List of top Mathematics Questions asked in JEE Main

10, 30, 68, 130, ___ ,350
find the missing number?

Let \( S = \{ z \in \mathbb{C} : |z - 1| = 1 \} \) and \((\sqrt{2} - 1)(z + \overline{z}) - i(z - \overline{z}) = 2\sqrt{2}.\)
Let \( z_1, z_2 \in S \) be such that \( |z_1| = \max_{z \in S} |z| \) and \( |z_2| = \min_{z \in S} |z| \).  
Then \( \sqrt{2}|z_1 - z_2|^2 \) equals:

\(L_1: γ^-=(i+2j+3k)+λ(i-j+k)\);
\(L_2: γ^-=(4i+5j+6k)+μ(i+j-k)\),
intersect \(L_1\) and \(L_2\) at P and Q respectively. If \((α, β, γ)\) is the mid point of the line segment PQ, then \(2(α, β, γ\)) is equal to

If \( z = \frac{1}{2} - 2i \), is such that \( |z + 1| = \alpha z + \beta (1 + i) \), \( i = \sqrt{-1} \) and \( \alpha, \beta \in \mathbb{R} \), then \( \alpha + \beta \) is equal to:

If \(f(x) - f(y) = ln\bigg(\frac{x}{y}\bigg) +x-y\), then find \(\sum^{20}_{k=1}f'\bigg(\frac{1}{k^2}\bigg)\)

Let \( A = \{ n \in [100, 700] \cap \mathbb{N} : n \text{ is neither a multiple of 3 nor a multiple of 4} \} \).
Then the number of elements in \( A \) is:

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On respectively, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is

If \( f(t) = \int_0^{\pi} \frac{2x \, dx}{1 - \cos^2 t \sin^2 x} \), \( 0 < t < \pi \), then the value of \[ \int_0^{\frac{\pi}{2}} \frac{\pi^2 \, dt}{f(t)} \] equals _____.

The values of $m, n$, for which the system of equations
$x + y + z = 4,$
$2x + 5y + 5z = 17,$
$x + 2y + mz = n$
has infinitely many solutions, satisfy the equation :

Let \( y = y(x) \) be the solution of the differential equation \[ (x + y + 2)^2 \, dx = dy, \quad y(0) = -2. \] Let the maximum and minimum values of the function \( y = y(x) \) in \( \left[ 0, \frac{\pi}{3} \right] \) be \( \alpha \) and \( \beta \), respectively. If \[ (3\alpha + \pi)^2 + \beta^2 = \gamma + \delta\sqrt{3}, \quad \gamma, \delta \in \mathbb{Z}, \] then \( \gamma + \delta \) equals \( \dots \).

If the mirror image of the point \(P(3,4,9)\) in the Line 
\(\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}\) is \((α,β,γ)\) then find \(14(a+ẞ+y)\) is:

Let \(α\) and \(β\) the roots of equation \(px^2 + qx - r = 0\), where \(P≠ 0\). If \(p,q,r\) be the consecutive term of non constant G.P and \(\frac{1}{α} + \frac{1}{β} = \frac{3}{4}\) then the value of \((α - β)^2\) is:

If \(lim_{x\rightarrow 0} \frac{\sqrt 1 + \sqrt{1+x^4}-\sqrt 2}{x^4}=A\) and \(lim_{x \rightarrow 0} \frac{sin^2x}{\sqrt 2 - \sqrt{1+cosx}}=B\), then \(AB^3\) = ____.

If \(f(x)=\frac {4x+3}{6x-4}\), \(x≠\frac 23 \)and \((fof)(x)=g(x)\), where \(g:R-[\frac 23→R→{\frac 23}]\). Then \((gogog)(4)\) is equal to

How many times 3 comes from 1 to 1000?

\(3, a, b, c\) are in Ap and \(3, a-1, b+1, c+9\) are in GP. Then AM of \(a, b, c\) is

If \(f(x)\) = \(\begin {bmatrix} Cos x& -sinx & 0\\sinx & cos x& 0\\0&0&1 \end {bmatrix} \)Statement I \(⇒ f(x).f(y) = f(x+y)\) Statement II \(⇒f(-x) =0 \) is invertible

Let S = {1,2,3,..., 20}, R₁ = {(a, b): a divide b}, R₂ = {(a, b): a is integral multiple of b} and a, b ∈ S. n(R₁ - R₂) = ?

\(\int^1_0\frac{1}{\sqrt{3+x}+\sqrt{1+x}}dx=a+b\sqrt2+c\sqrt3\) then \(2a-3b-4c\) is equal to _____.

let \(S\) be the set of positive integral values of a for which \(\frac {ax^2+2(a+1)x+9a+4}{x^2+8x+32}< 0,\) \(∀x∈R\). Then, the number of elements in \(S\) is

\(f(y - 2)^2 = (x - 1)\) and \(x - 2y + 4 = 0\) then find the area bounded by the curves between the coordinate axis in first quadrant (in sq. units).

If \(cos 2x-a \sin x=2a-7\) then range of \(a\) is:

If \(\frac{dy}{dx}\)= \(\frac{(x+y-2)}{(x-y)}\), and y(0) = 2, find y(2)

In the expansion of \((1 + x)(1 - x^2) (1 + \frac 3x + \frac {3}{x^2}+ \frac {1}{x^3})^5\) the sum of coefficients of \(x^3\) and \(x^{-13}\) is