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1 + 2 + 3 + 4 +......+ n ≥ (n+n^2)/2 ...
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If P(x) is a polynomial such that P(x2+1)={P(x)}2+1 and P(0)=0,then ∂P/∂x is equal to: (a)-1 (b)0 (c)1 (d)none of these ...
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\hspace{-16}$Find Range of $\bf{f(x)=\frac{\sin^{-1}(x)}{2}+\frac{\cos^{-1}(x)}{3}+\frac{\tan^{-1}(x)}{4}}$ ...
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\hspace{-16}\mathbb{I}$f $\bf{n \; \mathbb{\in \mathbb{N}}}$. Then find value of $\bf{n}$ in \\\\ $\bf{\tan^{-1}\left(\frac{1}{11}\right)+n.\tan^{-1}\left(\frac{1}{7}\right)=\tan^{-1}\left(\frac{1}{n}\right)}$ ...
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I=∫ 6x3+x2-2x+1/2x-1 . Integrate this function. ...
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A person throws a bottle into a dustbin at the same height as he is 2m away at an angle of 45°. The velocity of the bottle thrown is: Q 1. g 2. √g 3. 2g 4.√2g g comes inside the root in respective cases. ...
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Find ∫ ( 1/x6 + 1/x8 )1/3dx i.e integrate cubic root of (1/x6+1/x8) ...
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Q : The potential in a region varies as V = 4x2. Find the charge (in C) enclosed by a cube of side 1 m having its center at Origin. ...
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Find ∫ ( 1/x6 + 1/x8 )1/3dx i.e integrate cubic root of (1/x6+1/x8) ...
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x^2 - a*x + b = 0 x^2 - b*x + a = 0 Both these equations have positive,integral and distinct roots. Find a and b. ...
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Given: f(x) =ax2+bx+c g(x)= px2+qx+r such that f(1)=g(1), f(2)=g(2) and f(3)-g(3) = 2 . Find f(4)-g(4). The q is easy but i want a shorter method... ...
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Find ∫ ( 1/x6 + 1/x8 )1/3dx i.e integrate cubic root of (1/x6+1/x8) ...
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find ∫ x3-2/ (x3+1)3 dx ...
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\hspace{-16}$If $\bf{x^4 + 8x^3 + 18x^2 + 8x + a=0}$ has a $\bf{4}$ Diff. $\bf{\mathbb{R}}$oots.\\\\ Then $\bf{\mathbb{R}}$ange of $\bf{a}$ is ...
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∫sin2(log x) dx also ∫ log x/(1 + log x)2 dx ...
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solve for least values x and y... 2(sin x + sin y) - 2 cos(x-y)=3. ...
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If the equation y=1+x-2√x represents a parabola then coordinates of vertex are? Please explain how you solved it! Answer is (1/4,1/4) ...
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If A is an Invertible Matrix, Show that det(AT A)>0 ...
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If a , b and c are angles in triangle such cot a + cot b + cot c = √3 prove that abc is an equalitial triangle. ...
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The sum of roots of the equation x + 1 - 2 log2 (2x + 3) + 2 log4 (10 - 2-x) = 0 is a) log211 b) log212 c) log213 d) log214 ...
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Let z=a(cos π/5 + isin π/5), a∈r, | a | ≤1. Then z2010 +z2011............. equals? a) z2010/1-a b) a2010/1-a c) za2010/1-z d) a2010/1-z ...
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1. *Image* 2. Let Points P,Q correspond to the complex numbers a,b in the complex plane. If |a| = 4 and 4a2-2ab+b2 = 0 , then the area of the triangle OPQ, (O = Origin) is : ...
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Q. A rod is placed tilted like a ladder is placed having its contact with ground as well as with the perpendicular wall. the rod is making an angle 37° with the horizontal. If the end touching the ground of the rod is being ...
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\hspace{-16}$Find Minimum value of $\mathbf{xy}\;,$ Given that\\\\ \begin{Bmatrix} \bold{x^2+y^2+z^2=7} \\\\ \bold{xy+yz+zx=4} \end{Bmatrix}\\\\\\ Where $\mathbf{x,y,z\in\mathbb{R}}$ ...
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find the remainder when 21990 is divided by 1990? ...
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1 + 2w +3w2 +..... nwn-1 find the sum where,w = nth root of unity ...
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Find the smallest value for the function : f(x) = |x-2| + |x+3| + |x-4| ...
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Find the smallest value for the function : f(x) = |x-2| + |x+3| + |x-4| ...
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*Image* *Image* *Image* *Image* *Image* *Image* *Image* please provide solutions. ...
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Find the points where f(x) is not differentiable. f(x)=|x-1|3 +|x-2|5+|x-3| ...
