List of top Mathematics Questions asked in JEE Main

There are ten boys B1, B2, …, B10 and five girls G1, G2,…, G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group, is ________
Let c, k∈ R. If f(x) = (c + 1)x2 + (1 – c2)x + 2k and f(x + y) = f(x) + f(y) – xy, for all x, y ∈ R, then the value of |2(f(1) + f(2) + f(3) + ......+f (20))| is equal to _____.
The mean and variance of the data \(4, 5, 6, 6, 7, 8, x, y\), where \(x<y\), are \(6\) and \(\frac{9}{4}\), respectively. Then \(x^4+y^2\) is equal to
Let \(f(x) = ax^2 + bx + c\) be such that f(1) = 3, f(-2) = λ and f(3) = 4. If f(0) + f(1) + f(-2) + f(3) = 14, then λ is equal to

Let a line L1 be tangent to the hyperbola
\(\frac{x²}{16} - \frac{y²}{4} = 1\)
and let L2 be the line passing through the origin and perpendicular to L1. If the locus of the point of intersection of L1 and L2 is
\(( x² + y²)² = αx² + βy²,\)
then α + β is equal to___.

Let \(A = \sum_{i=1}^{10} \sum_{j=1}^{10} \min(i, j)\)
and 
\(B = \sum_{i=1}^{10} \sum_{j=1}^{10} \max(i, j)\)
Then A + B is equal to___________.

\(50 tan\) \(\left (3tan^{-1} (\frac{1}{2}) + 2 cos^{-1} (\frac{1}{√5})\right) + 4\sqrt2 tan \left (\frac{1}{2} tan^{-1} (2\sqrt2)\right)\) is equal to ____.

If
\((^{40}C_0) + (^{41}C_1) + (^{42}C_2) + ...... + (^{60}C_{20}) \frac{m}{n} ^{60}C_{20}\)
m and n are coprime, then m + n is equal to _____.

Let \(S={z∈C:|z−2|≤1,and(1+i)+\overline{z}(1−i)≤2}. \)Let \(|z−4i|\) attains minimum and maximum values, respectively, at z1∈s and z2∈s. If \(5(|z_1|^2+|z_2|^2=α+β√5\)  where α and β are integers, then the value of α+β is equal to _________.
Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is __________.
Let f(x) = |(x – 1)(x2 – 2x – 3)| + x – 3, x ∈ R. If m and M are, respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal to

The integral
\(\frac{24}{\pi} \int_{0}^{\sqrt{2}} \frac{2 - x^2}{(2 + x^2) \sqrt{4 + x^4}} \, dx\)
is equal to _______.

Let \(P1:\overrightarrow{r}.(2\^i+\^j−3\^k )=4\) be a plane. Let \(P_2\) be another plane which passes through points  \((2, - 3, 2)\), \((2, - 2, -3)\) and \((1, -4, 2)\). If the direction ratios of the line of intersection of \(P_1\) and \(P_2\) be \(16, α,β,\) then the value of \(α + β\) is equal to _____ .
The value of b > 3 for which \(12∫_3^b \frac{1}{(x^2-1)(x^2-4)}dx=log_e(\frac{40}{40}) \) is equal to.
Let \(→{b}=^i+^j+λ k\) , λ ∈ R. If vector a is a vector such that → a×→ b= 13^i −^j−4^k and→ a.→ b+ 21 =0, then (→ b − → a) . ( → k − ^ j ) + ( → b + → a ) . ( ^ i − ^ k ) is equal to 
The odd natural number $a$, such that the area of the region bounded by $y=1, y=3, x=0$, $x=y^a$ is $\frac{364}{3}$, equal to :
Let $P$ be the plane containing the straight line $\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}$ and perpendicular to the plane containing the straight lines $\frac{ x }{2}=\frac{ y }{3}=\frac{ z }{5}$ and $\frac{ x }{3}=\frac{ y }{7}=\frac{ z }{8}$ If $d$ is the distance of $P$ from the point $(2,-5,11)$, then $d ^2$ is equal to :
Let A be a $2 \times 2$ matrix with det $( A )=-1$ and $\operatorname{det}(( A + I )(\operatorname{Adj}( A )+ I ))=4$. Then the sum of the diagonal elements of A can be:
Let \(S_1=\left\{z_1 \in C:\left|z_1-3\right|=\frac{1}{2}\right\}\) and \(S _2=\left\{ z _2 \in C :\left| z _2-\right| z _2+1||=\left| z _2+\right| z _2-1||\right\}\) Then, for \(z_1 \in S_1\) and \(z_2 \in S_2\), the least value of \(\left|z_2-z_1\right|\) is :
Let \(\overset{→}a = \hat{i}- \hat{J}+2\hat{K}\) and \(\overset{→}b\) be a vector such that \(\overset{→}a×\overset{→}b=2\hat{i}−\hat{k} \) and \(\overset{→}a⋅\overset{→}b=3\). Then the projection of \(\overset{→}b\) on the vector \(\overset{→}a-\overset{→}b\) is :
Let \(\vec a\)=\(\hat i\)−\(\hat j\)+2\(\hat k\) and \(\vec b\) be a vector such that 
\(\vec a\)×\(\vec b\)=2\(\hat i\)−\(\hat k\) and \(\vec a\)⋅\(\vec b\)=3. 
Then the projection of  \(\vec b\) on the vector \(\vec a\)−\(\vec b\) is :
If A and B are two events such that \(P(A)=\frac1{3},P(B)=\frac1{5}\)  and \(P(A∪B)=\frac1{2}\) then \(P(\frac{A}{B'}) + P(\frac{B}{A'})\) is equal to
\(lim_{n→∞} \frac1{2^n}(\frac1{\sqrt{1-1/2^n}} +\frac1{\sqrt{1-\frac2{2^n}}}+\frac1{\sqrt{1-\frac3{2^n}}}+...+\frac1{\sqrt{1-\frac{2^n-1}{2^n}}})\) is equal to
Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from {A, B, C, D, E} or a number from {1, 2, 3, 4, 5} with the repetition of characters allowed. If the number of passwords in S whose at least one character is a number from {1, 2, 3, 4, 5} is \(α\) × 56, then \(α\) is equal to _______.
Let f be a differentiable function in \((0, \frac{π}{2})\). If \(∫_{cosx} ^1 t^2f(t)dt=sin^3x+cosx\), then \(\frac{1}{\sqrt3}f'(\frac{1}{\sqrt3})\) is equal to