List of top Questions asked in JEE Main

If 0 \(<\) x \(<\) 1 and y = \(\frac{1}{2}x^2 + \frac{2}{3}x^3 + \frac{3}{4}x^4 + ...\), then the value of e\(^{1+y}\) at x = \(\frac{1}{2}\) is :

If \( \lim_{x \to \infty} (\sqrt{x^2 - x + 1} - ax) = b \), then the ordered pair (a, b) is :

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 :

A box open from top is made from a rectangular sheet of dimension a \(\times\) b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to:

The area of the region bounded by the parabola \((y-2)^2 = (x-1)\), the tangent to it at the point whose ordinate is 3 and the x-axis is :

Let A(a, 0), B(b, 2b + 1) and C(0, b), b \(\neq\) 0, |b| \(\neq\) 1, be points such that the area of triangle ABC is 1 sq. unit, then the sum of all possible values of a is :

If two tangents drawn from a point P to the parabola \(y^2 = 16(x-3)\) are at right angles, then the locus of point P is :

Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is :

The Boolean expression \((p \land q) \Rightarrow ((r \land q) \land p)\) is equivalent to :

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 _________.

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 _________.

\(3 \times 7^{22} + 2 \times 10^{22} - 44\) when divided by 18 leaves the remainder _________.

If \( \int \frac{2e^x + 3e^{-x}}{4e^x + 7e^{-x}} dx = \frac{1}{14}(ux + v \log_e(4e^x + 7e^{-x})) + C \), where C is a constant of integration, then u + v is equal to _________.

Two circles each of radius 5 units touch each other at the point (1, 2). If the equation of their common tangent is 4x + 3y = 10, and C\(_1\)(\(\alpha\), \(\beta\)) and C\(_2\)(\(\gamma\), \(\delta\)), C\(_1\) \(\neq\) C\(_2\) are their centres, then \(|(\alpha+\beta)(\gamma+\delta)|\) is equal to _________.

Let A(sec\(\theta\), 2tan\(\theta\)) and B(sec\(\phi\), 2tan\(\phi\)), where \(\theta+\phi=\pi/2\), be two points on the hyperbola \(2x^2-y^2=2\). If (\(\alpha\), \(\beta\)) is the point of the intersection of the normals to the hyperbola at A and B, then \((2\beta)^2\) is equal to _________.

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 _________.

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 be the sum of all solutions (in radians) of the equation \(\sin^4\theta + \cos^4\theta - \sin\theta \cos\theta = 0\) in [0, 4\(\pi\)]. Then \(\frac{8S}{\pi}\) is equal to _________.

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If \(\mu\) is the average marks of girls and \(\sigma^2\) is the variance of marks of 50 candidates, then \(\mu + \sigma^2\) is equal to _________.

In the following logic circuit the sequence of the inputs A, B are (0, 0), (0, 1), (1, 0) and (1, 1). The output Y for this sequence will be :

Two plane mirrors \( M_1 \) and \( M_2 \) are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from \( M_1 \) and \( M_2 \) respectively. The shortest distance between the images thus formed is : (Take \( \sqrt{5} = 2.3 \))

An object is placed at the focus of concave lens having focal length f. What is the magnification and distance of the image from the optical centre of the lens ?

A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (\( b \gg a \)). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the coefficient of mutual inductance between the two loops is :

Consider a galvanometer shunted with \( 5 \Omega \) resistance and \( 2% \) of current passes through it. What is the resistance of the given galvanometer ?

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil :