Let $f(x)=a^{x}\ (a>0)$ be written as $f(x)=f_{1}(x)+f_{2}(x)$, where $f_{1}(x)$ is an even function and $f_{2}(x)$ is an odd function. Then $f_{1}(x+y)+f_{1}(x-y)$ equals:

1

If $f(1)=1,\ f'(1)=3$, then the derivative of $f(f(f(x)))+(f(x))^{2}$ at $x=1$ is:

Topic: JEE Main 2019 (8 April Evening Shift)

2

Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function satisfying $f'(3)+f'(2)=0$. Then $\displaystyle \lim_{x\to…

Topic: JEE Main 2019 (8 April Evening Shift)

3

Let $f(x)=\displaystyle\int_{0}^{x} g(t),dt$ where $g$ is a non-zero even function. If $f(x+5)=g(x)$, then $\displaysty…

Topic: JEE Main 2019 (8 April Evening Shift)

4

If three distinct numbers $a,b,c$ are in G.P. and the equations $a x^{2}+2bx+c=0$ and $d x^{2}+2ex+f=0$ have a common r…

Topic: JEE Main 2019 (8 April Evening Shift)

5

If a point $R(4,y,z)$ lies on the line segment joining the points $P(2,-3,4)$ and $Q(8,0,10)$, then the distance of $R$…

Topic: JEE Main 2019 (8 April Evening Shift)

6

Let the numbers $2, b, c$ be in an A.P. and $ A = \begin{bmatrix} 1 & 1 & 1 \\ 2 & b & c \\ 4 & b^2 & c^2 \end{bmatr…

Topic: JEE Main 2019 (8 April Evening Shift)

7

The number of integral values of $m$ for which the equation $(1+m^{2})x^{2}-2(1+3m)x+(1+8m)=0$ has no real root is:

Topic: JEE Main 2019 (8 April Evening Shift)

8

If $z=\dfrac{\sqrt{3}}{2}+\dfrac{i}{2}\ \ (i=\sqrt{-1})$, then $\left(1+iz+z^{5}+iz^{8}\right)^{9}$ is equal to:

Topic: JEE Main 2019 (8 April Evening Shift)

9

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is $10$ and one…

Topic: JEE Main 2019 (8 April Evening Shift)

1

Let $\vec a=3\hat{i}+2\hat{j}+x\hat{k}$ and $\vec b=\hat{i}-\hat{j}+\hat{k}$, for some real $x$. Then $\left|\vec a\tim…

Topic: JEE Main 2019 (8 April Evening Shift)

2

If the fourth term in the binomial expansion of $\left(\sqrt{,x^{\frac{1}{1+\log_{10}x}}+x^{\frac{1}{12}},}\right)^{6}$…

Topic: JEE Main 2019 (8 April Evening Shift)

3

Let $S(\alpha)={(x,y):, y^{2}\le x,\ 0\le x\le \alpha}$ and $A(\alpha)$ be the area of the region $S(\alpha)$. If for a…

Topic: JEE Main 2019 (8 April Evening Shift)

4

If the system of linear equations$x-2y+kz=1$$2x+y+z=2$$3x-y-kz=3$has a solution $(x,y,z)$ with $z\ne0$, then $(x,y)$ li…

Topic: JEE Main 2019 (8 April Evening Shift)

5

A student scores the following marks in five tests: $45,,54,,41,,57,,43$. His score is not known for the sixth test. If…

Topic: JEE Main 2019 (8 April Evening Shift)

6

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at le…

Topic: JEE Main 2019 (8 April Evening Shift)

7

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius $3$ is:

Topic: JEE Main 2019 (8 April Evening Shift)

8

The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0,1,2,3,4,5$ (repeti…

Topic: JEE Main 2019 (8 April Evening Shift)

9

Suppose the points $(h,k)$, $(1,2)$ and $(-3,4)$ lie on the line $L_1$. If a line $L_2$ passing through the points $(h,…

Topic: JEE Main 2019 (8 April Evening Shift)

10

If $\displaystyle \int \frac{dx}{x^{3}(1+x^{6})^{2/3}}=x,f(x),(1+x^{6})^{1/3}+C$ where $C$ is a constant of integration…

Topic: JEE Main 2019 (8 April Evening Shift)