List of top Questions asked in JEE Main, KCET

\( \int_{-\pi/4}^{\pi/4} \frac{32 \cos^4 \theta}{1 + e^{\sin \theta}} \, d\theta \) is equal to:

In an AC series circuit supply voltage \(V_{\text{rms}} = 100\) volts; \(R = 80\,\Omega\), \(X_L = 80\,\Omega\) and source frequency is \(f = 50\) Hz. Find the power factor.

An object is placed in air (\(n_1 = 1\)) at a distance \(4R\) from a spherical refracting surface that separates air from a medium of refractive index \(n_2 = 1.4\). The surface has a radius of curvature \(R\), with its centre lying in the second medium. Find the magnitude of magnification of the image formed.

In the expansion of \( (1 + \alpha x)^{26} \) and \( (1 - \alpha x)^{28} \), the coefficient of the middle term is the same, then the value of \( \alpha \) is:

A block of mass \(m\) is released from height \(h\) on a smooth plane. If the normal force on the top of the circular part is \(3mg\), find \(h\).

Consider the reaction:

Find the number of moles of benzene formed if the efficiency of reaction is 60%.

The value of \( \lim_{x \to 0} \frac{x^2 \sin^2 x}{x^2 - \sin^2 x} \) is equal to:

Electric field at the centre of a semi-circular ring of radius \(10\,\text{cm}\) is \(100\,\text{V/m}\). Find the charge on the ring if the charge distribution is uniform.

Select the correct statements : (a) Glucose has 2 anomeric forms.
(b) Both forms have difference in configuration at \(C_1\) carbon.
(c) \(\alpha\)-form has more melting point than \(\beta\)-form.
(d) Specific rotation of \(\alpha\)-form is \(+19^\circ\) and \(\beta\)-form has \(+112^\circ\).
(e) \(\alpha\)-form crystallises at \(307^\circ\) and \(\beta\)-form crystallises at \(371^\circ\).

Find dimensions of \( \dfrac{A}{B} \) if \[ \left( P + \frac{A^2}{B} \right) + \frac{1}{2}\rho V^2 = \text{constant}, \] where \( P \rightarrow \) pressure, \( \rho \rightarrow \) density, \( V \rightarrow \) speed.

In a screw gauge, when the circular scale is given five complete rotations, it moves linearly by \(2.5\,\text{mm\). If the circular scale has 100 divisions, the least count of the screw gauge is:}

The reaction follows 1st order reaction \( \text{R} \rightarrow \text{P} \) Find the fraction of molecules dissociated in time \( t \). \([k_1 = \text{Rate constant}]\)

Statement-1: Heat capacity at constant volume is always greater than heat capacity at constant pressure.
Statement-2: At constant volume as work done is zero, heat given to the chaotic motion is reflected by increase in temperature.

An ideal gas is placed in a container at \( (P_1, V_1, T_1) \) and another ideal gas is placed in a different container at \( (P_2, V_2, T_2) \) are mixed at final pressure of \( P \) and final volume of \( V \). Calculate the final temperature.

Consider the differential equation $\frac{dy}{dx} = (x^2 + x + 1)(y^2 - y + 1)$. If $y(0) = \frac{1}{2}$, then the value of $2(y(1)) - 1$ is

If coefficient of $x^3$ in $(1+x)^3 + (1+x)^4 + \dots + (1+x)^{99} + (1+kx)^{100}$ is $\binom{100}{3} \left( \frac{101}{4} - 43n \right)$, then the value of $(k^3 + 43n)$ is

For the reaction
\[ \text{A} + \text{B} \rightleftharpoons \text{C}, \quad K_p = 2.7 \times 10^{-5} \] Calculate \( K_p \) for the reaction
\[ \frac{1}{3} \text{A} + \frac{1}{3} \text{B} \rightleftharpoons \frac{1}{3} \text{C} \]

Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{a, b, c\}$ then total number of functions from $A$ to $B$ which are not onto are

If $\int_{-2}^2 ([\sin x] + |x \sin x|) dx = 2 \sin 2 - 4 \cos 2 - \beta$, then the value of $|\beta|$ where $[\cdot]$ is GIF is

Length of rods are \( \ell \) and \(2\ell\) respectively and their Young's modulus are \( \gamma \) and \(2\gamma\) respectively. Given: \[ \ell = 0.314\,\text{m}, \quad R = 0.2\,\text{mm} \,(\text{same}), \quad \gamma = 2\times10^9 \]

Find the total extension \( \Delta \ell \).

(A) Bond angle Cr–O–Cr in \( \text{CrO}_7^{2-} \) is 126° (B) \( \text{Na}_2\text{Cr}_2\text{O}_7 \) is used as primary standard solution in titration. (C) \( \text{K}_2\text{Cr}_2\text{O}_7 \) oxidises \( \text{Fe}^{2+} \) into \( \text{Fe}^{3+} \) in acidic medium. (D) \( \text{CrO}_4^{2-} \) and \( \text{Cr}_2\text{O}_7^{2-} \) are interconvertible by changing pH.

Let mean and median of 9 observations 8, 13, a, 17, 21, 51, 103, b, 67 are 40 and 21 respectively where a > b. If mean deviation about median is 26 then 2a is :-