List of top Mathematics Questions asked in JEE Main

Statement (P $\Rightarrow$ Q) $\land$ (R $\Rightarrow$ Q) is logically equivalent to :

Let $\theta$ be the angle between the planes $P_1: \vec{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=9$ and $P_2: \hat{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=15$ Let $L$ be the line that meets $P_2$ at the point $(4,-2,5)$ and makes an angle $\theta$ with the normal of $P_4$ If $\alpha$ is the angle between $L$ and $P_2$, then $\left(\tan ^2 \theta\right)\left(\cot ^2 \alpha\right)$ is equal to

Let for $x \in R$ $f(x)=\frac{x+|x|}{2} \text { and } g(x)=\begin{cases}x, & x<0 \\x^2, & x \geq 0\end{cases} $

Then area bounded by the curve $y=(f \circ g)(x)$ and the lines $y=0,2 y-x=15$ is equal to

From the top A of a vertical wall AB of height 30 m, the angles of depression of the top P and bottom Q of a vertical tower PQ are 15$^\circ$ and 60$^\circ$ respectively. B and Q are on the same horizontal level. If C is a point on AB such that CB = 15 m, then the area (in m$^2$) of the quadrilateral BCPQ is equal to :

If the variance of the frequency distribution

x_i	Frequency f_t
2	3
3	6
4	16
5	$\alpha$
6	9
7	5
8	6

is 3 , then $\alpha$ is equal to

The number of real roots of the equation $\sqrt{x^2-4 x+3}+\sqrt{x^2-9}=\sqrt{4 x^2-14 x+6}$, is:

Let A be the point (1, 2) and B be any point on the curve $ x^2 + y^2 = 16 $. If the centre of the locus of the point P, which divides the line segment AB in the ratio 3:2 is the point C ($ \alpha, \beta $), then the length of the line segment AC is:

One vertex of a rectangular parallelepiped is at the origin O and the lengths of its edges along x, y and z axes are 3, 4 and 5 units respectively. Let P be the vertex (3, 4, 5). Then the shortest distance between the diagonal OP and an edge parallel to z axis, not passing through O or P is :

$( S 1)(p \Rightarrow q) \vee(p \wedge(\sim q))$ is a tautology(S2) $((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)$ is a contradictionThen

Let $A=\begin{pmatrix}1 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & 12 & -3\end{pmatrix}$ Then the sum of the diagonal elements of the matrix $(A+I)^{11}$ is equal to :

If $(20)^{19}$ + $2(21)(20)^{18} + 3(21)^2 (20)^{17} +$ $\cdots + 20(21)^{19} =$ $k(20)^{19}$, then $k$ is equal to _____ :

A wire of length $20 m$ is to be cut into two pieces A piece of length $l_1$ is bent to make a square of area $A_1$ and the other piece of length $l_2$ is made into a circle of area $A_2$ If $2 A_1+3 A_2$ is minimum then $\left(\pi l_1\right): l_2$ is equal to:

If $\sin ^{-1} \frac{\alpha}{17}+\cos ^{-1} \frac{4}{5}-\tan ^{-1} \frac{77}{36}=0,0<\alpha<13$, then $\sin ^{-1}(\sin \alpha)+\cos ^{-1}(\cos \alpha)$ is equal to

A pair of dice is rolled 5 times. let getting a total of 5 in a single throw is considered as success. If probability of getting atleast four success is $\frac{x}{3}$ then x is equal to

If the maximum distance of normal to the ellipse $\frac{x^2}{4}+\frac{y^2}{b^2}=1, b<2$, from the origin is 1 , then the eccentricity of the ellipse is

If area bounded by region ${x, y)| |x^{2}-2| ≤ y ≤ x}$ is A, then 6A + 16$\sqrt{2}$ is?

Among the statements :
$(S1)$ $(( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )$
$(S2)$$(( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))$

Three dice are thrown. Then the probability that no outcomes is similar is p/q then q – p is (where p and q are co-prime)

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to ______.

Let a circle of radius 4 be concentric to the ellipse $ 15x^2 + 19y^2 = 285 $. Then the common tangents are inclined to the minor axis of the ellipse at the angle:

Let a die be rolled $ n $ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $ \frac{k}{2^{15}} $, then $ k $ is equal to:

The area enclosed by $y = |x-1| + |x-2|$ and $y = 3$

Orthocentre of triangle having vertices as A (1,2), B(3,-4), C(0,6) is

If n $\in$ [10,100] and n $\in$ N, then how many such n are possible where 3n - 3 is divisible by 7?

Let the image of the point P(1, 2, 6) in the plane passing through the points A(1, 2, 0), B(1, 4, 1) and C(0, 5, 1) be Q (α, β, γ). Then (α² + β² + γ²) is equal to