrac{dy}{dx}+1=0;\; y(-1)=0$
Topic: JAMIA MILLIA ISLAMIA MCA 2022
If the matrix product $AB=0$, then which is true?
Topic: JAMIA MILLIA ISLAMIA MCA 2022
Which statement is false?
Topic: JAMIA MILLIA ISLAMIA MCA 2022
The function $f$ is defined in $[-5,5]$ as
$
f(x)=
\begin{cases}
x, & \text{if }x\text{ is rational}\\
-x, & \text{if…
Topic: JAMIA MILLIA ISLAMIA MCA 2022
The relation $R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$ on $A=\{1,2,3\}$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2022
For real numbers $x,y$, define $x\,R\,y$ iff $x-y+\sqrt{2}$ is irrational.
Then the relation $R$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2022
If $f(x)=ax^7+bx^3+cx-5$, where $a,b,c$ are real constants, and $f(-7)=7$,
then the range of $f(7)+17\cos x$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2022
If $z$ is any complex number with $|z-3-2i|\le2$, then the minimum of $|\,2z-6+5i\,|$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2022
