Let the set of all values of $r$, for which the circles $(x + 1)^2 + (y + 4)^2 = r^2$ and $x^2 + y^2 - 4x - 2y - 4 = 0$ intersect at two distinct points be the interval $(\alpha, \beta)$. Then $\alpha\beta$ is equal to
Previous 10 Questions — JEE Main 2026 (22 January Morning Shift)
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If the image of the point $P(1, 2, a)$ in the line
$\frac{x-6}{3} = \frac{y-7}{2} = \frac{z-7}{-2}$
is $Q(5, b, c)$, …
Topic: JEE Main 2026 (22 January Morning Shift)
If the line $\alpha x + 2y = 1$, where $\alpha \in \mathbb{R}$, does not meet the hyperbola $x^2 - 9y^2 = 9$, then a po…
Topic: JEE Main 2026 (22 January Morning Shift)
Let $f : [1,\infty) \to \mathbb{R}$ be a differentiable function. If
$6\int_{1}^{x} f(t),dt = 3xf(x) + x^3 - 4$ for al…
Topic: JEE Main 2026 (22 January Morning Shift)
The number of distinct real solutions of the equation x|x+4| + 3|x+2| + 10 = 0 is
Topic: JEE Main 2026 (22 January Morning Shift)
If a random variable $x$ has the probability distributionthen $P(3 < x \le 6)$ is equal to:
Topic: JEE Main 2026 (22 January Morning Shift)
Let $P(\alpha,\beta,\gamma)$ be the point on the line
$\frac{x-1}{2} = \frac{y+1}{-3} = z$
at a distance $4\sqrt{14}$…
Topic: JEE Main 2026 (22 January Morning Shift)
Let $f(x) = x^{2025} - x^{2000},; x \in [0,1]$ and maximum value of the function $f(x)$ in the interval $[0,1]$ be $\le…
Topic: JEE Main 2026 (22 January Morning Shift)
Two distinct numbers a and b are selected at random from 1,2,3, ... ,50. The probability that their product ab is divis…
Topic: JEE Main 2026 (22 January Morning Shift)
Let the line $x = -1$ divide the area of the region
${(x,y) : 1 + x^2 \le y \le 3 - x}$
in the ratio $m : n$, $\gcd(m,n…
Topic: JEE Main 2026 (22 January Morning Shift)
Let the relation $R$ on the set $M = {1,2,3,\ldots,16}$ be given by
$R = {(x,y) : 4y = 5x - 3,; x,y \in M}$.
Then the…
Topic: JEE Main 2026 (22 January Morning Shift)
Next 10 Questions — JEE Main 2026 (22 January Morning Shift)
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If $A = \begin{bmatrix} 2 & 3 \ 3 & 5 \end{bmatrix}$, then the determinant of the matrix
$(A^{2025} - 3A^{2024} + A^{2…
Topic: JEE Main 2026 (22 January Morning Shift)
If the domain of the function
$f(x) = \sin^{-1}\left(\frac{5 - x}{3 + 2x}\right) + \log\left(\frac{1}{10 - x}\right)$
…
Topic: JEE Main 2026 (22 January Morning Shift)
The value of $\displaystyle \int_{-\pi/2}^{\pi/2} \frac{1}{[x] + 4},dx$, where $[\cdot]$ denotes the greatest integer f…
Topic: JEE Main 2026 (22 January Morning Shift)
The coefficient of $x^{48}$ in $(1 + x)^2(1 + x^2 + 3(1 + x)^3 + \cdots + 100(1 + x)^{100})$ is equal to
Topic: JEE Main 2026 (22 January Morning Shift)
If the chord joining the points $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ on the parabola $y^2 = 12x$ subtends a right angle at…
Topic: JEE Main 2026 (22 January Morning Shift)
The number of solutions of $\tan^{-1}(4x) + \tan^{-1}(6x) = \frac{\pi}{6}$, where $-\frac{1}{2\sqrt{6}} < x < \frac{1}{…
Topic: JEE Main 2026 (22 January Morning Shift)
Let the solution curve of the differential equation$xdy - ydx = \sqrt{x^2 + y^2},dx,; x>0,; y(1)=0$be $y = y(x)$. Th…
Topic: JEE Main 2026 (22 January Morning Shift)
If the sum of the first four terms of an A.P. is $6$ and the sum of its first six terms is $4$, then the sum of its fir…
Topic: JEE Main 2026 (22 January Morning Shift)
Let $\alpha = \frac{-1 + i\sqrt{3}}{2}$ and $\beta = \frac{-1 - i\sqrt{3}}{2}$, $i = \sqrt{-1}$. If
$(7 - 7\alpha + 9\…
Topic: JEE Main 2026 (22 January Morning Shift)
22. Let A be a 3 × 3 matrix such that A + A^T = O. If
$$
A \begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix}
= \begin{bmatrix…
Topic: JEE Main 2026 (22 January Morning Shift)
