List of top Mathematics Questions asked in JEE Main

Let a common tangent to the curves y² = 4x and (x – 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to ________.

If \(\begin{vmatrix} x+1 & x & x \\ x & x+ \lambda & x \\ x & x & x+ \lambda^2 \end{vmatrix}\)= \(\frac{9}{8}\) \((103x + 81)\), then \(λ\) and \(\frac{λ}{3}\) are roots of the equation

Let a, b, c and d be positive real numbers such that a + b + c + d = 11. If the maximum value of \(a^5b ^3c ^2d\) is \(3750\;\beta\), then the value of \(\beta\) is

Let A = {1, 3, 4, 6, 9} and B = {2, 4, 5, 8, 10}. Let R be a relation defined on A × B such that R = {(\((a_1, b_1),(a_2, b_2)\)) : \(a_1 ≤ b_2\) and \(b_1 ≤ a_2\)}. Then the number of elements in the set R is 

Let P be the plane passing through the points (5, 3, 0), (13, 3, –2) and (1, 6, 2). For α ∈ N, if the distances of the points A (3, 4, α) and B (2, α, a) from the plane P are 2 and 3 respectively, then the positive value of a is

The converse of ((~ p) ∧ q) ⇒ r is

The domain of the function f(x) = \(\frac{1}{\sqrt{[x]^2-3[x]-10}}\) is (where [x] denotes the greatest integer less than or equal to x)

If the radius of the largest circle with centre (2, 0) inscribed in the ellipse \(x^2 + 4y^2 = 36\) is r, then \(12r^2\) is equal to

Let the function f: [0,2] \(\rightarrow\) R be defined as \(f(x) =   \begin{cases}     e^{min}{x^2,x-[x]}       & \quad x \in[0,1]\\     e^{[x-log_ex]}  & \quad x\in[1,2]   \end{cases}\)
where [t] denotes the greatest integer less than or equal to t. Then the value of the integral \(\int^2_0xf(x)dx\) is 

The angle of elevation of the top P of a tower from the feet of one person standing due South of the tower is 45° and from the feet of another person standing due west of the tower is 30°. If the height of the tower is 5 meters, then the distance (in meters) between the two persons is equal to

If f : R \(\rightarrow\) R be a continuous function satisfying \(\int^{\frac{\pi}{2}}_0f(sin2x)sinxdx+\alpha\int^{\frac{\pi}{4}}_0f(cos2x)cosxdx=0\), then the value of \(\alpha\) is

Let f and g be two function defined by \(f(x) =   \begin{cases}     x+1       & \quad x<0\\    |x-1|,   & \quad x \geq0   \end{cases}\) and g(x) = \(f(n) =   \begin{cases}     x+1,       & \quad x<0 \\     1,  & \quad x\geq0   \end{cases}\) Then (gof)(x) is 

The range of f(x) = \(4\sin^{-1}(\frac{x^2}{x^2+1})\) is 

For α, β, z ∈ C and λ > 1, if \(\sqrt{λ - 1}\) is the radius of the circle |z - α|² + |z - β|² = 2λ, then |α - β| is equal to _____.

The sum of the coefficients of three consecutive terms in the binomial expansion of (1 + x)ⁿ⁺², which are in the ratio 1 : 3 : 5, is equal to

For \(a∈ C, let A = {z∈C : Re (a + z ) > Im ( a + z)}\) and \(B = {z∈C : Re (a + z ) < Im ( a + z)}.\) Then among the two statements: 
(S₁) : If \(Re (a), Im (a) > 0\), then the set A contains all the real numbers 
(S₂): If \(Re (a), Im (a) < 0,\) then the set B contains all the real numbers

Let the line passing through the points P (2, –1, 2) and Q (5, 3, 4) meet the plane x – y + z = 4 at the point R. Then the distance of the point R from the plane x + 2y + 3z + 2 = 0 measured parallel to the line \(\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}\) is equal to

If four distinct points with position vectors \(\overrightarrow a,\overrightarrow b,\overrightarrow c\)  and \(\overrightarrow d\)  are coplanar, then \([\overrightarrow a \overrightarrow b \overrightarrow c]\) is equal to

If the system of linear equations
7x +11y + αz = 13
5x + 4y + 7z = β
175x + 194y + 57z = 361
has infinitely many solutions, then α + β + 2 is equal to:

If the \(1011^{th}\) term from the end in the binominal expansion of \((\frac{4x}{5}-\frac{5}{2x})^{2022}\) is 1024 times \(1011^{th}\) term from the beginning, then |x| is equal to

Let the tangent to the parabola \(y^2 = 12x\) at the point (3, α) be perpendicular to the line 2x + 2y = 3. Then the square of distance of the point (6, – 4) from the normal to the hyperbola \(α^2 x^2 – 9y^2 = 9α^2\) at its point (α– 1, α + 2) is equal to__

The number of points, where the curve \(f(x) = e^{8x} - e^{6x} - 3e^{4x} - e^{2x} + 1\), \(x ∈ R\) cuts x-axis, is equal to

For \(k ∈ N\), if the sum of the series \(1 + \frac{4}{k}+\frac{8}{k^2}+\frac{13}{k^3}+\frac{19}{k^4}+..\)..  is 10, then the value of k is___

If A is the area in the first quadrant enclosed by the curve \(C: 2x^2 – y + 1 = 0\), the tangent to C at the point (1, 3) and the line x + y = 1, then the value of 60A is ________

Let A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6). Then the number of functions f: A→B satisfying f(1) + f(2) = f(4)-1 is equal to _________ .