List of top Questions asked in JEE Main

In the figure shown, what is the current (in Ampere) drawn from the battery ?
You are given: \(R_1 = 15\ \Omega\), \(R_2 = 10\ \Omega\), \(R_3 = 20\ \Omega\), \(R_4 = 5\ \Omega\), \(R_5 = 25\ \Omega\), \(R_6 = 30\ \Omega\), \(E = 15\) V

The tangent and the normal lines at the point \(\left(\sqrt{3}, 1\right)\) to the circle \(x^2 + y^2 = 4\) and the x-axis form a triangle. The area of this triangle (in square units) is :

If the eccentricity of the standard hyperbola passing through the point (4,6) is 2, then the equation of the tangent to the hyperbola at (4,6) is :

The sum \(\sum_{k=1}^{20} k\,\frac{1}{2^k}\) is equal to

The tangent to the parabola \(y^2 = 4x\) at the point where it intersects the circle \(x^2 + y^2 = 5\) in the first quadrant, passes through the point :

Two vertical poles of heights, 20 m and 80 m stand a part on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is :

Which one of the following statements is not a tautology?

If \(z = \frac{\sqrt{3}}{2} + \frac{i}{2}\) (\(i = \sqrt{-1}\)), then \((1 + iz + z^5 + iz^8)^9\) is equal to :

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at \((0, 5\sqrt{3})\), then the length of its latus rectum is :

Let \(f : \mathbb{R} \to \mathbb{R}\) be a differentiable function satisfying \(f^{\prime}(3) + f^{\prime}(2) = 0\). Then \(\lim_{x \to 0}\left(\frac{1 + f(3 + x) - f(3)}{1 + f(2 - x) - f(2)}\right)^{\frac{1}{x}}\) is equal to

Let \(\vec{a} = 3\hat{i} + 2\hat{j} + x\hat{k}\) and \(\vec{b} = \hat{i} - \hat{j} + \hat{k}\), for some real \(x\). Then \(|\vec{a} \times \vec{b}| = r\) is possible if :

Let \(f(x) = a^x\) (\(a \gt 0\)) be written as \(f(x) = f_1(x) + f_2(x)\), where \(f_1(x)\) is an even function of \(f_2(x)\) is an odd function. Then \(f_1(x + y) + f_1(x - y)\) equals

Let \(f : [-1, 3] \to \mathbb{R}\) be defined as
\(f(x) = \begin{cases}|x| + [x], & -1 \le x \lt 1\\ x + |x|, & 1 \le x \lt 2\\ x + [x], & 2 \le x \le 3\end{cases}\)
where \([t]\) denotes the greatest integer less than or equal to \(t\). Then, \(f\) is discontinuous at:

If a point \(R(4, y, z)\) lies on the line segment joining the points \(P(2, -3, 4)\) and \(Q(8, 0, 10)\), then the distance of \(R\) from the origin is :

Let the number \(2, b, c\) be in an A.P. and \(A = \begin{bmatrix}1 & 1 & 1\\ 2 & b & c\\ 4 & b^2 & c^2\end{bmatrix}\). If \(\det(A) \in [2, 16]\), then \(c\) lies in the interval :

If the fourth term in the binomial expansion of \(\left(\sqrt{x^{\left(\frac{1}{1 + \log_{10} x}\right)}} + x^{\frac{1}{12}}\right)^{6}\) is equal to 200, and \(x \gt 1\), then the value of \(x\) is :

A student scores the following marks in five tests : 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is

The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of digits is allowed) is :

Suppose that the points \((h, k)\), \((1, 2)\) and \((-3, 4)\) lie on the line \(L_1\). If a line \(L_2\) passing through the points \((h, k)\) and \((4, 3)\) is perpendicular to \(L_1\), then \(\frac{k}{h}\) equals :

Let \(S(\alpha) = \{(x, y) : y^2 \le x,\ 0 \le x \le \alpha\}\) and \(A(\alpha)\) is area of the region \(S(\alpha)\). If for a \(\lambda\), \(0 \lt \lambda \lt 4\), \(A(\lambda) : A(4) = 2 : 5\), then \(\lambda\) equals

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :

If the system of linear equations
\(x - 2y + kz = 1\)
\(2x + y + z = 2\)
\(3x - y - kz = 3\)
has a solution \((x, y, z)\), \(z \ne 0\), then \((x, y)\) lies on the straight line whose equation is :

100 mL of a water sample contains 0.81 g of calcium bicrabonate and 0.73 g of magnesium bicarbonate. The hardness of this water sample expressed in terms of equivalents of \(\mathrm{CaCO_3}\) is : (Molar mass of calcium bicarbonate is 162 g mol^-1 and magnesium bicarbonate is 146 g mol^-1)

Adsorption of a gas follows freundlich adosorbed isotherm. x is the mass of the gas adsorbed on mass m of the adsorbent. The plot \(\log \frac{x}{m}\) versus \(\log p\) is shown in the given graph. \(\frac{x}{m}\) is proportional to :