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 minimum number of elements required to be added in $R$, in order to make the relation symmetric, is equal to:

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Let $\overrightarrow{AB} = 2\hat{i} + 4\hat{j} - 5\hat{k}$ and $\overrightarrow{AD} = \hat{i} + 2\hat{j} + \lambda \hat…

Topic: JEE Main 2026 (22 January Morning Shift)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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…

Topic: JEE Main 2026 (22 January Morning Shift)