List of top Questions asked in JEE Main

The increasing order of pKa for the following phenols is 
(A) 2,4-Dinitrophenol 
(B) 4-Nitrophenol 
(C) 2,4,5-Trimethylphenol 
(D) Phenol 
(E) 3-Chlorophenol 
Choose the correct answer from the option given below :

Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at \(100.15\degree C\). When 0.2 mol of NaCl is added to the resulting solution, it was observed that the solution froze at \(–0.8\degree C\). The solubility product of PbCl2 formed is ________ \(\times 10^{–6}\) at 298 K. (Nearest integer) Given: \(Kb = 0.5 K \text{ kg mol}^{–1}\) and \(Kf = 1.8 K \text{ kg mol}^{–1}\).
Assume molality to be equal to molarity in all cases.
The number of molecules or ions from the following, which do not have odd number of electrons are ______.
(A) NO2
(B) ICI4- 
(C) BrF3 
(D) CIO2 
(E) NO22+ 
(F) NO

Following figure shows dependence of molar conductance of two electrolytes on concentration. Λo m is the limiting molar conductivity. The number of incorrect statement(s) from the following is ________ 
molar conductance
(A) \(\Lambda \text{o m}\) for electrolyte A is obtained by extrapolation. 
(B) For electrolyte B, \(\Lambda \text{m}\) vs \(\sqrt c\) graph is a straight line with intercept equal to o \(\Lambda \text{m}\)
(C) At infinite dilution, the value of degree of dissociation approaches zero for electrolyte B. 
(D) Λo m for any electrolyte A or B can be calculated using \(\lambda0\) for individual ions.

The sum of bridging carbonyls in W(CO)6 and Mn2(CO)10 is_____.

Following chromatogram was developed by adsorption of compound 'A' on a 6 cm TLC glass plate. Retardation factor of the compound 'A' is_____ \(\times 10^{–1}\).
Chromatogram

17 mg of a hydrocarbon (M.F. C10H16) takes up 8.40 mL of the H2 gas measured at \(0\degree C\) and 760 mm of Hg. Ozonolysis of the same hydrocarbon yields
Ozonolysis of the hydrocarbon
The number of double bond/s present in the hydrocarbon is_______.
Let [x] denote the greatest integer ≤ x. Consider the function \(f(x)=max \{x^2,1+[x] \}\). Then the value of the integral \(∫_0^2 f(x)dx\) is
Let the tangents at the points A(4, –11) and B(8, –5) on the circle \(x^2+y^2-3x+10y-15=0\), intersect at the point C. Then the radius of the circle, whose centre is C and the line joining A and B is its tangent, is equal to
Let \(f(\theta)=3[sin^4(\frac{3\pi}{2}-\theta)+sin^4(3\pi+θ)]-2(1-sin^22\theta)\) and \(S=\{\theta∈[0,\pi]:f'(\theta)=-\frac{\sqrt3}{2}\}\). If \(4\beta \sum_{\theta∈S}\theta\), then \(f(\beta)\) is equal to
Consider the following system of equations
\(\alpha x + 2y + z = 1\)
\(2\alpha x + 3y + z = 1\)
\(3x + \alpha y + 2z = b\)
For some \(\alpha,\beta∈R\) then which of the following is NOT correct?
Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is
If p, q and r are three propositions, then which of the following combination of truth values of p, q and r makes the logical expression \({(p∨q)∧((∼p)∨r)}🡢((∼q)∨r)\) false?
If the vectors \(\overrightarrow{a} =\lambda \hat{i}+\mu\hat{j}+4\hat{k}\), \(\overrightarrow{b}=-2\hat{i}+4\hat{j}-2\hat{k}\) and \(\overrightarrow{c}=2\hat{i}+3\hat{j}+\hat{k}\) are coplanar and the projection of \(\overrightarrow{a}\) on the vector \(\overrightarrow{b}\) is \(\sqrt{54}\) units, then the sum of all possible values of \(\lambda + \mu\) is equal to
A light ray emits from the origin making an angle \(30\degree\) with the positive x-axis. After getting reflected by the line \(x + y = 1\), if this ray intersects x-axis at Q, then the abscissa of Q is
The domain of \(f(x)=\frac{log_{x+1}(x-2)}{e^{2logx}-(2x+3)}\), \(x∈R\) is
Let \(y = f(x)\) be the solution of the differential equation \(y(x + 1)dx - x^2dy = 0\), \(y(1) = e\). Then \(lim_{x→0^-} f (x)\) is equal to
For two non-zero complex numbers z1 and z2, if Re(z1z2) = 0 and Re(z1 + z2), then which of the following are possible?
A. Im(z1) > 0 and Im(z2) > 0 |
B. Im(z1) < 0 and Im(z2) > 0 
C. Im(z1) > 0 and Im(z2) < 0 
D. Im(z1) < 0 and Im(z2) < 0 
Choose the correct answer from the options given below
Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If μ and σ2 represent mean and variance of X, respectively, then 10(μ2+σ2) is equal to
Let a1, a2, a3, … be a G.P of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then a1 a9+a2 a4 a9+a5+a7 is equal to __________.
Let the equation of the plane P containing the line \(x+10=\frac{8-y}{2}=z\) be \(ax + by + 3z = 2(a + b)\) and the distance of the plane P from the point (1, 27, 7) be c. Then a2+b2+c2 is equal to ____________.
Let \(f : R → R\) be a differentiable function that satisfies the relation \(f(x + y) = f(x) + f(y) – 1, ∀x, y ∈R\). If \(f'(0) = 2\), then \(|f(–2)|\) is equal to ___________.
Let the co-ordinates of one vertex of \(\Delta ABC\) be \(A(0, 2, \alpha)\) and the other two vertices lie on the line \(x+\frac{\alpha}{5}=y-\frac{1}{2}=z+\frac{4}{3}\) For \(\alpha∈Z\), if the area of \(\Delta ABC\) is 21 sq. units and the line segment BC has length \(2\sqrt{21}\) units, then α2 is equal to ___________.
Let a b, and c be three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D be \(a-b+c\), \(λa-3b+4c\), \(-a+2b-3c\) and \(2a-4b+6c\) respectively. If AB AC , and AD are coplanar, then λ is equal to ____.
Let the coefficients of three consecutive terms in the binomial expansion of (1 + 2x)n be the ratio 2 : 5 : 8. Then the coefficient of the term, which is in the middle of these three terms, is _______.