If the four distinct points $(4,6)$, $(-1,5)$, $(0,0)$ and $(k,3k)$ lie on a circle of radius $r$, then $10k+r^2$ is equal to

1

The sum $1+\dfrac{1+3}{2!}+\dfrac{1+3+5}{3!}+\dfrac{1+3+5+7}{4!}+\cdots$ up to $\infty$ terms is equal to

Topic: JEE Main 2025 (3 April Evening Shift)

2

Let $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=\left|,|x+2|-2|x|,\right|$. If $m$ is the number of points of local…

Topic: JEE Main 2025 (3 April Evening Shift)

3

If the domain of the function $f(x)=\log_{7}!\big(1-\log_{4}(x^{2}-9x+18)\big)$ is $(\alpha,\beta)\cup(\gamma,\delta)$,…

Topic: JEE Main 2025 (3 April Evening Shift)

4

The number of solutions of the equation $(4-\sqrt{3})\sin x-2\sqrt{3}\cos^2 x=-\dfrac{4}{1+\sqrt{3}},\ x\in[-2\pi,\tfra…

Topic: JEE Main 2025 (3 April Evening Shift)

5

If the probability that the random variable $X$ takes the value $x$ is given by $P(X=x)=k(x+1)3^{-x},\ x=0,1,2,3,\ldots…

Topic: JEE Main 2025 (3 April Evening Shift)

6

The distance of the point $(7,10,11)$ from the line $\dfrac{x-4}{1}=\dfrac{y-4}{0}=\dfrac{z-2}{3}$ along the line $\dfr…

Topic: JEE Main 2025 (3 April Evening Shift)

7

The integral $\displaystyle \int_{0}^{\pi}\frac{8x,dx}{4\cos^{2}x+\sin^{2}x}$ is equal to

Topic: JEE Main 2025 (3 April Evening Shift)

8

Let the mean and variance of five observations $x_1=1,\ x_2=3,\ x_3=a,\ x_4=7,\ x_5=b,\ a>b$ be $5$ and $10$ respective…

Topic: JEE Main 2025 (3 April Evening Shift)

9

Let $A={-2,-1,0,1,2,3}$. Let $R$ be a relation on $A$ defined by $xRy$ iff $y=\max{x,1}$. Let $l$ be the number of elem…

Topic: JEE Main 2025 (3 April Evening Shift)

10

Let the equation $x(x+2)(12-k)=2$ have equal roots. Then the distance of the point $\left(k,\dfrac{k}{2}\right)$ from t…

Topic: JEE Main 2025 (3 April Evening Shift)