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INTEGRATE: 1) (x3+3)/x6(x2+1). Upper limit=∞;Lower limit=0 2) xe-x/( 1-e-2x ). Upper limit=0;Lower limit=∞. 3) If f(x) be a function satisfying f'(x)=f(x) with f((0)=1 and g be the function satisfying f(x) + g(x)=x2,then ...
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If f(x)=∫xa 1/f(x) dx (x>0) and ∫1a 1/f(x) dx= 2 ,then f(50) is: ...
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Five men A,B,C,D,E are wearing caps of black or white colour without each knowing the colour of his cap.It is known that a man wearing a black cap always speaks the truth while a man wearing a white cap always lies.If they ma ...
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if a x x x x b x x = f(x)-xf/(x). x x c x x x x d then f(x)=? ...
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Find the numebr of solutions of the equation- 8[x2 - x] + 4[x]=13+12[sinx],where [.]denotes the G.I.F. ...
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Find the numebr of solutions of the equation- 8[x2 - x] + 4[x]=13+12[sinx],where [.]denotes the G.I.F. ...
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*Image* ...
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\lim_{x\rightarrow \infty} 100[((x+1)(x+2)...(x+100))^{1/100} - x] ...
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\lim_{x\rightarrow \infty} 100[((x+1)(x+2)...(x+100))^{1/100} - x] ...
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\lim_{x\rightarrow \infty} 100[((x+1)(x+2)...(x+100))^{1/100} - x] ...
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Q1: *Image* a)-1 b)loge1 c)1 d)none q2: *Image* a) 1/2 sin3a b) 1/2 cosec2a c)sin3a d)cosec3a q3: *Image* a)1 b)-1 c)0 d)none q4:if 0<x<y then *Image* a)e b)x c)y d)none q5: *Image* a)1 b) sinx/x c) x/sinx d)none ...
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Given that a, b, and c are all positive, and that ab = 21, ac = 18, and bc = 42, ï¬nd a + b + c. ...
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*Image* ...
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*Image* ...
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If ω be the angle which a focal chord of a parabola makes with the axis, prove that the length of the chord is 4acosec2ω ...
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The minimum distance of the centre of the ellipse x2/16 + y2/9 = 1 from the chord of contact of mutually perpendicular tangents of the ellipse is????? ...
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Three children,each accompanied by a guardian,seek admission in a school.The principal wants to interview all the 6 persons one after the other,subject to the condition that no child is interviewed before its guardian.In how ...
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If 'a' is a complex number such that |a|=1.Find the values of a,so that equation az2+z+1=0 has one purely imaginary root. ...
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When any three points are selected from a circle, what is the probability that they will form an obtuse-angled triangle? ...
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∫ dx/sec2x + tan2x ...
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Find all values of x which satisfies this equation, sin5x+cos3x=1 ...
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If f(x1) + f(x2) = f{(x1+x2)/(1+x1x2)} , find f(x). ...
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Show that Δ < s2/4 ...
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Nine hundred distinct n-digit positive number are to be formed using only the digits 2, 5 & 7. The smallest value of n for which this is possible is (a) 6 (b) 7 (c) 8 (d) 9 ...
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If a0, a1, a2,... are the coefficients in the order of expression of (1+x+x2)n, prove that a02-a12+a22-.....+(-1)n-1an-12=(1/2)an(1-(-1)nan) ...
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Find the number of ordered triplets of natural numbers (x, y, z) satisfying xyz≤10 ...
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Newton's 3rd law states that to every action there is an equal and opposite reaction on two different bodies.... But, A ball has mass m. it goes and hits a wall with f=ma. let this force be f1. now change the frame of referen ...
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Why is the value of log-3-27 ≠3? Because... log-3-27 = log-3(-3 * 9)=log-3-3 + log-39 = 1 + 2 = 3 ...
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The value of lim (n -> ∞) [sum (r varies 1 to n) {1/2r}], where [.] -> G.I.F is ................ ...
