List of top Questions asked in JEE Main

From the photoelectric effect experiment, following observations are made Identify which of these are correct
A. The stopping potential depends only on the work function of the metal
B. The saturation current increases as the intensity of incident light increases
C. The maximum kinetic energy of a photo electron depends on the intensity of the incident light
D. Photoelectric effect can be explained using wave theory of light
Choose the correct answer from the options given below:

Statement I: For colloidal particles, the values of colligative properties are of small order as compared to values shown by true solutions at the same concentration
Statement II: For colloidal particles, the potential difference between the fixed layer and the diffused layer of the same charges is called the electrokinetic potential or zeta potential
In the light of the above statements, choose the correct answer from the options given below

Correct statement is:

Let $\vec{\alpha}=4 \hat{i}+3 \hat{j}+5 \hat{k}$ and $\vec{\beta}=\hat{i}+2 \hat{j}-4 \hat{k}$ Let $\vec{\beta}_1$ be parallel to $\vec{\alpha}$ and $\vec{\beta}_2$ be perpendicular to $\vec{\alpha}$ If $\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2$, then the value of $5 \vec{\beta}_2 \cdot(\hat{i}+\hat{j}+\hat{k})$ is

The value of the integral:$\int\limits_{\frac{3 \sqrt{2}}{4}}^{\frac{3 \sqrt{3}}{4}} \frac{48}{\sqrt{9-4 x^2}} d x$ is equal to

Let $p$ and $q$ be two statements Then $\sim(p \wedge(p \Rightarrow \sim q))$ is equivalent to

The ratio of wavelengths of proton and deuteron accelerated by potential $V_p$ and $V_d$ is $1: \sqrt{2}$ Then, the ratio of $V_p$ to $V_d$ will be

$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)$is equal to

The number of molecules from the following which contain only two lone pair of electrons is _____ .
$H_2O, N_2, CO, XeF_4, NH_3, NO, CO_2, F_2$

The number of elements in the set $\{n ∈ Z : n^2-10n+19| < 6\}$ is __.

Let the plane P pass through the intersection of the planes $2 x+3 y-z=2$and $x+2 y+3 z=6,$ and be perpendicular to the plane $2 x+y-z+1=0$If d is the distance of P from the point (-7,1,1), then $d^2$ is equal to :

Let A,B,C be 3×3 matrices such that A is symmetric and B and C are skew symmetric. Consider the statements:
(S1) A¹³B²⁶ − B²⁶A¹³ is symmetric.
(S2) A²⁶C¹³ − C¹³A²⁶ is symmetric.Then:

The number of functions $f:\{1,2,3,4\} \rightarrow\{ a \in: Z|a| \leq 8\}$ satisfying $f(n)+\frac{1}{n} f( n +1)=1, \forall n \in\{1,2,3\}$ is

Let $\vec{a}=-\hat{i}-\hat{j}+\hat{k}, \vec{a} \cdot \vec{b}=1$ and $\vec{a} \times \vec{b}=\hat{i}-\hat{j}$. Then $\vec{a}-6 \vec{b}$ is equal to

Let f: R→R be a function such that $f(x)=\frac{x^2+2x+1}{x^2+1}$. Then

Let $ \mathbf{a} $ be a non-zero vector parallel to the line of intersection of the two planes described by $ i + j + k $ and $ -i - j - k $. If $ \theta $ is the angle between the vector $ \mathbf{a} $ and the vector $ \mathbf{b} = -2i - 2j + 2k $, and $ \left| \mathbf{a} \right| = 6 $, then ordered pair $ (\mathbf{a} \cdot \mathbf{b}) $ is equal to:

Let $T$ and $C$ respectively be the transverse and conjugate axes of the hyperbola $16 x^2-y^2+64 x+4 y$ $+44=0$. Then the area of the region above the parabola $x^2=y+4$, below the transverse axis $T$ and on the right of the coujugate axis $C$ is:

Let $P(x_0, y_0)$ be the point on the hyperbola $3x^2 - 4y^2 = 36$, which is nearest to the line $3x + 2y = 1$. Then $\sqrt{2}(y_0 - x_0)$ is equal to:

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:

the points P and Q are respectively the circumcentre and the orthocentre of a ΔABC, then $ \overrightarrow{PA}+ \overrightarrow{PB}+ \overrightarrow{PC}$ is

If the local maximum value of the function f( x )=$(\frac{√3e}{2 sin x} )^{ sin^2x}$ ,$ x ∈ ( 0,\frac{π}{2} )$, is $\frac{k}{e}$, then $(\frac{k}{e})^8+\frac{k^8}{e^5}+k^8 $ is equal to

Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of $100$ consecutive positive integers $a_1, a_2, a_3, \ldots , a_{100}$ is $25$ Then $S$ is

Let $f(x)$ be a function such that $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in$ N If $f(1)=3$ and $\displaystyle\sum_{k=1}^n f(k)=3279$, then the value of $n$ is

Let $x, y, z>1$ and $A=\begin{bmatrix}1 & \log _x y & \log _x z \\ \log _y x & 2 & \log _y z \\ \log _z x & \log _z y & 3\end{bmatrix}$ Then ∣adj(adjA2)∣ is equal to

If $\lim\limits_{x\rightarrow0}\frac{e^{ax}-\cos(bx)-\frac{cxe^{-ce}}{2}}{1-\cos(2x)}=17$ ,then 5a² + b² is equal to