List of top Mathematics Questions asked in JEE Main

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is \(0.9\) and that of the second unit is \(0.8\). The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is \(p\), then \(98p\) is equal to \dots\dots.
If 'R' is the least value of 'a' such that the function \(f(x) = x^2 + ax + 1\) is increasing on \([1, 2]\) and 'S' is the greatest value of 'a' such that the function \(f(x) = x^2 + ax + 1\) is decreasing on \([1, 2]\), then the value of \(|R-S|\) is \dots\dots.
Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|2\vec{a} + 3\vec{b}| = |3\vec{a} + \vec{b}|\) and the angle between \(\vec{a}\) and \(\vec{b}\) is \(60^\circ\). If \(\frac{1}{8} \vec{a}\) is a unit vector, then \(|\vec{b}|\) is equal to :
A vertical pole fixed to the horizontal ground is divided in the ratio \(3 : 7\) by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground \(18\text{ m}\) away from the base of the pole, then the height of the pole (in meters) is :
The line \(12x \cos \theta + 5y \sin \theta = 60\) is tangent to which of the following curves ?
\(\csc 18^\circ\) is a root of the equation :
Let the equation of the plane, that passes through the point \((1, 4, -3)\) and contains the line of intersection of the planes \(3x - 2y + 4z - 7 = 0\) and \(x + 5y - 2z + 9 = 0\), be \(\alpha x + \beta y + \gamma z + 3 = 0\), then \(\alpha + \beta + \gamma\) is equal to :
If \(\frac{dy}{dx} = \frac{2^{x+y} - 2^x}{2^y}\), \(y(0) = 1\), then \(y(1)\) is equal to :
If \(p\) and \(q\) are the lengths of the perpendiculars from the origin on the lines, \(x \csc \alpha - y \sec \alpha = k \cot 2\alpha\) and \(x \sin \alpha + y \cos \alpha = k \sin 2\alpha\) respectively, then \(k^2\) is equal to :
The length of the latus rectum of a parabola, whose vertex and focus are on the positive \(x\)-axis at a distance \(R\) and \(S\) (\(S>R\)) respectively from the origin, is :
The sum of 10 terms of the series \( \frac{3}{1^2 \times 2^2} + \frac{5}{2^2 \times 3^2} + \frac{7}{3^2 \times 4^2} + \dots \) is :
Three numbers are in an increasing geometric progression with common ratio \( r \). If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference \( d \). If the fourth term of GP is \( 3 r^2 \), then \( r^2 - d \) is equal to :
The number of real roots of the equation \( e^{4x} + 2e^{3x} - e^x - 6 = 0 \) is :
Which of the following is not correct for relation \( R \) on the set of real numbers?

The probability distribution of random variable X is given by : 

Let \(p = P(1<X<4 | X<3)\). If \(5p = \lambda K\), then \(\lambda\) is equal to _________.
 

Let S = 1, 2, 3, 4, 5, 6, 9. Then the number of elements in the set T={A \(\subseteq\) S: A \(\neq \emptyset\) and the sum of all the elements of A is not a multiple of 3} is _________. 
 

Let \(z_1\) and \(z_2\) be two complex numbers such that \( \arg(z_1 - z_2) = \frac{\pi}{4} \) and \(z_1, z_2\) satisfy the equation \(|z-3| = \text{Re}(z)\). Then the imaginary part of \(z_1+z_2\) is equal to _________.
Two poles, AB of length a metres and CD of length a + b (b \(\neq\) a) metres are erected at the same horizontal level with bases at B and D. If BD = x and \(\tan(\angle ACB) = \frac{1}{2}\), then :
The value of the integral \( \int_{0}^{1} \frac{\sqrt{x} dx}{(1+x)(1+3x)(3+x)} \) is :
Let M and m respectively be the maximum and minimum values of the function \(f(x) = \tan^{-1}(\sin x + \cos x)\) in \([0, \pi/2]\). Then the value of \(\tan(M-m)\) is equal to :
If \(y(x) = \cot^{-1}\left(\frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}}\right), x \in \left(\frac{\pi}{2}, \pi\right)\), then \(\frac{dy}{dx}\) at \(x = \frac{5\pi}{6}\) is :
Let \( A = \begin{pmatrix} \lfloor x+1 \rfloor & \lfloor x+2 \rfloor & \lfloor x+3 \rfloor \\ \lfloor x \rfloor & \lfloor x+3 \rfloor & \lfloor x+3 \rfloor \\ \lfloor x \rfloor & \lfloor x+2 \rfloor & \lfloor x+4 \rfloor \end{pmatrix} \), where \( \lfloor t \rfloor \) denotes the greatest integer less than or equal to \( t \). If \( \det(A) = 192 \), then the set of values of \( x \) is the interval:
Let \( Z \) be the set of all integers,
\( A = \{(x, y) \in Z \times Z : (x - 2)^2 + y^2 \leq 4\} \),
\( B = \{(x, y) \in Z \times Z : x^2 + y^2 \leq 4\} \) and
\( C = \{(x, y) \in Z \times Z : (x - 2)^2 + (y - 2)^2 \leq 4\} \)
If the total number of relations from \( A \cap B \) to \( A \cap C \) is \( 2^p \), then the value of \( p \) is :
Let S be the mirror image of the point Q(1, 3, 4) with respect to the plane 2x - y + z + 3 = 0 and let R(3, 5, \(\gamma\)) be a point of this plane. Then the square of the length of the line segment SR is _________.
\(3 \times 7^{22} + 2 \times 10^{22} - 44\) when divided by 18 leaves the remainder _________.