List of top Questions asked in JEE Main

A letter 'A' is constructed of a uniform wire with resistance 1.0 \(\Omega\) per cm, The sides of the letter are 20 cm and the cross piece in the middle is 10 cm long. The apex angle is \(60^\circ\). The resistance between the ends of the legs is close to:

When two sound waves travel in the same direction in a medium, the displacements of a particle located at \(x\) at time \(t\) is given by :
\(y_1 = 0.05\cos(0.50\pi x - 100\pi t)\)
\(y_2 = 0.05\cos(0.46\pi x - 92\pi t)\)
where \(y_1\), \(y_2\) and \(x\) are in meters and \(t\) in seconds. The speed of sound in the medium is :

Figure shows the variation in temperature (\(\Delta T\)) with the amount of heat supplied (\(Q\)) in an isobaric process corresponding to a monoatomic (M), diatomic (D) and a polyatomic (P) gas. The initial state of all the gases are the same and the scales for the two axes coincide. Ignoring vibrational degrees of freedom, the lines \(a\), \(b\) and

\(c\) respectively correspond to :

Two simple pendulums of length 1 m and 4 m respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed number of oscillations equal to:

There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment 1 is filled with an ideal gas and Compartment 3 is filled with a real gas. Compartments 2 and 4 are vacuum. A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum.
Statement-1: No change in the temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands in vacuum.
Statement-2: The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential.

The probability of a man hitting a target is \(\frac{2}{5}\). He fires at the target \(k\) times (\(k\), a given number). Then the minimum \(k\), so that the probability of hitting the target at least once is more than \(\frac{7}{10}\), is :

A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it will be :

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement-1: A capillary is dipped in a liquid and liquid rises to a height \(h\) in it. As the temperature of the liquid is raised, the height \(h\) increases (if the density of the liquid and the angle of contact remain the same).
Statement-2: Surface tension of a liquid decreases with the rise in its temperature.

From the following, the quantity (constructed from the basic constants of nature), that has the dimensions, as well as correct order of magnitude, vis-a-vis typical atomic size, is:

If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are \(a\), \(b\) and \(c\) respectively,

then the corresponding ratio of increase in their lengths is :

Two springs of force constants 300 N/m (Spring A) and 400 N/m (Spring B) are joined together in series. The combination is compressed by 8.75 cm. The ratio of energy stored in A and B is \(\frac{E_A}{E_B}\). Then \(\frac{E_A}{E_B}\) is equal to:

A vector \(\vec{n}\) is inclined to \(x\)-axis at \(45^\circ\), to \(y\)-axis at \(60^\circ\) and at an acute angle to \(z\)-axis. If \(\vec{n}\) is a normal to a plane passing through the point \((\sqrt{2}, -1, 1)\) then the equation of the plane is :

If the lines \(\frac{x+1}{2} = \frac{y-1}{1} = \frac{z+1}{3}\) and \(\frac{x+2}{2} = \frac{y-k}{3} = \frac{z}{4}\) are coplanar, then the value of \(k\) is :

If \(x=\int_0^y\frac{dt}{\sqrt{1+t^2}}\), then \(\frac{d^2y}{dx^2}\) is equal to :

The area bounded by the curve \(y = \ln(x)\) and the lines \(y = 0\), \(y = \ln(3)\) and \(x = 0\) is equal to:

Let \(\vec{a} = 2\hat{i} - \hat{j} + \hat{k}\), \(\vec{b} = \hat{i} + 2\hat{j} - \hat{k}\) and \(\vec{c} = \hat{i} + \hat{j} - 2\hat{k}\) be three vectors. A vector of the type \(\vec{b} + \lambda\vec{c}\) for some scalar \(\lambda\), whose projection on \(\vec{a}\) is of magnitude \(\sqrt{\frac{2}{3}}\) is :

The vector \((\hat{i} \times \vec{a} \cdot \vec{b})\hat{i} + (\hat{j} \times \vec{a}\vec{b})\hat{j} + (\hat{k} \times \vec{a} \cdot \vec{b})\hat{k}\) is equal to:

The mean of a data set consisting of 20 observations is 40. If one observation 53 was wrongly recorded as 33, then the correct mean will be :

If \(a,b,c\) are sides of a scalene triangle, then the value of \(\begin{vmatrix}a&b&c\\b&c&a\\c&a&b\end{vmatrix}\) is :

Let \(f(x)=\frac{x^2-x}{x^2+2x}\), \(x\ne0,-2\). Then \(\frac{d}{dx}\left[f^{-1}(x)\right]\) (wherever it is defined) is equal to :

The matrix \(A^2+4A-5I\), where \(I\) is identity matrix and \(A=\begin{bmatrix}1&2\\4&-3\end{bmatrix}\), equals :

Let \(A=\{1,2,3,4\}\) and \(R:A\to A\) be the relation defined by \(R=\{(1,1),(2,3),(3,4),(4,2)\}\). The correct statement is :

Statement-1: The statement \(A\to(B\to A)\) is equivalent to \(A\to(A\vee B)\).
Statement-2: The statement \(\sim[(A\wedge B)\to(\sim A\vee B)]\) is a Tautology.

If each of the lines \(5x+8y=13\) and \(4x-y=3\) contains a diameter of the circle \(x^2+y^2-2(a^2-7a+11)x-2(a^2-6a+6)y+b^3+1=0\), then :

If \(a\) and \(c\) are positive real numbers and the ellipse \(\frac{x^2}{4c^2}+\frac{y^2}{c^2}=1\) has four distinct points in common with the circle \(x^2+y^2=9a^2\), then