Let $a,b$ be distinct positive reals. The $11^{\text{th}}$ term of a GP with first term $a$ and third term $b$ equals the $p^{\text{th}}$ term of another GP with first term $a$ and fifth term $b$. Then $p$ equals:

1

Let $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=\dfrac{x}{(1+2x^{4})^{1/4}}$, and $g(x)=f(f(f(f(x))))$. Then $18\di…

Topic: JEE Main 2024 (30 January Morning Shift)

2

The area (in square units) of the region bounded by the parabola $y^{2}=4(x-2)$ and the line $y=2x-8$ is:

Topic: JEE Main 2024 (30 January Morning Shift)

3

Let $S_n$ denote the sum of first $n$ terms of an arithmetic progression. If $S_{20}=790$ and $S_{10}=145$, then $S_{15…

Topic: JEE Main 2024 (30 January Morning Shift)

4

If the domain of the function $f(x)=\cos^{-1}!\left(\dfrac{2-|x|}{4}\right)+{\log_e(3-x)}^{-1}$ is $[-\alpha,\beta)-{\g…

Topic: JEE Main 2024 (30 January Morning Shift)

5

If $2\sin^3x+\sin2x\cos x+4\sin x-4=0$ has exactly $3$ solutions in the interval $\left[0,\dfrac{n\pi}{2}\right],,n\in\…

Topic: JEE Main 2024 (30 January Morning Shift)

6

If $z=x+iy$ with $xy\ne0$ satisfies $z^{2}+i\overline{z}=0$, then $|z^{2}|$ equals:

Topic: JEE Main 2024 (30 January Morning Shift)

7

Let $y=y(x)$ be the solution of the differential equation $\sec x,dy+{2(1-x)\tan x+x(2-x)},dx=0$ with $y(0)=2$. Then $y…

Topic: JEE Main 2024 (30 January Morning Shift)

8

Let $A(2,3,5)$ and $C(-3,4,-2)$ be opposite vertices of a parallelogram $ABCD$. If the diagonal $\overrightarrow{BD}= \…

Topic: JEE Main 2024 (30 January Morning Shift)

9

Two integers $x$ and $y$ are chosen with replacement from the set ${0,1,2,3,\ldots,10}$. Then the probability that $|x-…

Topic: JEE Main 2024 (30 January Morning Shift)

10

If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity …

Topic: JEE Main 2024 (30 January Morning Shift)