If the locus of a point whose distances from $(2,1)$ and $(1,3)$ are in the ratio $5:4$ is $ax^{2}+by^{2}+cxy+dx+ey+170=0$, then the value of $a^{2}+2b+3c+4d+e$ is:

1

If $\displaystyle \int \frac{1}{a^{2}\sin^{2}x+b^{2}\cos^{2}x},dx=\frac{1}{12}\tan^{-1}(3\tan x)+\text{constant}$, then…

Topic: JEE Main 2024 (6 April Evening Shift)

2

Let $0\le r\le n$. If ${}^{n+1}C_{r+1} : ^nC_{r} : ^{n-1}C_{r-1} = 55 : 35 : 21$, then $2n+5r$ is equal to:

Topic: JEE Main 2024 (6 April Evening Shift)

3

Suppose for a differentiable function $h$, $h(0)=0$, $h(1)=1$ and $h'(0)=h'(1)=2$. If $g(x)=h(e^{x}),e^{h(x)}$, then $g…

Topic: JEE Main 2024 (6 April Evening Shift)

4

If all words (with or without meaning) formed using all the letters of the word NAGPUR are arranged in dictionary order…

Topic: JEE Main 2024 (6 April Evening Shift)

5

If $P(6,1)$ is the orthocentre of the triangle whose vertices are $A(5,-2)$, $B(8,3)$ and $C(h,k)$, then the point $C$ …

Topic: JEE Main 2024 (6 April Evening Shift)

6

A software company sets up $n$ computer systems to finish an assignment in $17$ days. If $4$ systems crash at the start…

Topic: JEE Main 2024 (6 April Evening Shift)

7

Suppose the solution of the differential equation $ \displaystyle \frac{dy}{dx}=\frac{(2+\alpha)x-\beta y+2}{\beta x-2\…

Topic: JEE Main 2024 (6 April Evening Shift)

8

If the area of the region $\left\{(x, y): \frac{\mathrm{a}}{x^2} \leq y \leq \frac{1}{x}, 1 \leq x \leq 2,0

Topic: JEE Main 2024 (6 April Evening Shift)

9

Let $ABC$ be an equilateral triangle. A new triangle is formed by joining the midpoints of all sides of $\triangle ABC$…

Topic: JEE Main 2024 (6 April Evening Shift)

10

Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(3,-3,1)$ in the line $\dfrac{x-0}{1}=\dfrac{y-3}{1}=\dfrac{z-…

Topic: JEE Main 2024 (6 April Evening Shift)