Let three vectors $\vec a=\alpha\hat i+4\hat j+2\hat k,;\vec b=5\hat i+3\hat j+4\hat k,;\vec c=x\hat i+y\hat j+z\hat k$ form a triangle such that $\vec c=\vec a-\vec b$ and the area of the triangle is $5\sqrt{6}$. If $\alpha$ is a positive real number, then $\lvert\vec c\rvert$ is equal to:

1

If the domain of the function $f(x)=\sin^{-1}!\left(\dfrac{x-1}{2x+3}\right)$ is $\mathbb{R}-(\alpha,\beta)$, then $12\…

Topic: JEE Main 2024 (9 April Morning Shift)

1

Let $f(x)=ax^{3}+bx^{2}+cx+41$ be such that $f(1)=40,; f'(1)=2$ and $f''(1)=4$. Then $a^{2}+b^{2}+c^{2}$ is equal to:

Topic: JEE Main 2024 (9 April Morning Shift)

2

The parabola $y^{2}=4x$ divides the area of the circle $x^{2}+y^{2}=5$ in two parts. The area of the smaller part is eq…

Topic: JEE Main 2024 (9 April Morning Shift)

3

The solution of the differential equation $(x^{2}+y^{2}),dx-5xy,dy=0,; y(1)=0,$ is:

Topic: JEE Main 2024 (9 April Morning Shift)

4

Let $\lvert\cos\theta,\cos(60^\circ-\theta),\cos(60^\circ+\theta)\rvert\le \dfrac{1}{8},;\theta\in[0,2\pi]$. Then the s…

Topic: JEE Main 2024 (9 April Morning Shift)

5

If the sum of the series $ \dfrac{1}{1(1+d)} + \dfrac{1}{(1+d)(1+2d)} + \dots + \dfrac{1}{(1+9d)(1+10d)} $ is equal to …

Topic: JEE Main 2024 (9 April Morning Shift)

6

The coefficient of $x^{70}$ in $ x^{2}(1+x)^{98} + x^{3}(1+x)^{97} + x^{4}(1+x)^{96} + \dots + x^{54}(1+x)^{46} $ is $ …

Topic: JEE Main 2024 (9 April Morning Shift)

7

The frequency distribution of the age of students in a class of 40 students is given below.If the mean deviation about …

Topic: JEE Main 2024 (9 April Morning Shift)

8

Let a circle passing through $(2, 0)$ have its centre at the point $(h, k)$. Let $(x_c, y_c)$ be the point of intersect…

Topic: JEE Main 2024 (9 April Morning Shift)

9

Let $ \displaystyle \int \frac{2 - \tan x}{3 + \tan x} , dx = \frac{1}{2} \left( \alpha x + \log_e \left| \beta \sin x …

Topic: JEE Main 2024 (9 April Morning Shift)

10

Let $\alpha, \beta$ be the roots of the equation $ x^{2} + 2\sqrt{2}x - 1 = 0 $. The quadratic equation whose roots are…

Topic: JEE Main 2024 (9 April Morning Shift)