Let $f_k(x)=\dfrac{1}{k}\left(\sin^{k}x+\cos^{k}x\right)$ for $k=1,2,3,\ldots$ Then for all $x\in\mathbb{R}$, the value of $f_4(x)-f_6(x)$ is equal to

1

Let $\left(-2-\dfrac{1}{3}i\right)^{3}=e^{\frac{x+iy}{2\pi i}}\ (i=\sqrt{-1})$, where $x$ and $y$ are real numbers, the…

Topic: JEE Main 2019 (11 January Morning Shift)

2

Let $f\left( x \right) = \left\{ {\matrix{ { - 1} & { - 2 \le x < 0} \cr {{x^2} - 1,} & {0 \le x \le…

Topic: JEE Main 2019 (11 January Morning Shift)

3

Two integers are selected at random from the set $\{1,2,\ldots,11\}$. Given that the sum of selected numbers is even, t…

Topic: JEE Main 2019 (11 January Morning Shift)

4

The value of the integral $\displaystyle \int_{-2}^{2}\frac{\sin^{2}x}{[x]+\tfrac{1}{2}}\,dx$ (where $[x]$ denotes the …

Topic: JEE Main 2019 (11 January Morning Shift)

5

The sum of an infinite geometric series with positive terms is $3$ and the sum of the cubes of its terms is $\dfrac{27}…

Topic: JEE Main 2019 (11 January Morning Shift)

6

If the system of linear equations  $2x+2y+3z=a$  $3x-y+5z=b$  $x-3y+2z=c$  wher…

Topic: JEE Main 2019 (11 January Morning Shift)

7

If $\displaystyle \int \frac{\sqrt{\,1-x^{2}\,}}{x^{4}}\,dx = A(x)\left(\sqrt{\,1-x^{2}\,}\right)^{m} + C$, for a suita…

Topic: JEE Main 2019 (11 January Morning Shift)

8

Let $\vec{a}=\hat{i}+2\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+\lambda\hat{j}+4\hat{k}$ and $\vec{c}=2\hat{i}+4\hat{j}+(\lam…

Topic: JEE Main 2019 (11 January Morning Shift)

9

The sum of the real values of $x$ for which the middle term in the binomial expansion of $\left(\dfrac{x^{3}}{3}+\dfrac…

Topic: JEE Main 2019 (11 January Morning Shift)

10

The maximum value of the function $f(x)=3x^{3}-18x^{2}+27x-40$ on the set $S=\{x\in\mathbb{R}: x^{2}+30\le 11x\}$ is :

Topic: JEE Main 2019 (11 January Morning Shift)

1

Let $a_{1},a_{2},\ldots,a_{10}$ be a G.P. If $\dfrac{a_{3}}{a_{1}}=25$, then $\dfrac{a_{9}}{a_{5}}$ equals

Topic: JEE Main 2019 (11 January Morning Shift)

2

Let $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=\dfrac{x}{1+x^{2}},\ x\in\mathbb{R}$. Then the range of $f$ is :

Topic: JEE Main 2019 (11 January Morning Shift)