4(#) ∫(0 to pi/2) log sinx dx = ?
(A) pi/2 log 2
(B) - pi/2 log 2
Ans given B
(!)Continue the sequence
Newspaper , Hoarding , Television
(A) Press
(B) Media
(C) Broadcast
(D) Rumour
Ans given B My Ans C
(@) In ancient India scholars had no interest in political power or "material growth"
"material " stands for
(A) spiritual
(B) celestial
(C) psychic
(D) Internal
Ans given A my ans B
-
UP 0 DOWN 0 0 7
7 Answers
44($) If the lines y = mi x, i = 1,2,3. cut equal intercepts on the transversal line x + y = 1 , then
1+m1 , 1+ m2 , 1+m3 are in
(A) AP
(b) GP
(C) HP
(D) None
Ans given C i got B,C
39(1) Newspaper Hoarding and Television Broadcast.
(2) Material growth's meanings are vague here. I suppose it would be internal, but it rather means "worldly objects and desires".
(3) This is an NCERT integration question. Ans is -pi/2 log2.
1Q2)
I = \int_{0}^{\pi /2}{logsinxdx};also ;I=\int_{0}^{\pi /2}{logcosxdx}
adding these
2I = \int_{0}^{\pi /2}{(logsinx+logcosx)dx}=\int_{0}^{\pi /2}{log\left(\frac{sin2x}{2} dx\right)}
= \int_{0}^{\pi /2}{logsin2xdx}-\int_{0}^{\pi /2}{log2}dx
Let I1 = \int_{0}^{\pi /2}{logsin2xdx}
put 2x = t → dx = dt2
\frac{1}{2}\int_{0}^{\pi}{logsintdt}
\frac{1}{2}\int_{0}^{2.\frac{\pi}{2}}{logsinxdx} [ just replaced t by x ]
\frac{2}{2}\int_{0}^{\frac{\pi}{2}}{logsinxdx}=I
hence we got I1 = I
now we had 2I = I1 -\int_{0}^{\frac{\pi}{2}}{log2}
2I = I -\int_{0}^{\frac{\pi}{2}}{log2}
so I = -\int_{0}^{\frac{\pi}{2}}{log2}
4@Pritish : Y is the meaning vague
n how do u say internal I dont get u ??
@Manmay : I too have this solution ya (given in the solution)
But i wanted a shorter method (if any ) coz this is a qs from BITS exam na thats y
39Material growth means growth of wealth, possessions, etc. Phir toh answer is none of these...uttara..celestial means heavenly or that of outer space. It can't be growth of space.
It can't be internal growth as that would mean bodily growth. Neither can it be spiritual growth as that is the exact opposite of material growth...
Psyche is of the mind, so psychic growth is not the answer. Seems none of them is the answer.