If the domain of the function $f(x)=\log_{(10x^2-17x+7)}(18x^2-11x+1)$ is $(-\infty,a)\cup(b,c)\cup(d,\infty)-{e}$, then $90(a+b+c+d+e)$ equals:

1

Let $\vec a = 2\hat i + \hat j - 2\hat k,; \vec b = \hat i + \hat j$ and $\vec c = \vec a \times \vec b$. Let $\vec d$…

Topic: JEE Main 2026 (24 January Morning Shift)

2

Let $729, 81, 9, 1, \ldots$ be a sequence and $P_n$ denote the product of the first $n$ terms of this sequence. If $2\s…

Topic: JEE Main 2026 (24 January Morning Shift)

3

Let the lines $L_1:\ \vec r=\hat i+2\hat j+3\hat k+\lambda(2\hat i+3\hat j+4\hat k)$ and $L_2:\ \vec r=(4\hat i+\hat…

Topic: JEE Main 2026 (24 January Morning Shift)

4

Let a circle of radius $4$ pass through the origin $O$, the point $A(-\sqrt{3}a,0)$ and $B(0,-\sqrt{2}b)$, where $a$ an…

Topic: JEE Main 2026 (24 January Morning Shift)

5

If the function $f(x)=\dfrac{e^x\left(e^{\tan x}-1\right)+\ln(\sec x+\tan x)-x}{\tan x-x}$ is continuous at $x=0$, then…

Topic: JEE Main 2026 (24 January Morning Shift)

1

Let each of the two ellipses \( E_1:\ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \ (a > b) \) and \( E_2:\ \frac{x^…

Topic: JEE Main 2026 (24 January Morning Shift)

2

The value of $\dfrac{\sqrt{3}\csc20^\circ-\sec20^\circ}{\cos20^\circ\cos40^\circ\cos60^\circ\cos80^\circ}$ is equal t…

Topic: JEE Main 2026 (24 January Morning Shift)

3

Let $S={z\in\mathbb{C}:\left|\frac{z-6i}{z-2i}\right|=1 \text{ and } \left|\frac{z-8+2i}{z+2i}\right|=\frac{3}{5}}$ T…

Topic: JEE Main 2026 (24 January Morning Shift)

4

If $\cot x=\frac{5}{12}$ for some $x\in\left(\frac{\pi}{2},\frac{3\pi}{2}\right)$, then $\sin7x\left(\cos\frac{13x}{2}…

Topic: JEE Main 2026 (24 January Morning Shift)

5

Let $f(t)=\int \frac{1-\sin(\log_e t)}{1-\cos(\log_e t)}dt,; t>1$ If $f(e^{\pi/2})=-e^{-\pi/2}$ and $f(e^{\pi/4})=\al…

Topic: JEE Main 2026 (24 January Morning Shift)

6

Let $R$ be a relation defined on ${1,2,3,4}\times{1,2,3,4}$ by $R={((a,b),(c,d)):2a+3b=3c+4d}$ Then the number of ele…

Topic: JEE Main 2026 (24 January Morning Shift)

7

Let $A(1,0),; B(2,-1)$ and $C\left(\frac{7}{3},\frac{4}{3}\right)$ be three points. If equation of bisector of angle $…

Topic: JEE Main 2026 (24 January Morning Shift)

8

Let $S=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+\cdots$ (13 terms) If $13S=\frac{2^k}{n!}$, then $n+k$ is equal …

Topic: JEE Main 2026 (24 January Morning Shift)

9

Consider an A.P.: $a,a_2,\ldots,a_n$ If $a_2-a_1=-\frac{3}{4},; a_n-a_{n-1}=\frac{1}{4}$ and $\sum a_i=\frac{525}{2}$…

Topic: JEE Main 2026 (24 January Morning Shift)

10

Let \( \alpha, \beta \in \mathbb{R} \) be such that the function \( f(x)= \begin{cases} 2\alpha(x^2-2)+2\beta x, & x

Topic: JEE Main 2026 (24 January Morning Shift)