List of top Mathematics Questions asked in JEE Main

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :

If the length of the chord of the circle, \( x^2+y^2=r^2 \) (\(r>0\)) along the line, \( y-2x=3 \) is r, then \(r^2\) is equal to :

The area (in sq. units) of the region \( A=\{(x,y):(x-1)[x]\le y\le2\sqrt{x},\ 0\le x\le2\} \), where [t] denotes the greatest integer function, is :

\( \lim_{x\to0}\frac{x\left(e^{\left(\sqrt{1+x^2+x^4}-1\right)/x}-1\right)}{\sqrt{1+x^2+x^4}-1} \)

If \(x=1\) is a critical point of the function \( f(x)=(3x^2+ax-2-a)e^x \), then :

If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is :

If \( \alpha \) and \( \beta \) are the roots of the equation, \( 7x^2-3x-2=0 \), then the value of \( \frac{\alpha}{1-\alpha^2}+\frac{\beta}{1-\beta^2} \) is equal to :

The value of \( \left(\frac{-1+i\sqrt{3}}{1-i}\right)^{30} \) is :

If \( \int \frac{\cos\theta}{5+7\sin\theta-2\cos^2\theta}\,d\theta = A\log_e|B(\theta)|+C \), where C is a constant of integration, then \( \frac{B(\theta)}{A} \) can be :

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is _________.

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is :

The natural number \(m\), for which the coefficient of \(x\) in the binomial expansion of \(\left(x^{m}+\frac{1}{x^{2}}\right)^{22}\) is 1540, is ............. .

The negation of the Boolean expression \(x\leftrightarrow\ \sim y\) is equivalent to :

If \(2^{10}+2^{9}\cdot 3^{1}+2^{8}\cdot 3^{2}+\ldots+2\cdot 3^{9}+3^{10}=S-2^{11}\), then \(S\) is equal to :

If the volume of a parallelopiped, whose coterminus edges are given by the vectors \(\vec{a}=\hat{i}+\hat{j}+n\hat{k}\), \(\vec{b}=2\hat{i}+4\hat{j}-n\hat{k}\) and \(\vec{c}=\hat{i}+n\hat{j}+3\hat{k}\) \((n\ge 0)\), is 158 cu. units, then :

If the line, \(2x-y+3=0\) is at a distance \(\frac{1}{\sqrt{5}}\) and \(\frac{2}{\sqrt{5}}\) from the lines \(4x-2y+\alpha=0\) and \(6x-3y+\beta=0\), respectively, then the sum of all possible values of \(\alpha\) and \(\beta\) is :

Let \(f(x)=x\cdot\left[\frac{x}{2}\right]\), for \(-10\lt x\lt 10\), where \([t]\) denotes the greatest integer function. Then the number of points of discontinuity of \(f\) is equal to ______.

If the common tangent to the parabolas, \(y^2=4x\) and \(x^2=4y\) also touches the circle, \(x^2+y^2=c^2\), then \(c\) is equal to :

A survey shows that \(73\%\) of the persons working in an office like coffee, whereas \(65\%\) like tea. If \(x\) denotes the percentage of them, who like both coffee and tea, then \(x\) cannot be :

If the four complex numbers \(z,\ \overline{z},\ \overline{z}-2\,\mathrm{Re}(z)\) and \(z-2\,\mathrm{Re}(z)\) represent the vertices of a square of side 4 units in the Argand plane, then \(|z|\) is equal to :

The value of \(\displaystyle\int_{-\pi/2}^{\pi/2}\frac{1}{1+e^{\sin x}}\,dx\) is:

If the point \(P\) on the curve, \(4x^2+5y^2=20\) is farthest from the point \(Q(0,-4)\), then \(PQ^2\) is equal to:

If \((a,\ b,\ c)\) is the image of the point \((1,\ 2,\ -3)\) in the line \(\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}\), then \(a+b+c\) is :

If
\( \int\left(e^{2x}+2e^x-e^{-x}-1\right)e^{\left(e^x+e^{-x}\right)}dx = g(x)\,e^{\left(e^x+e^{-x}\right)}+c \)
where \(c\) is a constant of integration, then \(g(0)\) is equal to :

If \(3^{2\sin2\alpha-1}\), \(14\) and \(3^{4-2\sin2\alpha}\) are the first three terms of an A.P. for some \(\alpha\), then the sixth term of this A.P. is: