List of top Questions asked in JEE Main- 2023

If the shortest distance between the lines \(3x+2y-4z-5=0=5x-7y-17z+2\) and \(\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+1}{2}\) is \(\frac{10}{\sqrt{k}}\), then \(k\) is equal to ________.

\(\left(\sin 5^{\circ} \sin 55^{\circ} \sin 65^{\circ} \sin 75^{\circ}\right)^{-1}\) is equal to ________.

For \(p \in \mathbb{N}\), if the angle between pair of tangents drawn to the ellipse \(3x^{2}+2y^{2}=5\) from the point \((1, p)\) is \(\tan^{-1}\left(\frac{12}{\sqrt{5}}\right)\), then the distance of the vertex of the parabola \(y=x^{2}-px+p+1\) from the point \((-7,8)\) is equal to ________.

Let \(f(x)\) be a polynomial of degree 5 such that \(\lim_{x \to 0} \frac{f(x)}{x^{2}}=1\), \(f(-1)=-1\), \(f(x)-14x\) has an extrema at \(x=1\) and \(f(x)-10x\) has an extrema at \(x=-1\). Then \(f(2)\) is equal to ________.

Let three distinct normal be drawn to the parabola \(y^{2}+4y-6x-8=0\) from a point \((a, \mathrm{b})\) on the axis of the parabola. Then :

If the circles \(x^{2}+y^{2}-2 x-4 y+4=0\) and \(x^{2}+y^{2}-6 x-10 y+20+2 \sqrt{13}=0\) touch each other at the point \((a, \mathrm{b})\), then \((3 a-2 \mathrm{b})^{2}\) is equal to :

Given \({}^{n}C_{r}=\frac{n!}{r!(n-r)!}\), \(0 \leq r \leq n\) and n is a non-negative integer. Then a possible value of k for which the equality
\({}^{50}C_{k-1}+\sum_{r=1}^{50}{}^{100-r}C_{k-2}={}^{100}C_{49}\) holds, is

If an unbiased die, marked with \(-3,-2,-1,0,1,2\) on its faces, is thrown four times, then the probability of getting \(-1\) as the sum of outputs is :

If the angle between the line \(l: \frac{x-1}{2}=\frac{y+1}{1}=\frac{z-2}{2}\) and the plane \(\mathrm{P}: \lambda x+4y-7=0,\ \lambda \neq 0\), is \(\operatorname{cosec}^{-1}\left(\frac{3}{2}\right)\), then the sum of co-ordinates of the point where line \(l\) crosses the plane P is :

If \(I(x)=\int \frac{d x}{1-2 \sin ^{2} x \cos ^{2} x}\), then \(\tan \left(\sqrt{2}\left(I\left(\frac{\pi}{8}\right)-I(0)\right)\right)\) is equal to :

If the image of the point \((1,1,2)\) in the plane \(2 x-y+z+3=0\) is the point P, then the distance of P from origin is

If the statement
\(((\mathrm{p} * (\sim \mathrm{q})) \wedge(\mathrm{p} \vee \mathrm{q})) \Leftrightarrow \mathrm{p}\)
is a tautology, then \(*\) is :

Create an interesting sculpture, using basic 3D shapes of sports elements eg. different Balls, Bats etc. You can scale each object to any size of your choice, and use them as per your choice. Draw the effect of light and shadow on your composition. Use colours of your choice.

The domain of the function \(f(x)=\sin ^{-1}\left(\log _{2}((x-1)(x-2))\right)\) is :

Question figure shows 3D view of an object. Identify the most appropriate top view of the given 3D object looking in the direction of an arrow, from the given answers figures.

Draw the Sketch of the given image in detail.

Find out the total number of surfaces of the 3D object.

Identify the number of surfaces in the problem figure.

The question figure shows 3D view of an object. Identify the most appropriate elevation of the given 3D object, looking in the direction of an arrow, from the given answer figures.

The question figure shows the 3D view of an object. Identify the most appropriate view of the object looking in the direction of the arrow.

The question figure shows the 3D view of an object. Identify the most appropriate elevation (front view) looking in the direction of arrow.

The question figure is the 3D view of an object. Identify the most appropriate front view of the object looking in the direction of the arrow.

Let \( \alpha,\beta,\gamma\left(0<\alpha,\beta,\gamma<\frac{\pi}{2}\right) \) be the angles between non-zero vectors \( \vec{a} \) and \( \vec{b} \), \( \vec{b} \) and \( \vec{c} \), \( \vec{c} \) and \( \vec{a} \) respectively. If \( \theta \) is the angle that the vector \( \vec{a} \) makes with the plane containing \( \vec{b} \) and \( \vec{c} \), then

\( \lim_{x\rightarrow0^{+}}\frac{1}{\sqrt{x}}\left(\frac{1}{\sin x}-\frac{1}{x}\right) \)

The slope of the tangent to the curve \( y=y(x)=\int_{\sin^{-1}(x)}^{\cos^{-1}(x)}\sqrt{1+4\sin^{2}t}\,dt\ ;\ 0\le x\le1 \) at the point \( \left(\frac{1}{\sqrt{2}},0\right) \) on the curve is :