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 :

1

The mean of the data set comprising of $16$ observations is $16$. If one of the observations valued $16$ is deleted and…

Topic: JEE Main 2015 (Offline)

2

$\displaystyle \lim_{x\to 0} \frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to :

Topic: JEE Main 2015 (Offline)

3

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…

Topic: JEE Main 2015 (Offline)

4

If 12 different balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactl…

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5

Let $y(x)$ be the solution of the differential equation $(x\log x)\dfrac{dy}{dx}+y=2x\log x,\;(x\ge 1).$ Then $y(e)$…

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6

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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7

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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8

The integral $\displaystyle \int \frac{dx}{x^{2}(x^{4}+1)^{3/4}}$ equals :

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9

If $A=\begin{bmatrix} 1 & 2 & 2\\ 2 & 1 & -2\\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $AA^{T}=9I$…

Topic: JEE Main 2015 (Offline)

10

The set of all values of $\lambda$ for which the system of linear equations&nbsp;&nbsp;$2x_{1}-2x_{2}+x_{3}=\lambda x_{…

Topic: JEE Main 2015 (Offline)