List of top Questions asked in JEE Main- 2025

If the range of the function \( f(x) = \sqrt{3 - x} + \sqrt{5 + x} \) is \([\alpha, \beta]\), then \( \alpha^2 + \beta^2 \) is equal to:
If the line \( \arg(z) = \frac{\pi}{3} \) intersects the curve \( |z - 2\sqrt{3}i| = 2 \), \( z \in \mathbb{C} \), at two distinct points \(A\) and \(B\), then \(AB\) equals:
If the system of linear equations : \[ x+y+z=4,\quad x+2y+3z=6,\quad 4x+5y+\lambda z=\mu \] has more than one solution, then the value of \( \lambda+\mu \) is equal to:
If all the words, with or without meaning, made using all the letters of the word ``RANCHI'' are arranged as in a dictionary, then the word at \(560^{\text{th}}\) position is:
The number of integral terms in the binomial expansion of \[ \left(11^{\frac{1}{2}} + 17^{\frac{1}{8}}\right)^{1024} \] is:
Two persons \(A\) and \(B\) alternately throw a pair of dice. \(A\) wins if he throws a sum of \(4\) before \(B\) throws a sum of \(9\), and \(B\) wins if he throws a sum of \(9\) before \(A\) throws a sum of \(4\). The probability that \(A\) wins if \(B\) makes the first throw is:
Let the distance between the foci of an ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (a>b) \] be \(4\) and the distance between its directrices be \(10\). Then the length of its latus rectum is:
Let \(e_1\) and \(e_2\) be the eccentricities of the ellipse \(2x^2+9y^2=36\) and the hyperbola \(4x^2-9y^2=36\), respectively. Then the distance between the point of intersection of the lines \(5x-7y=3\) and \(3x+y=7\), and the point \( (9e_1^2,\;9e_2^2) \) is:
Let \(A(3,4)\), \(B(5,-2)\) and \(P(\alpha,\beta)\), \(\alpha\beta \neq 0\), be three points such that \(PA = PB\) and the area of \(\triangle PAB\) is \(10\). Then the distance of the point \(Q(2\alpha-5\beta,\; \alpha-\beta^2)\) from the line having intercepts \(3\) and \(1\) on the \(x\)- and \(y\)-axis respectively, is:
The number of integral values of \(n\), for which the equation \[ 3\cos x + 5\sin x = 2n + 1 \] has a solution, is:
Let the points \(A(a,-1,2)\), \(B(1,b,-4)\), \(C(-1,1,c)\) and \(D(1,-2,8)\) be the vertices of a parallelogram \(ABCD\). Then its area is equal to:
Let \((\alpha,\beta,\gamma)\) be the foot of the perpendicular from the point \((25,2,41)\) on the line \[ \frac{x-4}{3}=\frac{y+1}{7}=\frac{z-2}{3}. \] Then \(\alpha+\beta+\gamma\) is equal to:
Let \[ f(x)= \begin{vmatrix} -\cos x & \tan x & 3\sin x\\ 1 & -3x & 2x^2\\ x^3 & x & x^2 \end{vmatrix}. \] Then the value of \[ \lim_{x\to 0}\frac{(1+x)f(x)-3x\sin x}{x^3} \] is:
The area of the region \[ \{(x,y): \sin x \le y \le \sqrt{\pi^2-x^2}\} \] is:
Let \[ f(x)= \begin{cases} 3x, & x<0,\\ 1+x+[x], & 0\le x\le 2,\\ 5, & x>2, \end{cases} \] where \([x]\) denotes the greatest integer function. If \(\alpha\) and \(\beta\) are the number of points in \(\mathbb{R}\) where \(f\) is not continuous and is not differentiable respectively, then \(\alpha+\beta\) equals:
Let \[ f(x)=\int\left(\frac{1}{\log_e x}-\frac{2}{(\log_e x)^3}\right)\,dx. \] If \(f(e)=2e\), then \(f(e^2)\) is equal to:
Let the value of \(p\), such that the sum of the squares of the roots of the quadratic equation \[ x^2+(7-p)x+4=p \] has the least value, be \(\alpha\), and the corresponding roots be \(\beta\) and \(\gamma\). Then \(\alpha^3+\beta^3+\gamma^3\) equals \underline{\hspace{2cm}.}

Let \(25^x+25^{-x},\ \dfrac{\alpha}{3},\ 20^{1+x}+20^{1-x}\), where \(x,\alpha\in\mathbb{R}\), be the first three terms of an A.P. of increasing terms. For the least value of \(\alpha\), the sum of its first \(10\) terms is _____

If the circles \[ x^2+y^2-2x-8y+17=r \quad \text{and} \quad x^2+y^2-26x-18y+234=0 \] intersect at exactly one point, then the sum of all possible values of \(r\) is _______

Let \(\vec a = 2\hat i + 3\hat j + 5\hat k\), \(\vec b = \hat i - \hat j + 3\hat k\) and \(\vec c\) be a vector such that \[ \vec a \cdot \vec c = 104 \quad \text{and} \quad \vec a \times \vec c = \vec c \times \vec b. \] Then \(\vec b \cdot \vec c\) is equal to ______

The concept of scale is clearly associated with which of the following in reality?

BRICK : MASONRY :: TILES : ________

Identify the correct mirror image of the given figure along the \(XY\)-axis.
Five diagrams \(A, B, C, D,\) and \(E\) are given. Three out of these, when put together, form a square. Identify the correct set of diagrams.
A man is looking at a photograph of a woman and his friend asks him, “Who is she?” The man replies, “I have no brother or sister, but the father of the woman in the photograph is my father’s son.” Who is the woman in the photograph?