JEE MAIN 2014 Previous Year Questions (PYQs) – Page 1 of 2
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$\displaystyle \lim_{x\to 0}\frac{\sin(\pi \cos^{2}x)}{x^{2}}$ is equal to :
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Solution
Let the population of rabbits surviving at time $t$ be governed by the differential equation
$\dfrac{dp(t)}{dt}=\dfrac{1}{2}p(t)-200$. If $p(0)=100$, then $p(t)$ equals:
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Solution
The integral $\displaystyle \int_{0}^{\pi}\sqrt{1+4\sin^{2}\frac{x}{2}-4\sin\frac{x}{2}}\,dx$ equals:
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The area of the region described by
$A=\{(x,y):x^{2}+y^{2}\le 1 \text{ and } y^{2}\le 1-x\}$ is :
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Solution
The integral $\displaystyle \int (1+x-\frac{1}{x})e^{x+\frac{1}{x}}\,dx$ is equal to
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Solution
If $A$ is a $3\times 3$ non-singular matrix such that $AA' = A'A$ and
$B = A^{-1}A'$, then $BB'$ equals :
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If $\alpha,\beta \ne 0$, and $f(n) = \alpha^{n} + \beta^{n}$ and
$\begin{vmatrix}
3 & 1 + f(1) & 1 + f(2) \\
1+f(1) & 1 + f(2) & 1 + f(3) \\
1+f(2) & 1 + f(3) & 1 + f(4)
\end{vmatrix}
= K(1-\alpha)^{2}(1-\beta)^{2}(\alpha-\beta)^{2}$, then $K$ is equal to :
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If $g$ is the inverse of a function $f$ and $f'(x)=\dfrac{1}{1+x^{5}}$, then $g'(x)$ is equal to:
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If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha\log|x|+\beta x^{2}+x$ then
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Let $A$ and $B$ be two events such that $P(\overline{A\cup B})=\dfrac{1}{6}$,
$P(A\cap B)=\dfrac{1}{4}$ and $P(\overline{A})=\dfrac{1}{4}$, where $\overline{A}$
stands for the complement of the event $A$. Then the events $A$ and $B$ are :
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Solution
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