List of top Mathematics Questions asked in JEE Main

If \(x=x(y)\) is the solution of the differential equation, \(y\,\mathrm{d}x-\left(x+2y^{2}\right)\mathrm{d}y=0\), with \(x(-\pi)=\pi^{2}\), then \(x\) is equal to :

A ray of light is projected from the origin at angle of \(60^{\circ}\) with the positive direction of \(x\)-axis towards the line, \(y=2\), which gets reflected from the point \((\alpha, 2)\). Then the distance of the reflected ray of light from the point \((2,2)\) is :

The function \(f(x)=\mathrm{e}^{x+1}\left(4 x^{2}-16 x+11\right)\) is :

Let a function, \(f:(-1,3) \rightarrow \mathbf{R}\) be defined as \(f(x)=\min \{x[x],|x[x]-2|+2\}\), where \([x]\) denotes the greatest integer \(\leq x\). Then \(f\) is :

A bag contains 6 red balls and 10 green balls. 3 balls are drawn from it one by one randomly without replacement. If the 3^rd drawn ball is red, then the probability that the first two drawn balls are green is :

Which of the following is not equivalent to \(\sim p \wedge q\) ?

If a variable plane in 3-dimensional space moves in such a way that the sum of the reciprocals of its intercepts on the \(x\) and \(y\)-axes exceeds the reciprocal of its intercept on the \(z\)-axis by 2, then all such planes will pass through the point :

The area (in sq. units) of the region \(\left\{(x, y): \frac{1}{2} \leq y \leq \sin x,\ 0 \leq x \leq \pi\right\}\) is :

If \(\sum_{r=1}^{9}\left(\frac{r+3}{2^{r}}\right){}^{9}\mathrm{C}_{r}=\alpha\left(\frac{3}{2}\right)^{9}+\beta\), then \(\alpha+\beta\) is equal to :

If \(10\sin^4\alpha+15\cos^4\alpha=6\), \(\alpha\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\), then \(27\operatorname{cosec}^6\alpha+8\sec^6\alpha\) is equal to :

If \(A=\{1,2,3,4\}\), then the number of functions on the set \(A\), which are not one - one, is :

Let the data \(4, 10, x, y, 27\) be in the increasing order. If the median of the data is 18 and its mean deviation about mean is 7.6, then the mean of this data is :

If \(m\) be the least value of \(|z-3+i4|^2+|z-5-i2|^2\), \(z \in \mathbb{C}\) attained at \(z=z_0\), then the ordered pair \(\left(|z_0|, m\right)\) is equal to :

Let \(S_n\) denote the sum of the first \(n\) terms of an A.P., \(a_1, a_2, a_3, \ldots, a_n\). If \(a_5+a_9=1\) and \(S_9=6\), then which one of the following is not true ?

The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is ________ .

Suppose that a function \(f : R \to R\) satisfies \(f(x + y) = f(x)f(y)\) for all \(x, y \in R\) and \(f(1) = 3\). If \(\sum_{i=1}^{n} f(i) = 363\) then n is equal to ________ .

The sum of distinct values of \(\lambda\) for which the system of equations
\((\lambda - 1)x + (3\lambda + 1)y + 2\lambda z = 0\)
\((\lambda - 1)x + (4\lambda - 2)y + (\lambda + 3)z = 0\)
\(2x + (3\lambda + 1)y + 3(\lambda - 1)z = 0\)
has non-zero solutions, is ________ .

Consider the statement :
“For an integer n, if \(n^3 - 1\) is even, then n is odd.”
The contrapositive statement of this statement is :

Consider the data on x taking the values \(0, 2, 4, 8, \ldots, 2^n\) with frequencies \({}^nC_0, {}^nC_1, {}^nC_2, \ldots, {}^nC_n\) respectively. If the mean of this data is \(\frac{728}{2^n}\), then n is equal to ________ .

The angle of elevation of the summit of a mountain from a point on the ground is \(45^\circ\). After climbing up one km towards the summit at an inclination of \(30^\circ\) from the ground, the angle of elevation of the summit is found to be \(60^\circ\). Then the height (in km) of the summit from the ground is :

A plane P meets the coordinate axes at A, B and C respectively. The centroid of \(\Delta ABC\) is given to be \((1, 1, 2)\). Then the equation of the line through this centroid and perpendicular to the plane P is :

The probabilities of three events A, B and C are given by \(P(A)=0.6\), \(P(B)=0.4\) and \(P(C)=0.5\). If \(P(A\cup B)=0.8\), \(P(A\cap C)=0.3\), \(P(A\cap B\cap C)=0.2\), \(P(B\cap C)=\beta\) and \(P(A\cup B\cup C)=\alpha\), where \(0.85\le\alpha\le0.95\), then \(\beta\) lies in the interval :

If \(y = \left(\frac{2}{\pi}x - 1\right)\mathrm{cosec}\,x\) is the solution of the differential equation,
\(\frac{dy}{dx} + p(x)\,y = \frac{2}{\pi}\mathrm{cosec}\,x\), \(0 \lt x \lt \frac{\pi}{2}\),
then the function \(p(x)\) is equal to :

If \(\alpha\) and \(\beta\) are the roots of the equation \(2x(2x+1)=1\), then \(\beta\) is equal to :

If the tangent to the curve, \(y = f(x) = x\log_e x\), \((x \gt 0)\) at a point \((c, f(c))\) is parallel to the line-segment joining the points \((1, 0)\) and \((e, e)\), then \(c\) is equal to :