List of top Mathematics Questions asked in JEE Main

The general solution of $\cot \theta +\tan \theta =2$

Two adjacent sides of a parallelogram ABCD are given by  $\overrightarrow{AB}=2\hat{i}+10\hat{j}+11\hat{k} and \overrightarrow{AD}=-\hat{i}+2\hat{j}+2\hat{k}$.The side AD is rotated by an acute angel $\alpha$ in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle $\alpha$ is given by;

From an airplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the airplane are observed to be 30° and 60° respectively. The height at which the airplane is flying in km is :

Let a, b, c be such that b $(a+c)\ne 0.$ If $\left|\begin{array}{ccc}a& a+1& a-1\\ -b& b+1& b-1\\ c& c-1& c+1\end{array}\right|+\left|\begin{array}{ccc}a+1& b+1& c-1\\ a-1& b-1& c+1\\ (-1{)}^{n+2}a& (-1{)}^{n+1}b& (-1{)}^{n}c\end{array}\right|=0$Then the value of $n$ is?

$\displaystyle \lim _{n \rightarrow \infty}\left[\frac{1}{1+n}+\frac{1}{2+n}+\frac{1}{3+n}+\ldots+\frac{1}{2 n}\right]$ is equal to

If $4^{{\log }_{10}[x+1]}-6^{{\log }_{10}x}-2\cdot 3^{{\log }_{10}[x^2+2]}=0$ then the value of $\frac{1}{20x}$ is

The rank of $\left[\begin{array}{lll}4& 0& 0\\ 0& 3& 0\\ 0& 0& 5\end{array}\right]$ is equal to

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non-coplanar vectors and $\lambda$ is a real number, then$[\lambda (\overrightarrow{a}+\overrightarrow{b}){\lambda }^2\overrightarrow{b}\lambda \overrightarrow{c}]=[\overrightarrow{a}\overrightarrow{b}+\overrightarrow{c}\overrightarrow{b}]$ for

If ⁿ⁺¹C_r+1: ⁿC_r: ^n-1C_r-1 = 55: 35: 21 then the value of n + r is _____.

For any two statements $p$ and $q$, the negation of the expression $p\vee (\sim p\wedge q)$ is:

Find the domain for function $$f(x)=[\sin x]\cos \left(\frac{\pi }{[x-1]}\right)$$

If the function $f(x)=x^3+e^{x/2}$ and $g(x)=f^{-1}$, then the value of $g^{\text{'}}(1)$ is

Let 4^1+x + 4^1-x, \(\frac{k}{2}\), 16^x + 16^-x are in A. P. then least value of k is____

If f(x) = 3ax³ + bx² + cx + 1 and f(1) = 41, f'(1) = 2 and f''(2)= 4, then find (a² + b² + c²).

if  $∫_{-1}^1 \frac{cos \, \alpha x}{1+3^x} dx = \frac2{\pi} $ then $\alpha$ is

A = {2,4,6,8}, B = {3,7,6,9}. R: A × B → A × B such that (a₁, b₁) R (a₂, b₂) ⇔ a₁ + a₂ = b₁ + b₂ where (a₁, b₁) ∈ A, (a₂, b₂) ∈ B. Find the number of elements in the relation.2)= 4, then find (a² + b² + c²).

If A is 3 x 3 matrix, det(3adj (2 adj A)) = 2^-13. 3^-10 and det(3adj (2A)) = 2^-m. 3^-n, then find 2m + 2n.d by 21?

A, B and C are given as
A = αî + 4j + 5k
B = 2î + 5j + 6k
C=A+B
|C| = | A - B |
Find the value of α and |C|² is:

A circle passes through (0, 0) and (1, 0) and touches the circle x² + y² = 9. Then the locus of the centre of the circle is:

Tetrahedral dice having outcomes (1, 2, 3, 4) has 3 outcomes a, b, c (which are visible). Probability that ax² + bx + c = 0 has real roots is m/n (m, n are coprime), then m + n =?

If solution of differential equation xdy - ydx = xy(xdy - ydx) and y(1) = 1 is α|y| = |x|e^{(xy - β)} then (α + β) is equal to

A triangle is drawn inside a bounded region of y² = 2x and x = 24. Then maximum area of triangle is

Bag X contains five one-rupee coins, four five rupee coins. Bag Y contains 4 one rupee and 5 five rupees. Bag Z contains 3 one-rupee coins and 6 five rupee coins. If 1 rupee coin is selected at random, what is the probability it is drawn from bag Y?

A circle x² + y² = 8 and a parabola y² = 2x are given. Find area bounded by these two curves in first quadrant which lie inside the circle and outside the parabola.