List of top Questions asked in JEE Main

A metal wire of length 0.5 m and cross-sectional area 10–4 m2 has breaking stress 5 × 108 Nm–2. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ ms–1
The statement (p∧q) ⇒ (p∧r) is equivalent to :
Given below are two statements.
Statement-I: Stannane is an example of a molecular hydride.
Statement-II: Stannane is a planar molecule
In the light of the above statement, choose the most appropriate answer from the options given below.
In liquation process used for tin (Sn), the metal
When ethanol is heated with conc. H2SO4, a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer’s reagent, is
Let 
\(\begin{array}{l} f\left(x\right)=3^{\left(x^2-2\right)^3+4},x\in \mathbb{R}.\end{array}\)
Then which of the following statements are true? 
P : x = 0 is a point of local minima of f
Q : x = √2 is a point of inflection of f 
R : f ′ is increasing for x > √2
Portland cement contains ‘X’ to enhance the setting time. What is ‘X’?
Let \(\vec{a} = 3\hat{i} + \hat{j}\) and \(\vec{b} = \hat{i} + 2\hat{j} + \hat{k}\).
Let \(\vec{c}\) be a vector satisfying \(\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda \vec{c}\)
If \(\vec{b}\) and \(\vec{c}\) are non-parallel, then the value of \(λ\) is
Which of the following compounds is an example of hypnotic drug?
Two identical thin metal plates has charge q1 and q2 respectively such that q1 > q2. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is
A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is stretched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.
The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x × 10–4 N. The value of x is _______. [use g = 10 m/s2]
A modulating signal 2sin (6.28 × 106) t is added to the carrier signal 4sin(12.56 × 109) t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be ______MHz.
The angle of elevation of the top of a tower from a point A due north of it is α and from a point B at a distance of 9 units due west of A is \(\cos^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
If the distance of the point B from the tower is 15 units, then cot α is equal to :

Let a1, a2, a3,…. be an A.P. If
\(\begin{array}{l} \displaystyle\sum\limits_{r=1}^\infty\frac{a_r}{2^r}=4,\end{array}\)
then 4a2 is equal to ________.

\(\sum_{r=1}^{20}\)(r2+1)(r!) is equal to
Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of (\(\frac{\sqrt{24}+1}{\sqrt{34}}\))n, in the increasing powers of 134 be 64:1.If the sixth term from the beginning is \(\frac{\alpha}{\sqrt{34}}\), then α is equal to ___________.
If \(f(\alpha)\) =\(\int_{1}^{\alpha}\frac{log_{10}t}{1+t}dt\) , \(\alpha>0\), then f(e3) + f(e–3) is equal to :

Let \(S=\left\{(x,y)∈\N×\N:9(x−3)^2+16(y−4)^2≤144\right\}\)
and \(T=\left\{(x,y)∈\R×\R:(x−7)^2+(y−4)^2≤36\right\}.\)
Then n(S ⋂ T) is equal to ____ .

If the tangent to the curve y = x3 – x2 + x at the point (a, b) is also tangent to the curve y = 5x2 + 2x – 25 at the point (2, –1), then |2a + 9b| is equal to _____ .

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

A thermodynamic system is taken from an original state D to an intermediate state

If [t] denotes the greatest integer ≤ t, then the number of points, at which the function
\(f(x) = 4|2x + 3| + 9\lfloor x + \frac{1}{2} \rfloor - 12\lfloor x + 20 \rfloor\)
is not differentiable in the open interval (–20, 20), is ____ .

Let \(\hat a\) and \(\hat b\) be two unit vectors such that the angle between them is \(\frac{\pi}{4}\). If θ is the angle between the vectors (\(\hat a\)+\(\hat b\)) and (\(\hat a\)+2\(\hat b\)+2(\(\hat a\)×\(\hat b\))), then the value of 164 cos2θ is equal to :
Let m1, m2 be the slopes of two adjacent sides of a square of side a such that \(a^2 + 11a + 3(m_1^2 + m_2^2) = 220\). If one vertex of the square is \((10(\cos \alpha - \sin \alpha), 10(\sin \alpha + \cos \alpha))\), where \(\alpha \in \left(0, \frac{\pi}{2}\right)\)and the equation of one diagonal is \((\cos \alpha - \sin \alpha)x + (\sin \alpha + \cos \alpha)y = 10\), then \(72(\sin^4 \alpha + \cos^4 \alpha) + a^2 - 3a + 13\) is equal to :
Let \(S = \{θ ∈ (0, 2π) : 7 cos^2θ – 3 sin^2θ – 2 cos^22θ = 2\}\). 
Then, the sum of roots of all the equations \(x^2 – 2 (tan^2θ + cot^2θ) x + 6 sin^2θ = 0, θ ∈ S\), is _______.