JEE MAIN 2015 Previous Year Questions (PYQs) – Page 1 of 2
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If the function.
$g\left( x \right) = \left\{ {\matrix{ {k\sqrt {x + 1} ,} & {0 \le x \le 3} \cr {m\,x + 2,} & {3 < x \le 5} \cr } } \right.$
is differentiable, then the value of $k+m$ is :
$g\left( x \right) = \left\{ {\matrix{ {k\sqrt {x + 1} ,} & {0 \le x \le 3} \cr {m\,x + 2,} & {3 < x \le 5} \cr } } \right.$
is differentiable, then the value of $k+m$ is :
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4
Solution
The mean of the data set comprising of $16$ observations is $16$. If one of the
observations valued $16$ is deleted and three new observations valued $3,4$
and $5$ are added to the data, then the mean of the resultant data is:
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Solution
$\displaystyle \lim_{x\to 0} \frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to :
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Solution
Let $\alpha$ and $\beta$ be the roots of equation $x^{2}-6x-2=0$.
If $a_{n}=\alpha^{n}-\beta^{n}$, for $n\ge 1$, then the value of $\dfrac{a_{10}-2a_{8}}{2a_{9}}$ is equal to :
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Solution
If 12 different balls are to be placed in 3 identical boxes, then the probability
that one of the boxes contains exactly 3 balls is :
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Solution
Let $y(x)$ be the solution of the differential equation
$(x\log x)\dfrac{dy}{dx}+y=2x\log x,\;(x\ge 1).$ Then $y(e)$ is equal to :
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Solution
The area (in sq. units) of the region described by $\{(x,y):y^{2}\le 2x \text{ and } y\ge 4x-1\}$ is :
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Solution
The integral $\displaystyle \int_{2}^{4}\dfrac{\log x^{2}}{\log x^{2}+\log(36-12x+x^{2})}\,dx$ is equal to :
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Solution
The integral $\displaystyle \int \frac{dx}{x^{2}(x^{4}+1)^{3/4}}$ equals :
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Solution
If $A=\begin{bmatrix}
1 & 2 & 2\\
2 & 1 & -2\\
a & 2 & b
\end{bmatrix}$ is a matrix satisfying the equation $AA^{T}=9I$, where $I$ is $3\times 3$ identity matrix, then the ordered pair $(a,b)$ is equal to :
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Solution
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