List of top Questions asked in JEE Main

If the maximum value of the term independent of t in the expansion of (t2x\(^{\frac{1}{5}}\)+\(\frac{(1−x)^{\frac{1}{10}}}{t}\)),x≥0 is K, then 8 K is equal to__________.
Identify the correct Logic Gate for the following output (Y) of two inputs A and B.
Logic Gate for the following output (Y) of two inputs A and B
A \(\sqrt{34}\) m long ladder weighing 10kg leans on a frictionless wall. Its feet rest on the floor 3m away from the wall as shown in the figure. If Ff and Fw are the reaction forces of the floor and the wall, then ratio of \(\frac{F_w}{F_f}\) will be: (Use g = 10 m/s2)
A √(34)m long ladder weighing 10kg
A mixture of hydrogen and oxygen has volume 2000 \(cm^3\), temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:[Take gas constant R = 8.3 \(JK^{–1}\) \(mol^{–1}\)]

Water falls from a 40 m high dam at the rate of \(9 \times 10^4\) kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is: (Take g=10ms-2)

In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement
 
Masses
Fig. 
Arrange the four graphs in descending order of total work done; where W1, W2, W3 and W4 are the work done corresponding to figure a, b, c and d respectively.
total work done corresponding to figure a, b, c, d
Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be
A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 μF. The new capacitance of the system, if half of the space between them is filled with a dielectric material of dielectric constant K = 3 (as shown in figure), will be :
A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 μF
Let a, b be two non-zero real numbers. If p and r are the roots of the equation x2 – 8ax + 2a = 0 and q and s are the roots of the equation x2 + 12bx + 6b = 0, such that \(\frac{1}{p}\),\(\frac{1}{q}\),\(\frac{1}{r}\),\(\frac{1}{s}\) are in A.P., then a–1 – b–1 is equal to _________.
If \(x=∑_{n=0}^∞a^n,y=∑_{n=0}^∞b^n,z=∑_{n=0}^∞c^n\), where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc≠ 0, then :
Let a be an integer such that  \(lim _{x→7} \frac{18−[1−x]}{[x−3a]}\) exists, where [t] is greatest integer \(≤ t\). Then \(a\) is equal to :
A water drop of radius 1 μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is \(1.8 \times 10^{–5} Nsm^{–2}\) and its density is negligible as compared to that of water \((10^6 gm^{–3})\). Terminal velocity of the water drop is
Let f(x)=\(\left\{\begin{matrix}  |4x^2-8x+5|, & if\,8x^2-6x+1\geq0 \\   |4x^2-8x+5|, & if\,8x^2-6x+1<0 \end{matrix}\right.\) where [α] denotes the greatest integer less than or equal to α.Then the number of points in R where f is not differentiable is
The number of distinct real roots of \(x^4 – 4x + 1 = 0\) is :
The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 – 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :

Let the equation of two diameters of a circle x2 + y2 – 2x + 2fy + 1 = 0 be 2px – y = 1 and 2x + py = 4p. Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3x2 – y2 = 3 passing through the centre of the circle is equal to _______.

The sum of diameters of the circles that touch (i) the parabola 75x2 = 64(5y – 3) at the point (\(\frac{8}{5},\frac{6}{5}\)) and (ii) the y-axis is equal to _______.
The value of the integral \(∫^2_{-2}\frac{ |x^3+x|}{(e^x|x|+1)}dx\) is equal to:
The equivalent resistance between points A and B in the given network is:
 equivalent resistance between points A and B in the given network
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : At 10°C, the density of a 5 M solution of KCl [atomic masses of K & Cl are 39 & 35.5 g \(mol^{–1}\) respectively], is ‘x’ g \(ml^{–1}\). The solution is cooled to –21°C. The molality of the solution will remain unchanged.
Reason (R) : The molality of a solution does not change with temperature as mass remains unaffected with temperature.
In the light of the above statements, choose the correct answer from the options given below.
A bar magnetic having a magnetic moment of 2.0 × 105 JT–1, is placed along the direction of uniform magnetic field of magnitude B = 14 × 10–5 T. The work done in rotating the magnet slowly through 60° from the direction of field is:
Based upon VSEPR theory, match the shape (geometry) of the molecules in List-I with the molecules in
List-II and select the most appropriate option.
  List-I                            List-II
(Shape)                    (Molecules)
(A) T-shaped             (I) XeF4
(B) Trigonal planar     (II) SF4
(C) Square planar       (III) CIF3
(D) See-saw                (IV) BF3
Match List-I with List-II
List-I
(A) Spontaneous process
(B) Process with \(ΔP = 0\), \(ΔT = 0\)
(C) \(ΔH_{reaction}\)
(D) Exothermic Process
List-II
(I) \(ΔH < 0\)
(II) \(ΔG_{T,P} < 0\)
(III) Isothermal and isobaric process
(IV) [Bond energies of molecules in reactants] – [Bond energies of product molecules]
Choose the correct answer from the options given below :
Match List-I with List-II
 List I List II
A.Lyophilic colloidiLiquid-liquid colloid
B.EmulsioniiProtective colloid
C.Positively chargediii\(FeCl_3 + NaOH\)
D.Negatively chargediv\(FeCl_3 + hot\; water\)

Choose the correct answer from the options given below :