List of top Mathematics Questions asked in JEE Main

If \(a=sin^{-1}(sin\ 5)\) and \(b=cos^{-1}(cos\ 5)\), then \(a^2+b^2=\)

\(z_1^3+z_2^3=20+15i\) then \(|z_1^4+z_2^4|\) is equal to

Let \(f:→R→(0,∞)\) be increasing function such that \(Lt_{x→∞}\frac {f(7x)}{f(x)}=1\), then \(Lt_{x→∞}[\frac {f(5x)}{f(x)}-1]\) is equal to

The remainder when \(64^{{32}^{32}}\) is divided by 9 is.

If \(\frac {3cos\ 2x+cos^32x}{cos^6x-sin^6x}=x^3-x^2+6\), then find sum of roots.

If \(f(x) =ln(\frac {1-x^2}{1+x^2})\) then value of \(225(f'(x) – f''(x))\) at \(x=\frac 12\)

The number of ways to distribute 8 identical books into 4 distinct bookshelf is (where any bookshelf can be empty)

The mean of 5 observations is \(\frac {24}{5}\) and variance is \(\frac {194}{25}\) . If the mean of first four observations is \(\frac 72\) , then the variance of first four observations is

If first term of non-constant GP be \(\frac 18\) and every term is AM of next two, then \( \displaystyle\sum_{r=1}^{20} T_r- \displaystyle\sum_{r=1}^{18} T_r\) is

\((α, β)\) lie on the parabola \(y^2 = 4x\) and \((α, β)\) also lie on chord with midpoint \((1,\frac 54)\) of another parabola \(x^2 = 8y\), then value of \(|(8 – β)(α – 28)|\) is

In which interval the function \(f(x) = \frac {x}{(x^2-6x-16)}\) is increasing?

A = {1, 2, 3, 4} minimum number of elements added to make an equivalence relation on set A containing (1, 3) & (1, 2) in it.

Area bounded by \(0 ≤ y ≤ \text {min}(x^2+ 2, 2x + 2)\), \(x∈[0, 3]\), then \(12A\) is

The value of \(∫_{\frac \pi6}^{\frac \pi3}\sqrt {1-sin2x\ dx}\) is

Let \(a_1,a_2,a_3\), ..., an, be in A. P. and \(S_n\) denotes the sum of first \(n\) terms of this A. P. is \(S_{10}\) =\(390, \frac{a_{10}}{a_{50}} =\frac{15}{7}\), then \(S_{15} -S_5 =\) _________.

The value of integrate \(∫^1_0 (2x^3 - 3x^2 - x + 1)^\frac{1}{3}dx\) is :

Let the system of equations \(x+2y+3z = 5\), \(2x+3y+z = 9\), \(4x+3y+λz = μ\) have an infinite number of solutions. Then \(λ + 2μ\) is equal to

If the domain of the function \(f(x)\) = \(\frac{\sqrt{x^2-25}}{(4-x^2)}+ \log(x^2+2x-15)\) is \((-∞, α) ∪ (β, ∞)\), then \(α^2+β^2\) is equal to \(b\)

The number of solution of the equation \(4sin^2 x-4cos^3 x+9-4cos x = 0\), \(x ∈ [-2\pi, 2\pi]\)

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:

Let m and n be the coefficient of \(7^{th}\) and \(13^{th}\) term in expansion of \(\bigg(\frac{1}{3x^{\frac{1}{3}}} +\frac{1}{2x^{\frac{2}{5}}}\bigg)^{18}\), then \(\bigg(\frac{m}{n}\bigg)^{\frac{1}{3}}\) is:

Let vertex \(A(2, 3, 1), B(3, 2, -1), C(-2, 1, 3)\). If \(AD\) is angle bisector of angle \(A\), then projection of \(\overrightarrow{AD}\) on \(\overrightarrow{AC}\) is equal to:

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

Two integers \( x \) and \( y \) are chosen with replacement from the set \( \{0, 1, 2, 3, \ldots, 10\} \). Then the probability that \( |x - y| > 5 \) is: