List of top Questions asked in JEE Main- 2023

If \([t]\) denotes the greatest integer \(\leq t\), then the number of points, at which the function \(f(x) = [x + x^3] + |x - x^3| + \left|x + \frac{1}{2}\right|\) is not differentiable in the open interval \((-10, 10)\), is ________.

Let the equation of the hyperbola with foci \((1, 5), (1, -1)\) and eccentricity \(\sqrt{3}\) be \(x^2 - 2y^2 + ax + by + c = 0\). Then \(|a + b + c|\) is equal to ________.

If \( \mathrm{S}_n \) denotes the sum of first n terms of the series \( 7 + 10 + 16 + 25 + 37 + \ldots \), then \( \mathrm{S}_{30} - \mathrm{S}_{20} \) is equal to ________.

If \(\int \frac{dx}{(3x^2 + 5)\sqrt{10x^2 + 7}} = -\frac{1}{\sqrt{580}} \log_e |f(x)| + C\) where C is an arbitrary constant, then \(f(0)\) is equal to ________.

The number of ways in which 30 identical pens can be distributed among 12 students so that each student gets at least one pen and exactly two students get at least two pens each, is ________.

The curve \( y = x^2 + 1 \) divides the area enclosed by the curves \( y + |x| = 3 \) and \( y = |x - 1| \) in the ratio m : n, where m and n are coprime, then m + n is equal to ________.

The domain of the function \( f(x) = \cos^{-1}\left(\frac{x^2 - 3x + 2}{x^2 + 2x - 1}\right) \) is :

Which of the following statements is a tautology ?

Let \( X \) have the binomial distribution \( \mathrm{B}(n, p) \). If its mean is 3 and variance is 2, then \( \mathrm{P}\left(X < \frac{n}{4}\right) \) is equal to :

Let \(\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}\), \(\vec{b} = \hat{i} - \hat{j} + 2\hat{k}\), \(\vec{c} = 2\hat{i} + \hat{j} - 4\hat{k}\) be three vectors. If \(\vec{r}\) is the vector such that \(\vec{r} \times \vec{a} = (\vec{b} + \vec{c}) \times \vec{a}\) and \(\vec{r} \cdot (\vec{b} - \vec{c}) = 0\), then \(\vec{r} \cdot (\hat{i} + \hat{j} - \hat{k})\) is equal to :

If the plane \(y = \alpha x - \beta z + \gamma\) passing through the point \((1, -1, 3)\) is perpendicular to each of the planes \(2x + y + z = 1\) and \(3x - 2y + 2z = 0\), then \(\alpha + \beta + \gamma\) is equal to :

Let \(\mathrm{A}_i(x_i, y_i)\), \(i = 1, 2, 3\) be points on the circle \(x^2 + y^2 = 10\) such that \(\mathrm{A}_1\) lies in the \(1^{\mathrm{st}}\) quadrant and it is the image of point \(\mathrm{A}_2\) with respect to \(y\)-axis. If the distance of point \(\mathrm{A}_1\) from each of the points \(\mathrm{A}_2\) and \(\mathrm{A}_3\) is 2, then twenty times the area of the \(\Delta\,\mathrm{A}_1 \mathrm{A}_2 \mathrm{A}_3\) is

The probability that a randomly selected root of the equation \( 1 + x + x^2 + \ldots + x^{118} = 0 \) satisfies the equation \( x^7 = 1 \), is

The remainder when \(7^{89}\) is divided by 15 is

Let \(\mathrm{PL} = 8\) units and \(\mathrm{QM} = 2\) units be two parallel line segments such that the line segments \(\mathrm{PM}\) and \(\mathrm{QL}\) intersect at the point \(\mathrm{R}\). If \(\mathrm{PL}\) and \(\mathrm{QM}\) are tangents to a circle passing through points \(\mathrm{P}, \mathrm{Q}, \mathrm{R}\) then radius of this circle is

A box contains 7 red and 9 white balls. The number of ways of drawing 8 balls such that there are at least three balls of each colour, is :

Use the basic 2D shapes found in a motor cycle and create an interesting 2D composition of your choice, colour with any three colours of your choice.

For some \(\alpha \in \mathbb{N}\), let \(\mathrm{PQR}\) be a triangle with two fixed vertices \(\mathrm{P}(2, 5)\) and \(\mathrm{Q}(\alpha, -11)\). If the point \(\mathrm{R}\) moves on the line \(l_1 : 9x + 7y + \alpha = 0\), then the centroid of \(\Delta \mathrm{PQR}\) moves on the line \(l_2\), which is parallel to \(l_1\) at a distance \(\frac{20}{3\sqrt{130}}\) units from it. If the distance of \(\mathrm{Q}\) from \(l_2\) is \(\frac{k}{3\sqrt{130}}\), then k is equal to :

Let \([t]\) denote the greatest integer function. If \(\int_0^1 [1 + x^2 + x^4]\,\mathrm{d}x = a\), then \(36a - 25a^2 + 8a^3 - a^4\) is equal to

The diagram shows the supply and demand of different users for different items. Which of the following is/are correct?

A. Sanitizer only meet 50% of the demand
B. Cosmetics has the least supply among all.
C. Among all, two items have equal demand but difference in supply
D. Among all, two items have equal supply and two items have equal demand.
Choose the correct answer from the options given below:-

In the figure mentioned below find the missing series:-

Sheet is folded in marked format and cut led at last as shown. Identify from the options below, how the pattern will be made when it is fully unfolded?

Draw a proportionate sketch of given reference image. Use black and white rendering techniques of your choice.

Choose the correct option amongst the answer figures which complete the series.

The second figure in the first part of the problem figures bears certain relationship to the first figure. Similarly, one of the figures of answer figures bears the same relationship to the first figure of the second part. Identify the correct option from the given answer figures.