List of top Questions asked in JEE Main

If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are three non-zero vectors and \(\hat{\mathbf{n}}\) is a unit vector perpendicular to \(\mathbf{c}\) such that: \(\mathbf{a} = \alpha \mathbf{b} - \hat{\mathbf{n}}, \, (\alpha \neq 0)\) and \( \mathbf{b} \cdot \mathbf{c} = 12 \), then \( \mathbf{c} \times (\mathbf{a} \times \mathbf{b}) \) is equal to:

If [t] denotes the greatest integer \(≤ 1\), then the value of \(3\frac{(e - 1)^2}{e}\) is:

Let the solution curve y = y(x) of the differential equation\(\frac{dy}{dx} - \frac{3x^5 \tan^{-1}(x^3)}{(1 + x^6)^{3/2}} y = 2x \exp\left(x^3 - \frac{\tan^{-1}(x^3)}{1 + x}\right)^6\)pass through the origin. Then y(1) is equal to:

A straight line cuts off the intercepts OA = a and OB = b on the positive directions of the x-axis and y-axis, respectively. If the perpendicular from the origin O to this line makes an angle of \(\frac{\pi}{6}\) with the positive direction of the y-axis and the area of △OAB is \(\frac{98\sqrt{3}}{3},\) then a² − b² is equal to:

Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions \(f : S → P(S)\), where \(P(S)\) denotes the power set of S, such that \(f(n) ⊂ f(m)\) where \(n < m,\) is:

Let α be the area of the larger region bounded by the curve y² = 8x and the lines y = x and x = 2, which lies in the first quadrant. Then the value of 3α is equal to:

An electron with energy $01\, keV$ moves at right angle to the earth's magnetic field of $1 \times 10^{-4} Wbm ^{-2}$ The frequency of revolution of the electron will be (Take mass of electron $=90 \times 10^{-31} kg$ )

If $\lambda_1<\lambda_2$ are two values of $\lambda$ such that the angle between the planes $P_1: \vec{r}(3 \hat{i}-5 \hat{j}+\hat{k})=7$ and $P_2: \vec{r} \cdot(\lambda \hat{i}+\hat{j}-3 \hat{k})=9$ is $\sin ^{-1}\left(\frac{2 \sqrt{6}}{5}\right)$, then the square of the length of perpendicular from the point $\left(38 \lambda_1, 10 \lambda_2, 2\right)$ to the plane $P_1$ is _____

Let the lines l₁ :  \(\frac{x+5}{3} =\frac{y+4}{1}=\frac{z−α}{−2}\)  and l₂ :3x+2y+z–2=0=x–3y+2z-13 be coplanar. If the point P(a, b, c) on l₁ is nearest to the point Q(-4,-3, 2), then |a| + |b|+|c| is equal to

An object is taken to a height above the surface of earth at a distance $\frac{5}{4} R$ from the centre of the earth Where radius of earth, $R =6400 km$ The percentage decrease in the weight of the object will be

The sum of the maximum and minimum values of the function |5x-7|+[x²+2x] is the interval $\left[\frac{5}{4}, 2\right]$, where $[t]$ is the greatest integer $\leq t$ is ______

The value of $12 \int\limits_0^3\left|x^2-3 x+2\right| d x$ is

Let $f:(0,1) \rightarrow R$ be a function defined by $f(x)=\frac{1}{1-e^{-x}}$, and $g(x)=(f(-x)-f(x))$ Consider two statements (I) $g$ is an increasing function in $(0,1)$ (II) $g$ is one-one in $(0,1)$Then,

Calculate the ratio of radii of second and third bohr orbit of H-atoms

The electric current in a circular coil of 2 turns produces a magnetic induction $B _1$ at its centre The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction $B _2$ at its centre The ratio of $\frac{ B _2}{ B _1}$ is :

Let 𝛂 be the remainder (22)\(^{2022}\) + (2022)\(^{22}\) is divided by 3 and ꞵ be the remainder when the same is divided by 7 then 𝛂\(^2\) + ꞵ\(^2\) is?

The work function for two metals are 9eV and 4.5eV. Find the approx. difference between their threshold wavelength. (use hc = 1240 eV - nm)

Let the plane P : 4x – y + z = 10 be rotated by an angle \(\frac{π}{2}\) about its line of intersection with the plane x + y – z = 4. If α is the distance of the point (2, 3, -4) from the new position of the plane P, then 35α is

If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are three non-zero vectors and \(\hat{n}\) is a unit vector perpendicular to \(\vec{c}\) such that \(\vec{a}\)=\(\alpha \vec{b}\)-\(\hat{n}\), \(\alpha \neq 0\) and \(\vec{b}\) .\( \vec{c}\)=12, then |\(\vec{c} \times(\vec{a} \times \vec{b})\)| is equal to:

The charge flowing in a conductor changes with time as $Q(t)=\alpha t-\beta t ^2+\gamma^3$ Where $\alpha, \beta$ and $\gamma$ are constants Minimum value of current is :

Choose the correct option. 

Let the area enclosed by the $x$-axis, and the tangent and normal drawn to the curve $4 x^3-3 x y^2+6 x^2-5 x y-8 y^2+9 x+14=0$ at the point $(-2,3)$ be $A$. Then $8 A$ is equal to ______

Let $S$ be the set of all $a \in N$ such that the area of the triangle formed by the tangent at the point $P ( b, c), b, c \in N$, on the parabola $y^2=2$ ax and the lines $x=b, y=0$ is $16$ unit ${ }^2$, then $\displaystyle\sum_{a \in S} a$ is equal to _____