List of top Mathematics Questions asked in JEE Main

A complex number 'z' satisfy both \(|z-6|=5\) & \(|z+2-6i|=5\) simultaneously. Find the value of \(z^3 + 3z^2 - 15z + 141\).

If \( A = \{1,2,3,4,5,6\} \) and \( B = \{1,2,3,\ldots,9\} \), then the number of strictly increasing functions \( f : A \to B \) such that \( f(i) \neq i \) for all \( i = 1,2,3,4,5,6 \) is:

If the end points of chord of parabola \(y^2 = 12x\) are \((x_1, y_1)\) and \((x_2, y_2)\) and it subtend \(90^\circ\) at the vertex of parabola then \((x_1x_2 - y_1y_2)\) equals :

If $f(a)$ is the area bounded in the first quadrant by $x=0$, $x=1$, $y=x^2$ and $y=|ax-5|-|1-ax|+ax^2$, then find $f(0)+f(1)$.

The value of \[ \binom{100}{50} + \binom{100}{51} + \binom{100}{52} + \dots + \binom{100}{100} \] is:

If in the expansion of \( (1 + x^2)^2(1 + x)^n \), the coefficients of \( x \), \( x^2 \), and \( x^3 \) are in arithmetic progression, then the sum of all possible values of \( n \) (where \( n \geq 3 \)) is:

The coefficient of \( x^{48} \) in the expansion of \[ 1 + (1+x) + 2(1+x)^2 + 3(1+x)^3 + \dots + 100(1+x)^{100} \] is

In the binomial expansion of \( (ax^2 + bx + c)(1 - 2x)^{26} \), the coefficients of \( x, x^2 \), and \( x^3 \) are -56, 0, and 0 respectively. Then, the value of \( (a + b + c) \) is

If $2(\vec a \times \vec c)+3(\vec b \times \vec c)=0$, where $\vec a=2\hat i-5\hat j+5\hat k$, $\vec b=\hat i-\hat j+3\hat k$ and $(\vec a-\vec b)\cdot\vec c=-97$, find $|\vec c \times \vec k|^2$.

If $2(\vec a \times \vec c)+3(\vec b \times \vec c)=0$, where $\vec a=2\hat i-5\hat j+5\hat k$, $\vec b=\hat i-\hat j+3\hat k$ and $(\vec a-\vec b)\cdot\vec c=-97$, find $|\vec c \times \vec k|^2$.

If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \[ \vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c}), \] \( |\vec{a}| = 1,\; |\vec{b}| = 4,\; |\vec{c}| = 2 \) and the angle between \( \vec{b} \) and \( \vec{c} \) is \( 60^\circ \), then find \( |\vec{a} \cdot \vec{c}| \):

Let the lines \[ L_1:\ \vec r=(\hat i+2\hat j+3\hat k)+\lambda(2\hat i+3\hat j+4\hat k),\ \lambda\in\mathbb R \] \[ L_2:\ \vec r=(4\hat i+\hat j)+\mu(5\hat i+2\hat j+\hat k),\ \mu\in\mathbb R \] intersect at the point $R$. Let $P$ and $Q$ be the points lying on the lines $L_1$ and $L_2$ respectively, such that \[ |PR|=\sqrt{29}\quad \text{and}\quad |PQ|=\sqrt{\frac{47}{3}}. \] If the point $P$ lies in the first octant, then find $27(QR)^2$.

If three vectors are given as shown. If the angle between vectors \( \mathbf{p} \) and \( \mathbf{q} \) is \( \theta \) where \( \cos \theta = \frac{1}{\sqrt{3}} \), \( |\mathbf{p}| = 2 \), and \( |\mathbf{q}| = 2 \), then the value of \( |\mathbf{p} \times (\mathbf{q} - 3\mathbf{r})|^2 - 3|\mathbf{r}|^2 \) is:

For given vectors \( \mathbf{a} = -\hat{i} + \hat{j} + 2\hat{k} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k} \), where \( \mathbf{c} = \mathbf{a} \times \mathbf{b} \) and \( \mathbf{d} = \mathbf{c} \times \mathbf{b} \), then the value of \( (\mathbf{a} - \mathbf{b}) \cdot \mathbf{d} \) is:

Let \( S \) be the number of 4-digit numbers \( abcd \), where \[ a>b>c>d \] and let \( P \) be the number of 5-digit numbers \( abcde \), where the product of digits is 20. Find \( S + P \):

If the product \[ \left( \frac{1}{\binom{15}{0}} + \frac{1}{\binom{15}{1}} \right) \left( \frac{1}{\binom{15}{1}} + \frac{1}{\binom{15}{2}} \right) \cdots \left( \frac{1}{\binom{15}{12}} + \frac{1}{\binom{15}{13}} \right) \] is equal to \[ \frac{\alpha^{13}}{\binom{14}{0} \binom{14}{1} \binom{14}{2} \cdots \binom{14}{12}}, \] then \( 30\alpha \) is equal to:

If \( A = \{ 1, 2, 3, 4, 5, 6 \}, B = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \} \), then the number of strictly increasing functions from \( A \to B \) such that \( f(i) \neq i \) for \( i = 1, 2, 3, 4, 5, 6 \) is

\[ \left(\frac{1}{^{15}C_0}+\frac{1}{^{15}C_1}\right) \left(\frac{1}{^{15}C_1}+\frac{1}{^{15}C_2}\right) \cdots \left(\frac{1}{^{15}C_{12}}+\frac{1}{^{15}C_{13}}\right) = \frac{\alpha^{13}}{^{14}C_0\cdot {}^{14}C_1\cdot {}^{14}C_2\cdots {}^{14}C_{12}} \] If so, then find the value of \(30\alpha\).

If all the letters of the word 'UDAYPUR' are arranged in all possible permutations and these permutations are listed in dictionary order, then the rank of the word 'UDAYPUR' is

Number of 4 letter words with or without meaning formed from the letters of the word PQRSTTUVV is: