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Discuss the continuity of the function f(x)= x3+x2+1 ...
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IF ∫(sin 3θ + sin θ)esin θ cos θ dθ = (Asin 3θ + Bcos 2θ + Csin θ + D cos θ + E)esin θ + c find A, B , C , D , E ANS---> -4 , -12 , -20 , 0 , 32 respectively ...
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Find the no. of ways of arranging 5 identical green, 4 identical blue and 3 identical yellow balls in a row such that none of the identical balls form a block (or in other words...comes serially :-). ...
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1. If y= cosec x (cot–1x) thendy/dx a. x/ 1-x2 b) -x/ 1+x2 c) x/ 1+x2 d) None 5. If A and B are such events that P(A) > 0 and P(B) ≠1 then P( A/B ) is equal to a) 1– P(A∪B)/P(B) b) P(A)/P(B) c)1-P(A)/P(B) d)1-P(B/A ...
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If A and B are two independent events such taht P(A)>0 and P(B)≠1 ,then P(A/B)= ? ...
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have you read reflections .... the magazine brought out by the admins of this site?? check it out.... http://reflections.targetiit.com/ well going through it i came across a sum and the solution... iam posting both of them... ...
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thnx avik ...
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if y = x/ln|cx| where c is a arbitrary constant, is the general son. of differential equation dy/dx = y/x + \phi \left(\frac{x}{y} \right) , then the function \phi \left(\frac{x}{y} \right) is--- ans.----> - y2/x2 ...
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5. The solution of the differential equation cos2 xdy/dx+y = tan x is (a) y = tanx + ce–tan x (b) y = (tanx + 1) + cetanx (c) y = (tanx – 1) + cetanx (d) y = (tanx – 1) + ce–tanx 6. The solution of the differential eq ...
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Find the probability distribution of the number obtained by throwing a dice once ...
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\int \frac{sinx+sin^{3}x}{cos2x}dx = Acosx + Blog\left|f(x) \right| + c A) A=1/4,B=-\frac{1}{\sqrt{2}}, f(x)=\frac{\sqrt{2}cosx -1}{\sqrt{2}cosx +1} B) A=1/2,B=-\frac{3}{4\sqrt{2}}, f(x)=\frac{\sqrt{2}cosx +1}{\sqrt{2}cosx -1 ...
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\int \frac{1}{2e^{2x}+3e^{x}+1}dx ans ------> -\frac{1}{2}log\left| e^{-2x}+3e^{-x}+2 \right| + \frac{3}{2}log \left|\frac{e^{-x}+1}{e^{-x}+2} \right| + c ...
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2. 1-x2 + 1-y2 = a(x-y) then dy/dx is a) (1-x2)/(1-y2) b) (1-y2)/ (1-x2) c) ( 1-x2)/(1-y2 ) d) 1-y2)/ (1-x2) ...
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\int \frac{t. ( 1- t ^2 ) ^{\frac{-7}{4}}}{ \sqrt{t + 4 }.\sqrt{1- t^2 }+ \sqrt{t+ 5 }.\sqrt{1- t^2}} ...
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\int \left(\frac{cotx+cosecx-1}{cotx - cosecx+1} \right)dx ans ------> ln\left|2sin^{2}\frac{x}{2} \right|+c ...
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Q1. \int_{-1}^{1}{\frac{d(tan^{-1}\frac{1}{x})}{dx}dx} Q2. \int_{-1}^{3}{(tan^{-1}\frac{x^2+1}{x}+tan^{-1}\frac{x}{x^2+1})dx} ...
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for practice \text{if x,y,and z are the distances from vetrices A,B,and C to orthocentre respectively then prove that }\\ \frac{a}{x}+\frac{b}{y}+\frac{c}{z}=\frac{abc}{xyz} ...
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\int (x^{2}+2x + 3)\sqrt{x^{2}+x+1}dx please help. ans nahin pata mujhe... full soln. hi likhiyo. aur haan dekhene walon sirf dekho maat try karo aur post the soln. ...
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A bag contains tickets numbered 1,2,3..........50 of which 5 tickets x1,x2,x3,x4,x5 are drawn at random and arranged in ascending order of magnitude x1<x2<x3<x4<x5.What is the probability that x3=30? ...
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Find the value of k so that the function f(x) = kx + 1, if x ≤ π = cos x, if x ≥ π Is continuous at x = π. ...
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2e^{-1/4}<\int_{0}^{2}{e^{x^{2}-x}}dx<2e^{2} .PROVE THE INEQUALITY. this one is definitely a mind freak. ...
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\int_{0}^{1} \left(1- x^2 \right)^{\frac{5}{2}} ...
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find the point inside the traingle such that sum of squares of the distances of that point from vertices of triangle is minimum i hav read somewer its centriod is it correct? if correct how u prove it? ...
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\int \left\{1+ 2tanx(tanx + secx ) \right\}^{1/2}dx ans---> lnsecx(secx + tanx) +c ...
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\int \frac{cosx - sinx}{\sqrt{8-sin2x}}dx ans-----> sin ^{-1}\left(\frac{sinx + cosx}{3} \right)+c ...
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\int f(x)sinxcosx dx = \frac{1}{2(a^{2}-b^{2})}log (f(x)) + c THEN f(x) = ???? ans GIVEN ----> \frac{1}{a^{2}sin^{2}x + b^{2}cos^{2}x} ...
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find the minimum value of (3sinx-4cosx-10) * (3sinx+4cosx-10) ...
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total no of functions f from the set A={0,1,2} to set B={0,1,2,3,4,5,6,7} such that f(i)<=f(j) for all i<j.i,j ε A...is answer 10C3 ...