List of top Questions asked in JEE Main

A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If \(\angle BAC=90^\circ\), and \(\mathrm{ar}(\Delta ABC)=5\sqrt{5}\) sq. units, then the abscissa of the vertex C is :

Let \([t]\) denote the greatest integer \(\le t\). Then the equation in \(x\), \([x]^2+2[x+2]-7=0\) has :

Let \(x_0\) be the point of local maxima of \(f(x)=\vec{a}\cdot(\vec{b}\times\vec{c})\), where \(\vec{a}=x\hat{i}-2\hat{j}+3\hat{k}\), \(\vec{b}=-2\hat{i}+x\hat{j}-\hat{k}\) and \(\vec{c}=7\hat{i}-2\hat{j}+x\hat{k}\). Then the value of \(\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}+\vec{c}\cdot\vec{a}\) at \(x=x_0\) is :

If \(1+(1-2^2\cdot 1)+(1-4^2\cdot 3)+(1-6^2\cdot 5)+\ldots+(1-20^2\cdot 19)=\alpha-220\beta\), then an ordered pair \((\alpha,\beta)\) is equal to :

If \((a+\sqrt{2}\,b\cos x)(a-\sqrt{2}\,b\cos y)=a^2-b^2\), where \(a \gt b \gt 0\), then \(\frac{dx}{dy}\) at \(\left(\frac{\pi}{4},\frac{\pi}{4}\right)\) is :

Let \(u=\frac{2z+i}{z-ki},\ z=x+iy\) and \(k>0\). If the curve represented by \(\mathrm{Re}(u)+\mathrm{Im}(u)=1\) intersects the \(y\)-axis at the points P and Q where \(PQ=5\), then the value of \(k\) is :

Two vertical poles \(AB=15\) m and \(CD=10\) m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is :

Let \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\ (a>b)\) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, \(\phi(t)=\frac{5}{12}+t-t^2\), then \(a^2+b^2\) is equal to :

If \(A=\begin{bmatrix}\cos\theta & i\sin\theta\\ i\sin\theta & \cos\theta\end{bmatrix},\ \left(\theta=\frac{\pi}{24}\right)\) and \(A^5=\begin{bmatrix}a & b\\ c & d\end{bmatrix}\), where \(i=\sqrt{-1}\), then which one of the following is not true?

Let \(y=y(x)\) be the solution of the differential equation, \(xy^{\prime}-y=x^2(x\cos x+\sin x),\ x>0\). If \(y(\pi)=\pi\), then \(y^{\prime\prime}\left(\frac{\pi}{2}\right)+y\left(\frac{\pi}{2}\right)\) is equal to :

A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If \(x\)% of the people read both the newspapers, then a possible value of \(x\) can be :

Let \(f(x)=|x-2|\) and \(g(x)=f(f(x)),\ x\in[0,4]\). Then \(\int_0^3 \left(g(x)-f(x)\right)dx\) is equal to :

The integral \(\int\left(\frac{x}{x\sin x+\cos x}\right)^2dx\) is equal to (where C is a constant of integration) :

Let \(f(x)=\int\frac{\sqrt{x}}{(1+x)^2}dx\ (x\ge 0)\). Then \(f(3)-f(1)\) is equal to :

Let \(\alpha\) and \(\beta\) be the roots of \(x^2-3x+p=0\) and \(\gamma\) and \(\delta\) be the roots of \(x^2-6x+q=0\). If \(\alpha,\beta,\gamma,\delta\) form a geometric progression. Then ratio \((2q+p):(2q-p)\) is :

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :

If 250 cm³ of an aqueous solution containing 0.73 g of a protein A is isotonic with one litre of another aqueous solution containing 1.65 g of a protein B, at 298 K, the ratio of the molecular masses of A and B is ______ \(\times 10^{-2}\) (to the nearest integer).

An acidic solution of dichromate is electrolyzed for 8 minutes using 2A current. As per the following equation
\(\mathrm{Cr_2O_7^{2-} + 14H^+ + 6e^- \to 2Cr^{3+} + 7H_2O}\)
The amount of \(\mathrm{Cr^{3+}}\) obtained was 0.104 g. The efficiency of the process (in %) is (Take : F = 96000 C, At. mass of chromium = 52) ______.

The volume (in mL) of 0.1 N NaOH required to neutralise 10 mL of 0.1 N phosphinic acid is ___________.

The incorrect statement(s) among (a) – (d) regarding acid rain is (are) :

(a) It can corrode water pipes.
(b) It can damage structures made up of stone.
(c) It cannot cause respiratory ailments in animals.
(d) It is not harmful for trees

\(6.023 \times 10^{22}\) molecules are present in 10 g of a substance 'x'. The molarity of a solution containing 5 g of substance 'x' in 2 L solution is _____ \(\times 10^{-3}\)

A mixture of one mole each of H₂ , He and O₂ each are enclosed in a cylinder of volume V at temperature T. If the partial pressure of H₂ is 2 atm, the total pressure of the gases in the cylinder is :

Match the following drugs with their therapeutic actions :

(i) Ranitidine	(a) Antidepressant
(ii) Nardil (Phenelzine)	(b) Antibiotic
(iii) Chloramphenicol	(c) Antihistamine
(iv) Dimetane (Brompheniramine)	(d) Antacid
	(e) Analgesic

The increasing order of the reactivity of the following compound in nucleophilic addition reaction is :

Propanal, Benzaldehyde, Propanone, Butanone

Consider the hypothetical situation where the azimuthal quantum number, \(l\), takes values 0, 1, 2, ....., n + 1, where n is the principal quantum number. Then, the element with atomic number :