List of top Mathematics Questions asked in JEE Main

Let \(f : \mathbb{R} \to \mathbb{R}\) be defined by \(f(x) = \frac{x}{1+x^2},\ x \in \mathbb{R}\). Then the range of f is :

The maximum value of the function \(f(x) = 3x^3 - 18x^2 + 27x - 40\) on the set \(S = \{x \in \mathbb{R} : x^2 + 30 \le 11x\}\) is :

Let \(f(x) = \begin{cases} -1, & -2 \le x \lt 0 \\ x^2 - 1, & 0 \le x \le 2 \end{cases}\) and \(g(x) = |f(x)| + f(|x|)\). Then, in the interval \((-2, 2)\), g is :

Let \([x]\) denote the greatest integer less than or equal to \(x\). Then \(\lim_{x \to 0} \frac{\tan(\pi \sin^2 x) + \left(|x| - \sin(x[x])\right)^2}{x^2}\)

The sum of the real values of \(x\) for which the middle term in the binomial expansion of \(\left(\frac{x^3}{3} + \frac{3}{x}\right)^8\) equals 5670 is :

The straight line \(x + 2y = 1\) meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :

A square is inscribed in the circle \(x^2 + y^2 - 6x + 8y - 103 = 0\) with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is :

If one real root of the quadratic equation \(81x^2 + kx + 256 = 0\) is cube of the other root, then a value of \(k\) is

The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is \(\frac{27}{19}\). Then the common ratio of this series is :

The area (in sq. units) of the region bounded by the curve \(x^2 = 4y\) and the straight line \(x = 4y - 2\) is :

The curve amongst the family of curves represented by the differential equation, \((x^2 - y^2)dx + 2xy\,dy = 0\) which passes through (1, 1) is :

With the usual notation, in \(\Delta\)ABC, if \(\angle A+\angle B=120^\circ\), \(a=\sqrt3+1\), \(b=\sqrt3-1\) then the ratio \(\angle A:\angle B\), is :

On which of the following lines lies the point of intersection of the line,
\(\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}\)
and the plane, \(x+y+z=2\) ?

Consider the following three statements :
P : 5 is a prime number
Q : 7 is a factor of 192
R : L.C.M. of 5 and 7 is 35
Then the truth value of which one of the following statements is true ?

If mean and standard deviation of 5 observations \(x_1, x_2, x_3, x_4, x_5\) are 10 and 3, respectively, then the variance of 6 observations \(x_1, x_2, \ldots, x_5\) and \(-50\) is equal to

Two sides of a parallelogram are along the lines, \(x + y = 3\) & \(x - y + 3 = 0\). If its diagonals intersect at (2, 4), then one of its vertex is :

Let \(a_1, a_2, a_3, \ldots, a_{10}\) be in G.P. with \(a_i \gt 0\) for \(i = 1, 2, \ldots, 10\) and S be the set of pairs \((r, k)\), \(r, k \in N\) (the set of natural numbers) for which
\(\begin{vmatrix} \log_e a_1^r a_2^k & \log_e a_2^r a_3^k & \log_e a_3^r a_4^k \\ \log_e a_4^r a_5^k & \log_e a_5^r a_6^k & \log_e a_6^r a_7^k \\ \log_e a_7^r a_8^k & \log_e a_8^r a_9^k & \log_e a_9^r a_{10}^k \end{vmatrix} = 0\).
Then the number of elements in S, is -

Let \(S = \left\{(x,y) \in R^2 : \frac{y^2}{1+r} - \frac{x^2}{1-r}\right\}\); \(r \ne \pm 1\).
Then S represents :

If \(\int_0^x f(t)\,dt = x^2 + \int_x^1 t^2 f(t)\,dt\) then \(f'\left(\frac12\right)\) is -

The positive value of \(\lambda\) for which the co-efficient of \(x^2\) in the expression \(x^2\left(\sqrt{x} + \frac{\lambda}{x^2}\right)^{10}\) is 720, is -

If the area of an equilateral triangle inscribed in the circle \(x^2 + y^2 + 10x + 12y + c = 0\) is \(27\sqrt{3}\) sq units then c is equal to :

Let f be a differentiable function such that \(f'(x) = 7 - \frac{3}{4}\frac{f(x)}{x}\), \((x \gt 0)\) and \(f(1) \ne 4\). Then \(\lim_{x \to 0^{+}} x\,f\left(\frac{1}{x}\right)\) :

The value of \(\lambda\) such that sum of the squares of the roots of the quadratic equation, \(x^2 + (3 - \lambda)x + 2 = \lambda\) has the least value is -

If \(\int x^5 \cdot e^{-4x^3}\,dx = \frac{1}{48}e^{-4x^3} f(x) + C\), where C is a constant of integration, then f(x) is equal to -

Let \(A = \begin{bmatrix} 2 & b & 1 \\ b & b^2+1 & b \\ 1 & b & 2 \end{bmatrix}\) where \(b \gt 0\).
Then the minimum value of \(\frac{\det(A)}{b}\) is -