List of top Mathematics Questions asked in JEE Main

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?

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

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

Two points (5, 2) and (2, a). Line passes through these points makes an angle of π/4 at origin. The product of all values of a is equal to

,Then the sum of elements of 10th row.

Number of 5 letters words made from the word “MATHEMATICS” is equal to

3 blue balls and 4 yellow balls are in a box. 3 balls are drawn at random. Let variance and mean be X & Y respectively then value of 3X + 4Y is: