List of top Mathematics Questions asked in COMEDK UGET

If [x][x] denotes the greatest integer function, then ∫14([x]−1)([x]−2)([x]−3)([x]−4)dx=\int\limits_{1}^{4} \left(\left[x\right] -1\right)\left(\left[x\right] -2\right)\left(\left[x\right] -3\right)\left(\left[x\right] -4\right)dx =
If log⁡2 sin⁡x−log⁡2cos⁡x−log⁡2(1−tan⁡2x)=−1\log_2 \: \sin x - \log_2 \cos x -\log_2(1 - \tan^2x) = - 1, then
If u=f(x2),v=g(x3),f′(x)=sin⁡xu = f(x^2) , v = g(x^3) , f'(x) = \sin x and g′(x)=cos⁡x,g'(x) = \cos x, then dudv= \frac{du}{dv} =
If x=3cos⁡t−2cos⁡3t,y=3sin⁡t−2sin⁡3t,x= 3 \cos t - 2 \cos^{3} t , y = 3\sin t - 2 \sin^{3} t , then d2ydx2t=π6 \frac{d^{2}y}{dx^{2}} t = \frac{\pi}{6} is
If tan⁡−1(xy)+log⁡x2+y2=0\tan^{-1} \left(\frac{x}{y}\right) + \log \sqrt{x^{2} +y^{2}} = 0 , then dxdy=\frac{dx}{dy} =
Let f(x)=log⁡(1+ex)−log⁡(1−x)x,x≠0f\left(x\right) = \frac{\log\left(1+ex\right)-\log\left(1-x\right)}{x} , x\ne0 . Then ff is continuous at x=0x = 0 if f(0)f(0) =
If 1−x2+1−y2=x−y\sqrt{1-x^{2} } + \sqrt{1- y^{2}} =x -y , then dydx=\frac{dy}{dx} =
A particular solution of dydx=(x+9y)2 \frac{dy}{dx} = (x+9y)^2 when x=0,y=127 x = 0, y = \frac{1}{27} is
A set AA has 55 elements. Then the maximum number of relations on AA (including empty relation) is
The angle between the asymptotes of the hyperbola x2−3y2=12x^2 - 3y^2 = 12 is
The amplitude of sin⁡π5+i(1−cos⁡π5)\sin \frac{\pi}{5} + i\left( 1 - \cos \frac{\pi}{5}\right)
If a=5,b=13,c=12a= 5, b = 13 , c = 12 in ΔABC\Delta ABC, then tan⁡B4\tan \frac{B}{4} is
The derivative of cos⁡−1(1−x21+x2)\cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) with respect to cot⁡−1(1−3x23x−x3)\cot^{-1} \left(\frac{1-3x^{2}}{3x-x^{3}}\right) is
The function f(x)={x2for x<12−xfor x≥1f(x) = \begin{cases} x^2 & \quad \text{for } x < 1\\ 2 - x & \quad \text{for } x \geq 1 \end{cases} is
The vectors a⃗=xi^+(x+1)j^+(x+2)k^\vec{a} = x \hat{i} + (x +1) \hat{j} + ( x +2 ) \hat{k} b⃗=(x+3)i^+(x+4)j^+(x+5)k^\vec{b} = (x + 3) \hat{i} + (x +4) \hat{j} + ( x + 5 ) \hat{k} , and c⃗=(x+6)i^+(x+7)j^+(x+8)k^\vec{c} = (x + 6) \hat{i} + (x + 7 ) \hat{j} + ( x + 8) \hat{k} are co-planar for
The value of [a⃗−b⃗      b⃗−c⃗      c⃗−a⃗][ \vec{a} - \vec{b} \,\,\,\,\,\, \vec{b} - \vec{c} \,\,\,\,\,\, \vec{c} - \vec{a} ] where ∣a⃗∣=1,∣b⃗∣=5,∣c⃗∣=3|\vec{a}| = 1 , |\vec{b} | = 5 , |\vec{c}| = 3
The maximum value of f(x)=log⁡xx,0<x<∞ f(x) = \frac{\log x}{x} , 0 < x < \infty is
If aa and b b are positive integers such that a2−b2a^2 - b^2 is a prime number, then a2−b2a^2 - b^2 is
Let $f(x) = \begin{cases} -2 \sin x, &x \leq - \pi /2 \\ a \sin x +b, & - \pi /2 < x < \pi /2 \\ \cos \, x , & x \geq \pi /2 \end{cases}thenthe?valuesofaandbsothat then the? values of a and b so that f(x)$ is continuous are
If the medians ADAD and BEBE of the triangle with vertices A(0,b),B(0,0),C(a,0)A(0, b), B(0, 0), C(a, 0) are mutually perpendicular, then
If xy=log⁡xx^y = \log x , then dydx\frac{dy}{dx} at the point where the curve cuts the x−axisx-axis is
If y=tan⁡−1(sec⁡x−tan⁡x)y = \tan^{-1} ( \sec x - \tan x) , then dydx= \frac{dy}{dx} =
If A,B,C,DA, B, C, D are four points and AB⃗=DC⃗\vec{AB} = \vec{DC} , then AC⃗+BD⃗=\vec{AC} + \vec{BD} =
tan⁡[12sin⁡−1(2x1+x2)+12cos⁡−1(1−x21+x2)]=\tan\left[\frac{1}{2} \sin^{-1} \left(\frac{2x}{1+x^{2}}\right) + \frac{1}{2} \cos^{-1} \left(\frac{1-x^{2}}{1+x^{2}}\right)\right] =
If x=log⁡abc,y=log⁡bca,z=log⁡cab,x = \log_a bc, y = \log_b ca, z = \log_c ab, then x1+x+y1+y+z1+z=\frac{x}{1+x} + \frac{y}{1+y} + \frac{z}{1+z } =