List of top Mathematics Questions asked in JEE Main

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

If the solution curve of the differential equation \(((tan−1y)−x)dy=(1+y^2)dx\) passes through the point \((1, 0)\), then the abscissa of the point on the curve whose ordinate is \(tan(1)\), is

The differential equation of the family of circles passing through the points (0, 2) and (0, –2) is

Let y = y(x) be the solution curve of the differential equation 

passing through the point (2, √(1/3)). Then √7 y(8) is

The sum of diameters of the circles that touch (i) the parabola \(75x^2 \)= \(64(5y – 3)\) at the point (\(\frac{8}{5}\), \(\frac{6}{5}\)) and (ii) the y-axis is equal to _______.
 

Let the equation of two diameters of a circle x² + y² – 2x + 2fy + 1 = 0 be 2px – y = 1 and 2x + py = 4p. Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3x² – y² = 3 passing through the center of the circle is equal to _______.

Let the tangent drawn to the parabola $y ^2=24 x$ at the point $(\alpha, \beta)$ is perpendicular to the line $2 x+2 y=5$. Then the normal to the hyperbola $\frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1$ at the point $(\alpha+4, \beta+4)$ does NOT pass through the point :

Let \(ABC\) be a triangle such that \(\overrightarrow{ BC }=\vec{ a }\), \(\overrightarrow{ CA }=\vec{ b }, \overrightarrow{ AB }=\vec{ c },|\vec{ a }|=6 \sqrt{2},|\vec{ b }|=2 \sqrt{3}\) and \(\vec{ b } \cdot \vec{ c }=12\) Consider the statements :\((S1): |(\vec{ a } \times \vec{ b })+(\vec{ c } \times \vec{ b })|-|\vec{ c }|=6(2 \sqrt{2}-1)\)\((S2): \angle ABC =\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\) Then

Let $E_1, E_2, E_3$ be three mutually exclusive events such that $P \left( E _1\right)=\frac{2+3 p }{6}$, $P \left( E _2\right)=\frac{2- p }{8}$ and $P \left( E _3\right)=\frac{1- p }{2}$ If the maximum and minimum values of $p$ are $p _1$ and $p _2$, then $\left( p _1+ p _2\right)$ is equal to :

The curve y(x) = ax³ + bx² + cx + 5 touches the x-axis at the point P (–2, 0) and cuts the y-axis at the point Q, where y is equal to 3. Then the local maximum value of y(x) is :

Let the solution curve of the differential equation $x d y=\left(\sqrt{x^2+y^2}+y\right) d x, x>0$, intersect the line $x =1$ at $y =0$ and the line $x=2$ at $y=\alpha$. Then the value of $\alpha$ is :

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to:

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $(p * q) \odot(p \odot \sim q)$ is a tautology, then the ordered pair $(*, \odot)$ is :