List of top Mathematics Questions asked in JEE Main

If \(\sum_{r=1}^{50} \tan^{-1}\frac{1}{2r^2} = p\), then the value of \(\tan p\) is :

Consider the two statements :
(S1) : \((p \to q) \lor (\neg q \to p)\) is a tautology.
(S2) : \((p \land \neg q) \land (\neg p \lor q)\) is a fallacy.
Then :

If the value of the integral \(\int_{0}^{5} \frac{x+[x]}{e^{x-[x]}} dx = \alpha e^{-1} + \beta\), where \(\alpha, \beta \in R, 5\alpha+6\beta=0\), and \([x]\) denotes the greatest integer less than or equal to x; then the value of \((\alpha + \beta)^2\) is equal to :

A circle C touches the line \(x=2y\) at the point (2, 1) and intersects the circle C\(_1\) : \(x^2 + y^2 + 2y - 5 = 0\) at two points P and Q such that PQ is a diameter of C\(_1\). Then the diameter of C is :

The point P\((-2\sqrt{6}, \sqrt{3})\) lies on the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) having eccentricity \(\frac{\sqrt{5}}{2}\). If the tangent and normal at P to the hyperbola intersect its conjugate axis at the points Q and R respectively, then QR is equal to :

The locus of the mid points of the chords of the hyperbola \(x^2-y^2=4\), which touch the parabola \(y^2 = 8x\), is :

Let \(y(x)\) be the solution of the differential equation \(2x^2 dy + (e^y - 2x)dx = 0, x>0\). If \(y(e)=1\), then \(y(1)\) is equal to :

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

The domain of the function \(\text{cosec}^{-1}\left(\frac{1+x}{x}\right)\) is :

A possible value of $\tan \left(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}\right)$ is :

The vector equation of the plane passing through the intersection of the planes $\vec{ r } .(\hat{ i }+\hat{ j }+\hat{ k })=1$ and $\vec{ r } .(\hat{ i }-2 \hat{ j })=-2,$ and the point (1,0,2) is :

The angle of elevation of a jet plane from a point A on the ground is $60^{\circ}$. After a flight of 20 seconds at the speed of $432 km /$ hour, the angle of elevation changes to $30^{\circ} .$ If the jet plane is flying at a constant height, then its height is :

Let $f: R \rightarrow R$ be defined as, $f(x) = \begin{cases} -55x, & \text{if } x < -5 \\ 2x^3 -3x^2 -120x, & \text{if } 5 \le x \le 4 \\ 2x^3 -3x^2-36x-336& \text{if } x > 4, \end{cases} $ Let $A=\{ x \in R : f$ is increasing $\} .$ Then $A$ is equal to

Let $R =\{( P , Q ) | P$ and $Q$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of (1,-1) is the set:

The pitch of the screw gauge is $1 mm$ and there are $100$ divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies $ 8$ divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while $72^{\text {nd }}$ division on circular scale coincides with the reference line. The radius of the wire is

The value of $-{ }^{15} C _{1}+2 .{ }^{15} C _{2}-3 .{ }^{15} C _{3}+\ldots $ $-15 .{ }^{15} C _{15}+{ }^{14} C _{1}+{ }^{14} C _{3}+{ }^{14} C _{5}+\ldots .+{ }^{14} C _{11}$ is

If $P$ is a point on the parabola $y=x^{2}+4$ which is closest to the straight line $y =4 x -1$, then the co-ordinates of $P$ are

If $n \geq 2$ is a positive integer, then the sum of the series ${ }^{n+1} C_{2}+2\left({ }^{2} C_{2}+{ }^{3} C_{2}+{ }^{4} C_{2}+\ldots .+{ }^{n} C_{2}\right)$ is:

Let $f$ be a twice differentiable function defined on $R$ such that $f (0)=1, f'(0)=2$ and $f'(x)\neq 0$ for all $x \in R$. If $\left|\begin{array}{cc}f(x) & f'(x) \\ f'(x) & f''(x)\end{array}\right|=0,$ for all $x \in R,$ then the value of $f (1)$ lies in the interval:

The value of the integral, \[ \int_{1}^{3} \left[ x^{2} - 2x - 2 \right] \, dx, \] where \( [x] \) denotes the greatest integer less than or equal to \( x \), is:

The total number of positive integral solutions $( x , y , z )$ such that $xyz =24$ is :

The negative of the statement $\sim p \wedge( p \vee q )$ is

If the curve $y=a x^{2}+b x+c, x \in R,$ passes through the point (1,2) and the tangent line to this curve at origin is $y = x ,$ then the possible values of $a , b , c$ are :