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 :

1

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

Topic: JEE Main 2015 (Offline)

2

The integral $\displaystyle \int_{2}^{4}\dfrac{\log x^{2}}{\log x^{2}+\log(36-12x+x^{2})}\,dx$ is equal to :

Topic: JEE Main 2015 (Offline)

3

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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4

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

Topic: JEE Main 2015 (Offline)

5

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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6

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…

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7

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

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8

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

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9

If the function. $g\left( x \right) = \left\{ {\matrix{ {k\sqrt {x + 1} ,} & {0 \le x \le 3} \cr {m\,x + 2,…

Topic: JEE Main 2015 (Offline)

1

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

Topic: JEE Main 2015 (Offline)

2

Let $f(x)$ be a polynomial of degree four having extreme values at $x=1$ and $x=2$. If $\displaystyle \lim_{x\to 0}\lef…

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3

Let $\tan^{-1}y=\tan^{-1}x+\tan^{-1}\left(\dfrac{2x}{1-x^{2}}\right)$, where $|x|

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4

Let $O$ be the vertex and $Q$ be any point on the parabola, $x^{2}=8y$. If the point $P$ divides the line segment $OQ$ …

Topic: JEE Main 2015 (Offline)

5

Locus of the image of the point $(2,3)$ in the line $(2x-3y+4)+k(x-2y+3)=0,\;k\in\mathbb{R},$ is a :

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6

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0,…

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7

If $m$ is the A.M. of two distinct real numbers $l$ and $n$ $(l,n>1)$ and $G_{1},G_{2}$ and $G_{3}$ are three geometric…

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8

The number of integers greater than $6000$ that can be formed, using the digits $3,5,6,7$ and $8$, without repetition, …

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9

A complex number $z$ is said to be unimodular if $|z|=1$. Suppose $z_{1}$ and $z_{2}$ are complex numbers such that $\d…

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10

Let $A$ and $B$ be two sets containing four and two elements respectively. Then, the number of subsets of the set $A\ti…

Topic: JEE Main 2015 (Offline)