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 $(h,k)$ and $(4,3)$ is perpendicular to $L_1$, then $\dfrac{k}{h}$ equals:

1

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)

2

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)

3

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)

4

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)

5

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)

6

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)

7

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)

8

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)

9

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 …

Topic: JEE Main 2019 (8 April Evening Shift)

10

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)

1

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)