List of top Questions asked in JEE Main, KCET

Suppose that two chords, drawn from the point (1, 2) on the circle \(x^2 + y^2 + x - 3y = 0\) are bisected by the y-axis. If the other ends of these chords are R and S, and the midpoint of the line segment RS is \((\alpha, \beta)\), then \(6(\alpha + \beta)\) is equal to:

Let the vertex A of a triangle ABC be (1, 2), and the mid-point of the side AB be (5, -1). If the centroid of this triangle is (3, 4) and its circumcenter is \((\alpha, \beta)\), then \(2(10\alpha + \beta)\) is equal to:

Let the line \(L_1 : x + 3 = 0\) intersect the lines \(L_2 : x - y = 0\) and \(L_3 : 3x + y = 0\) at the points A and B, respectively. Let the bisector of the obtuse angle between the lines \(L_2\) and \(L_3\) intersect the line \(L_1\) at the point C. Then \(BC^2 : AC^2\) is equal to:

Suppose that the mean and median of the non-negative numbers 21, 8, 17, \(a\), 51, 103, \(b\), 13, 67, \((a>b)\), are 40 and 21, respectively. If the mean deviation about the median is 26, then \(2a\) is equal to:

Let the smallest value of \(k \in \mathbb{N}\), for which the coefficient of \(x^3\) in \((1+x)^3 + (1+x)^4 + (1+x)^5 + \dots + (1+x)^{99} + (1 + kx)^{100}\), \(x \neq 0\), is \((43n + \frac{101}{4}) \binom{100}{3}\) for some \(n \in \mathbb{N}\), be \(p\). Then the value of \(p + n\) is:

The number of ways of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

Let \(A = \begin{bmatrix} 1 & 1 & 2 \\ -2 & 0 & 1\\ 1 & 3 & 5 \end{bmatrix}\). Then the sum of all elements of the matrix \(\operatorname{adj}(\operatorname{adj}(2(\operatorname{adj}A)^{-1}))\) is equal to:

Let \(S = \left\{ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} : a, b, c, d \in \{0, 1, 2, 3, 4\} \text{ and } A^2 - 4A + 3I = 0 \right\}\) be a set of \(2 \times 2\) matrices. Then the number of matrices in \(S\), for which the sum of the diagonal elements is equal to 4, is:

The number of functions \(f: \{1, 2, 3, 4\} \rightarrow \{a, b, c\}\), which are not onto, is:

Let \(z\) be a complex number such that \(|z + 2| = |z - 2|\) and \(\arg\left(\frac{z+3}{z-i}\right) = \frac{\pi}{4}\). Then \(|z|^2\) is equal to:

Let [·] denote the greatest integer function. If the domain of the function \[ f(x) = \cos^{-1}\left(\frac{4x + 2\lfloor x \rfloor}{3}\right) \] is \([\alpha, \beta]\), then \(12(\alpha + \beta)\) is equal to:

Two identical long current carrying wires are bent into the shapes shown. If the magnitude of magnetic fields at the centres \(P\) and \(Q\) of a semicircular arc are \(B_1\) and \(B_2\) respectively, then the ratio \( \dfrac{B_1}{B_2} \) is:

When a coil is placed in a time dependent magnetic field the power dissipated in it is \(P\). The number of turns, area of the coil and radius of the coil wire are \(N, A\) and \(r\) respectively. For a second coil the number of turns, area of the coil and radius of the coil wire are \(2N, 2A\) and \(3r\) respectively. If the first coil is replaced with second coil the power dissipated in it is \(\sqrt{2}\alpha P\). The value of \(\alpha\) is:

For the given circuit (shown in part A) the time dependent input voltage \(v_{in}(t)\) and corresponding output \(v_o(t)\) are shown in parts (B) and (C), respectively. Identify the components that are used in the circuit between \(X\) and \(Y\).}

Two short electric dipoles \(A\) and \(B\) having dipole moments \(p_1\) and \(p_2\) respectively are placed with their axes mutually perpendicular as shown in the figure. The resultant electric field at a point \(x\) is making an angle of \(60^\circ\) with the line joining points \(O\) and \(x\). The ratio of dipole moments \( \dfrac{p_2}{p_1} \) is:

The equation of a plane progressive wave is given by} \[ y = 5\cos\pi\left(200t - \frac{x}{150}\right) \] where \(x\) and \(y\) are in cm and \(t\) is in seconds. The velocity of the wave is ____ m/s.

Two charged conducting spheres \(S_1\) and \(S_2\) of radii \(8\) cm and \(18\) cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on \(S_1\) and \(S_2\) spheres are \(E_{S_1}\) and \(E_{S_2}\) respectively. The value of \( \dfrac{E_{S_1}}{E_{S_2}} \) is:

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of \( \Delta Q : \Delta U : \Delta W \) is:

A parallel plate air capacitor has a capacitance \(C\). When it is half filled as shown in the figure with a dielectric constant \(K=5\), the percentage increase in the capacitance is:

The position of an object having mass \(0.1\) kg as a function of time \(t\) is given as} \[ \vec r = (10t^2\hat{i}+5t^3\hat{j})\ \text{m}. \] At \(t=1\) s, which of the following statements are correct?} A.} Linear momentum \( \vec p = (2\hat{i}+1.5\hat{j})\) kg m/s. B.} Force acting on the object \( \vec F = (2\hat{i}+3\hat{j})\) N. C.} Angular momentum about origin \( \vec L = 15\hat{k}\) J s. D.} Torque about origin \( \vec \tau = 20\hat{k}\) N m. Choose the correct answer.

The velocity of a particle is given as} \[ \vec{v}=-x\hat{i}+2y\hat{j}-z\hat{k}\ \text{m/s}. \] The magnitude of acceleration at the point \((1,2,4)\) is _____ m/s\(^2\).

The diameter of a wire measured by a screw gauge of least count \(0.001\) cm is \(0.08\) cm. The length measured by a scale of least count \(0.1\) cm is \(150\) cm. When a weight of \(100\) N is applied to the wire, the extension in length is \(0.5\) cm measured by a micrometer of least count \(0.001\) cm. The error in the measured Young’s modulus is \(\alpha \times 10^9\) N/m\(^2\). The value of \(\alpha\) is:

The dimensional formula of \( \frac{1}{2}\varepsilon_0 E^2 \) (\(\varepsilon_0\) = permittivity of vacuum and \(E\) = electric field) is \(M^aL^bT^c\). The value of \(2a-b+c\) is:

If \[ \alpha=\int_{0}^{2\sqrt{3}} \log_2(x^2+4)\,dx + \int_{2}^{4} \sqrt{2^x-4}\,dx, \] then \(\alpha^2\) is equal to _____.