The function $f : \mathbb{N} \to \mathbb{N}$ defined by $f(x) = x - 5\left\lfloor \dfrac{\pi x}{5} \right\rfloor$, where $\mathbb{N}$ is the set of natural numbers and $\lfloor x \rfloor$ denotes the greatest integer $\le x$, is:

1

For two $3 \times 3$ matrices $A$ and $B$, let $A + B = 2B^T$ and $3A + 2B = I_3$, where $B^T$ is the transpose of $B$ …

Topic: JEE Main 2017 (9 April Morning Shift)

2

The coefficient of $x^{-5}$ in the binomial expansion of $\left( \dfrac{x+1}{x^{\frac{2}{3}} - x^{\frac{1}{3}} + 1} ;-;…

Topic: JEE Main 2017 (9 April Morning Shift)

3

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a parti…

Topic: JEE Main 2017 (9 April Morning Shift)

4

If three positive numbers $a, b$ and $c$ are in A.P. such that $abc = 8$, then the minimum possible value of $b$ is :

Topic: JEE Main 2017 (9 April Morning Shift)

1

The two adjacent sides of a cyclic quadrilateral are $2$ and $5$ and the angle between them is $60^\circ$. If the area …

Topic: JEE Main 2017 (9 April Morning Shift)

2

The equation $\operatorname{Im}\left( \dfrac{iz - 2}{z - i} \right) + 1 = 0,; z \in \mathbb{C},; z \neq i$ represents a…

Topic: JEE Main 2017 (9 April Morning Shift)

3

The sum of all real values of $x$ satisfying the equation $2^{(x-1)(x^{2} + 5x - 50)} = 1$ is:

Topic: JEE Main 2017 (9 April Morning Shift)

4

A value of $x$ satisfying the equation $\sin!\big(\cot^{-1}(1+x)\big) = \cos!\big(\tan^{-1} x\big)$ is:

Topic: JEE Main 2017 (9 April Morning Shift)

5

Let $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happen is $\dfrac{1}{12}$ and the prob…

Topic: JEE Main 2017 (9 April Morning Shift)

6

The sum of $100$ observations and the sum of their squares are $400$ and $2475$, respectively. Later on, three observat…

Topic: JEE Main 2017 (9 April Morning Shift)

7

If the vector $\vec{b} = 3\vec{j} + 4\vec{k}$ is written as the sum of a vector $\vec{b_1}$ parallel to $\vec{a} = \vec…

Topic: JEE Main 2017 (9 April Morning Shift)

8

From a group of $10$ men and $5$ women, four-member committees are to be formed, each of which must contain at least on…

Topic: JEE Main 2017 (9 April Morning Shift)

9

The eccentricity of an ellipse having centre at the origin, axes along the coordinate axes, and passing through the poi…

Topic: JEE Main 2017 (9 April Morning Shift)

10

If $\displaystyle \int_{1}^{2} \frac{dx}{(x^{2} - 2x + 4)^{\tfrac{3}{2}}} = \frac{k}{k+5}$, then $k$ is equal to:

Topic: JEE Main 2017 (9 April Morning Shift)