List of top Questions asked in JEE Main

Two flasks I and II shown below are connected by a valve of negligible volume. When the valve is opened, the final pressure of the system in bar is \(x \times 10^{-2}\). The value of x is _________. (Integer answer) 
[Assume - Ideal gas; 1 bar = 10\(^5\) Pa; Molar mass of N\(_2\) = 28.0 g mol\(^{-1}\); R=8.31 J mol\(^{-1}\) K\(^{-1}\)] 

 

Which one of the following chemicals is responsible for the production of HCl in the stomach leading to irritation and pain ? 

The correct structures of A and B formed in the following reactions are : 

 

The major product of the following reaction, if it occurs by S\(_N\)2 mechanism is : 

 

Choose the most appropriate answer from the options given below : 

Wires W\(_1\) and W\(_2\) are made of same material having the breaking stress of 1.25\(\times\)10\(^9\) N/m\(^2\). W\(_1\) and W\(_2\) have cross-sectional area of 8\(\times\)10\(^{-7}\) m\(^2\) and 4\(\times\)10\(^{-7}\) m\(^2\), respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _________ kg. (Use g = 10 m/s\(^2\)) 

 

A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m/s. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of v = _________ m/s so that the pendulum describes a circle. (Assume the string to be inextensible and g = 10 m/s\(^2\)) 

 

The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s\(^2\)): 

 

Match List - I with List - II. 

Choose the most appropriate answer from the options given below : 
 

If \( \int \frac{2e^x + 3e^{-x}}{4e^x + 7e^{-x}} dx = \frac{1}{14}(ux + v \log_e(4e^x + 7e^{-x})) + C \), where C is a constant of integration, then u + v is equal to _________.
Let S be the mirror image of the point Q(1, 3, 4) with respect to the plane 2x - y + z + 3 = 0 and let R(3, 5, \(\gamma\)) be a point of this plane. Then the square of the length of the line segment SR is _________.
Let S be the sum of all solutions (in radians) of the equation \(\sin^4\theta + \cos^4\theta - \sin\theta \cos\theta = 0\) in [0, 4\(\pi\)]. Then \(\frac{8S}{\pi}\) is equal to _________.
An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If \(\mu\) is the average marks of girls and \(\sigma^2\) is the variance of marks of 50 candidates, then \(\mu + \sigma^2\) is equal to _________.
The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m - n = 0 and mn + nl + lm = 0, is :
The equation of the plane passing through the line of intersection of the planes \( \vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1 \) and \( \vec{r} \cdot (2\hat{i} + 3\hat{j} - \hat{k}) + 4 = 0 \) and parallel to the x-axis is :
The Boolean expression \((p \land q) \Rightarrow ((r \land q) \land p)\) is equivalent to :
The area of the region bounded by the parabola \((y-2)^2 = (x-1)\), the tangent to it at the point whose ordinate is 3 and the x-axis is :
If 0 \(<\) x \(<\) 1 and y = \(\frac{1}{2}x^2 + \frac{2}{3}x^3 + \frac{3}{4}x^4 + ...\), then the value of e\(^{1+y}\) at x = \(\frac{1}{2}\) is :
If \( \lim_{x \to \infty} (\sqrt{x^2 - x + 1} - ax) = b \), then the ordered pair (a, b) is :
A box open from top is made from a rectangular sheet of dimension a \(\times\) b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to:
The set of all values of k \(>\) -1, for which the equation
(3x\(^2\)+4x+3)\(^2\) - (k+1)(3x\(^2\)+4x+3)(3x\(^2\)+4x+2) + k(3x\(^2\)+4x+2)\(^2\) = 0 has real roots, is :
Let [\(\lambda\)] be the greatest integer less than or equal to \(\lambda\). The set of all values of \(\lambda\) for which the system of linear equations x+y+z=4, 3x+2y+5z=3, 9x + 4y + (28 + [\(\lambda\)])z = [\(\lambda\)] has a solution is :
The addition of dilute NaOH to Cr\(^{3+}\) salt solution will give :
100 g of propane is completely reacted with 1000 g of oxygen. The mole fraction of carbon dioxide in the resulting mixture is \(x \times 10^{-2}\). The value of x is _________. (Nearest integer)
[Atomic weight : H=1.008; C=12.00; O=16.00]
The number of photons emitted by a monochromatic (single frequency) infrared range finder of power 1 mW and wavelength of 1000 nm, in 0.1 second is \(x \times 10^{13}\). The value of x is _________. (Nearest integer)
(h = 6.63 \(\times\) 10\(^{-34}\) Js, c=3.00 \(\times\) 10\(^8\) ms\(^{-1}\))