List of top Questions asked in JEE Main, KCET

Ratio of de-Broglie wavelengths of a proton and an alpha particle accelerated through the same potential is:

Two capacitors \( C \) and \( 2C \) charged to \( V \) and \( 2V \) respectively are connected in parallel with opposite polarity. The common potential is:

Minimum deviation for an equilateral prism is 30°, refractive index is:

In a meter bridge experiment to determine the value of unknown resistance, first the resistances \(2\,\Omega\) and \(3\,\Omega\) are connected in the left and right gaps of the bridge and the null point is obtained at a distance \(l\) cm from the left end. Now, when an unknown resistance \(x\,\Omega\) is connected in parallel to \(3\,\Omega\), the null point is shifted by \(10\,\text{cm}\) to the right. The value of \(x\) is ________ \(\Omega\).

An object is being dropped from a height \(h\) above the ground. Apart from the force of gravity, an additional drag force \(F=-kv\) acts on the object. Find the correct graph of velocity \(v\) versus time \(t\).

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed \(v\). If \(x\) is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to \(x^\alpha\), where \(\alpha\) is ______.

In a YDSE set up, a slab of width \( t \) is inserted in front of one slit. The interference pattern shifts by 0.2 cm on the screen. If the refractive index of the slab is 1.5, then \( t \) in \( \mu m \) (screen distance 50 cm and slits separation 1 mm) then \( N \) is ..............

Let \(f\) be a differentiable function satisfying \[ f(x)=1-2x+\int_0^x (t-x)f(t)\,dt,\quad x\in\mathbb{R}, \] and let \[ g(x)=\int_0^x \{f(t)+2\}^5(t-4)^6(t+12)^7\,dt. \] If \(p\) and \(q\) are respectively the points of local minima and local maxima of \(g\), then the value of \(|p+q|\) is _______.

If you draw an object measuring 1 cm on the paper, what would it be equivalent to at a scale of 1:100?

$L, C$ and $R$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $M L^2 T^{-4} A^{-2}$ corresponds to _________.

Number of solutions of \( \sqrt{3} \cos 2\theta + 8 \cos \theta + 3\sqrt{3} = 0, \theta \in [-3\pi, 2\pi] \) is:

A woman, unable to conceive after many years of regular unprotected coitus, went to a specialized clinic. On complete examination, the woman was found to be normal, while the male partner was diagnosed with Infertility and was unable to inseminate the female due to low sperm count. Suggest the appropriate Assisted Reproductive Technology (ART).

If \( \alpha,\beta \) where \( \alpha<\beta \), are the roots of the equation \[ \lambda x^2-(\lambda+3)x+3=0 \] such that \[ \frac{1}{\alpha}-\frac{1}{\beta}=\frac{1}{3}, \] then the sum of all possible values of \( \lambda \) is:

Let M be a $3 \times 3$ matrix such that $M \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}, M \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix}$ and $M \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} -1 \\ 1 \\ 1 \end{pmatrix}$. If $M \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 \\ 7 \\ 11 \end{pmatrix}$, then $x+y+z$ equals :

The vertices B and C of a triangle ABC lie on the line \( \frac{x}{1} = \frac{1-y}{2} = \frac{z-2}{3} \). The coordinates of A and B are (1, 6, 3) and (4, 9, 6) respectively and C is at a distance of 10 units from B. The area (in sq. units) of \( \triangle ABC \) is:

Let chord $PQ$ of length $3\sqrt{13}$ of the parabola $y^2 = 12x$ be such that the ordinates of points $P$ and $Q$ are in the ratio $1:2$. If the chord $PQ$ subtends an angle $\alpha$ at the focus of the parabola, then $\sin \alpha$ is equal to:

If \( \alpha \) and \( \beta \) (\( \alpha<\beta \)) are the roots of the equation \( (-2 + \sqrt{3})(\sqrt{x} - 3) + (x - 6\sqrt{x}) + (9 - 2\sqrt{3}) = 0 \), \( x \ge 0 \), then \( \sqrt{\frac{\beta}{\alpha}} + \sqrt{\alpha\beta} \) is equal to:

If the set of all solutions of \(|x^2 + x - 9| = |x| + |x^2 - 9|\) is \([\alpha, \beta] \cup [\gamma, \infty)\), then \((\alpha^2 + \beta^2 + \gamma^2)\) is equal to:

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are \( 2, 3, 5, 10, 11, 13, 15, 21 \), then the mean deviation about the median of all the 10 observations is:

If $f(x) = \min \{2x^2 + 3, 6x\} + |x-1| \cos(x^2 - \frac{1}{4})$, then the number of points of non derivability of $f(x)$ is/are

An organic compound (P) on treatment with aqueous ammonia under hot condition forms compound (Q) which on heating with Br₂ and KOH forms compound (R) having molecular formula C₆H₇N. Names of P, Q and R respectively are.

Which of the following compounds shows coordination isomerism?
(A) \( [\text{Fe(NH}_3)_6] [\text{Co(CN)}_6] \)
(B) \( [\text{Cr(NH}_3)_6] [\text{Co(CN)}_6] \)
(C) \( [\text{Co(NH}_3)_6] [\text{Co(CN)}_6] \)
(D) \( [\text{Ag(NH}_3)_2] [\text{Ag(CN)}_2] \)
(E) \( [\text{Fe(NH}_3)_6] [\text{Cr(CN)}_6] \)