Let $[x]$ denote the greatest integer function, and let $m$ and $n$ respectively be the numbers of the points where the function $f(x) = [x] + |x - 2|$, $-2 < x < 3$, is not continuous and not differentiable. Then $m + n$ is equal to:

1

Group $A$ consists of $7$ boys and $3$ girls, while group $B$ consists of $6$ boys and $5$ girls. The number of ways $4…

Topic: JEE Main 2025 (24 January Evening Shift)

2

Let the points $\left(\dfrac{11}{2},,\alpha\right)$ lie on or inside the triangle with sides $x+y=11$, $x+2y=16$ and $2…

Topic: JEE Main 2025 (24 January Evening Shift)

3

The equation of the chord of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$, whose mid-point is $(3,1)$, is:

Topic: JEE Main 2025 (24 January Evening Shift)

4

Let $\vec a = 3\hat{i}-\hat{j}+2\hat{k}$, $\vec b=\vec a \times (\hat{i}-2\hat{k})$ and $\vec c=\vec b \times \hat{k}$.…

Topic: JEE Main 2025 (24 January Evening Shift)

5

If the equation of the parabola with vertex $V!\left(\frac{3}{2},,3\right)$ and directrix $x+2y=0$ is $\alpha x^2+\beta…

Topic: JEE Main 2025 (24 January Evening Shift)

6

If $7 = 5 + \frac{1}{7}(5+\alpha) + \frac{1}{7^2}(5+2\alpha) + \frac{1}{7^3}(5+3\alpha) + \cdots$, then the value of $\…

Topic: JEE Main 2025 (24 January Evening Shift)

7

Let the position vectors of three vertices of a triangle be $4\vec p+\vec q-3\vec r$, $-5\vec p+\vec q+2\vec r$ and $2\…

Topic: JEE Main 2025 (24 January Evening Shift)

8

Suppose $A$ and $B$ are the coefficients of $30^{\text{th}}$ and $12^{\text{th}}$ terms respectively in the binomial ex…

Topic: JEE Main 2025 (24 January Evening Shift)

9

If the system of equations $x+2y-3z=2$, $2x+\lambda y+5z=5$, $14x+3y+\mu z=33$ has infinitely many solutions, then $\la…

Topic: JEE Main 2025 (24 January Evening Shift)

10

If $\alpha>\beta>\gamma>0$, then the expression $\cot ^{-1}\left\{\beta+\frac{\left(1+\beta^2\right)}{(\alpha-\beta)}\r…

Topic: JEE Main 2025 (24 January Evening Shift)

1

The number of real solution(s) of the equation $x^2 + 3x + 2 = \min{|x - 3|,; |x + 2|}$ is:

Topic: JEE Main 2025 (24 January Evening Shift)

2

Let $f:(0,\infty)\to\mathbb{R}$ be a function which is differentiable at all points of its domain and satisfies the con…

Topic: JEE Main 2025 (24 January Evening Shift)

3

The function $f:(-\infty,\infty)\to(-\infty,1)$, defined by $f(x)=\dfrac{2^x-2^{-x}}{2^x+2^{-x}}$, is:

Topic: JEE Main 2025 (24 January Evening Shift)