List of top Mathematics Questions

Let \(y = y(x)\) be the solution of the differential equation \(\sec(x) \frac{dy}{dx} + [2(1 - x) \tan(x) + x(2 - x)] = 0\) such that \(y(0) = 2\). Then \(y(2)\) is equal to:

The area (in square units) of the region bounded by the parabola \(y^2 = 4(x - 2)\) and the line \(y = 2x - 8\) is:

If \(A = {1, 2, 3, … 100}\), \(R = {(x, y) | 2x = 3y, x, y ∈ A}\) is symmetric relation on \(A\) and the number of elements in \(R\) is \(n\), the smallest integer value of \(n\) is

The value of \(\frac {120}{\pi^3}|∫_0^\pi\frac {x^2sinx.cosx}{(sinx)^4+(cosx)^4}dx|\) is

A parabola has vertex \((2, 3)\), equation of directrix is \(2x – y = 1\) and equation of ellipse is \(\frac {x^2}{a^2} +\frac {y^2}{b^2} =1\), \(e=\frac {1}{\sqrt 2}\) and ellipse passing through focur of parabola then square of length of latus rectum of ellipse is

If \((α, β, γ)\) is mirror image of the point \((2, 3, 4)\) with respect to the line \(\frac {(x-1)}{2}=\frac {(y-2)}{3}=\frac {(z-3)}{4}\). Then \(2α + 3β + 4γ\) is

The area of the region enclosed by the parabolas \(y = 4 – x^2\) and \(3y = (x – 4)^2\) is in (sq. unit)?

If 2^nd, 8^th, 44^th terms of A.P. are 1^st, 2^nd and 3^rd terms respectively of G.P. and first term of A.P. is 1 then the sum of first 20 terms of A.P. is

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