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If I_{n}=\int_{-\pi }^{\pi }{\frac{sin (nx)}{(1 + \pi ^{x})sin x}}dx, n = 0,1,2.... then A) I_{n} = I_{n+2} B) \sum_{m=1}^{10}{I_{2m+1}} = 10\pi C) \sum_{m=1}^{10}{I_{2m}} = 0 D) I_{n} = I_{n+1} (MULTIPLE OPTIONS CORRECT) ...

y = mx+2 will cut the pair of lines 2x2 - 3xy + y2 - x + y = 0 , at only one real point if m is equal to A) 1 B) -1 C) 2 D) -2 [multiple options correct] ...

Two identical thin rings each of radius R are co axially placed a R distance apart . If Q1 & Q2 are respectively the uniformly spread on the two rings , the work done in moving a charge "q" from the center of one ring to the ...

prove that teh lines represented by ax^3+bx^2y+cxy^2+dy^3=0 will bisect teh angles between teh oder two if (3a+c)^2(bc+2cd-3ad)=(b+3d)^2(bc+2ab-3ad) dbt ...

Why does not a ray get reflected in the same path of incident ray?(ie trace its original path) Both the laws of reflection holds true ,i.e.they lie in the same plane and angle i =angle r.......... ...

find \int_{0}^{\pi/4}{\frac{x dx}{cosx(cosx +sinx)}} ...

Can anyone plz explain the reason behind the trend of electron gain enthalpy in the following table *Image* btw in the above table there is a mistake in the atmospheric content row the -- should in case of Radon instead of Ne ...

1..∫ X2/(A+BX)2 dx ...

*Image* if charge is distributed uniformly in the x-y plane with charge density +(sigma) in 1st quad and -(sigma) in remainig quad then work done in miving a point charge q from (0,0,d) to (0,0,2d) is A) -(sigma)qd/4e B) (sig ...

Q1 If point moves insdie equilateral triangle of side length 3 unit such taht it is nearer to the angle bisectors of the triangle than to any sides.then calculate area traced by point P Q2 Let L1=y/b +z/c ;x=0 L2=x/a -z/c ;y= ...

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*Image* A FLEXIBLE CHAIN OF MASS M HANGS BETWEEN TWO FIXED POINTS AT A AND B AT THE SAME LEVEL.THE INCLINATION OF THE CHAIN WITH THE HORIZONTAL AT TWO POINTS OF SUPPORT IS THETA.THE TENSION AT THE MID POINT OF THE CHAIN IS 1- ...

http://timesofindia.indiatimes.com/india/Private-schools-free-to-fix-their-own-fees-says-Sibal/articleshow/5594581.cms NEW DELHI: In what comes as a blow to the efforts of city parents' associations which have been campaignin ...

...1..HOW ELECTRIC AND MAGNETIC FIELD CAN AFFECT RATE OF REACTION ?????? ...

1.calculate the no. of metal-metal bond of Co4(CO)12 if complex follows 18e- rule ???? ...

WITH t TIME TAKEN IN SECONDS AND I TAKEN IN AMPERE THE VARIATION OF I FOLLOWS THE EQUATION t2+I2=25.WHAT AMOUNT OF Ag WILL BE ELECTRODEPOSITED WITH THIS CURRENT FLOWING IN THE INTERVAL 0-5SEC.Ag-108. A 22mg B 66mg C 72mg D 88 ...

The locus of the orthocentre of the triangle formed by the lines ( 1 + p )x - py + p( 1 + p ) = 0, ( 1 + q )x - qy + q( 1 + q ) = 0, and y=0 (where p not equal to q ) is A) Hyperbola B) parabola C) ellipse D) straight line ...

1..stability of following carbanion can be explained by *Image* a.inductive effect. b.mesomeric effect c.s- character ...

If the sum of first n terms of an A.P. is cn2, then the sum of squares of these n terms is A) \frac{n(4n^{2}-1)c^{2}}{6} B) \frac{n(4n^{2}+1)c^{2}}{3} C) \frac{n(4n^{2}-1)c^{2}}{3} D) \frac{n(4n^{2}+1)c^{2}}{6} ...

A five digit number contains 1,2,3,4,5 without repetition.The probability that number is divisble by 1)4 2)12 3)24 A bag contains 6 red and 3 white balls .Four balls are drawn one by one and not replaced.The probablity that t ...

EVALUATE *Image* ...

Two particles A & B are moving as shown in the figure. At this moment of time the angular speed of A w.r.t. B is *Image* a)( va+vb)/r b)( va-vb)/r c)( vbsin \Theta b-vasin \Theta a)/r in the anticlockwise direction d)( vbsin ...

\lim_{n\rightarrow \infty}\frac{(\sum_{x=1}^{n}{x^4})(\sum_{x=1}^{n}{x^5})}{(\sum_{x=1}^{n}{x^t})(\sum_{x=1}^{n}{x^{9-t}})}=\frac{4}{5} ...

A Diverging Lens is placed with its pole at the origin and its principal axis along the x-axis.Equation of an incident ray is given by y=- x/2 +3. The focal length of the lens is 4 cm.Find the equation of the divergent ray?? ...

Which pair gives Cl2 at room temp ? A. conc HCl + KMnO4 B. NaCl + conc H2SO4 C. NaCl + MnO2 D. NaCl + conc HNO3 ...

\sum_{r=0}^{9}{\left(-1 \right)^r\cos^{10}\frac{r\pi}{10}} any short solution using complex? ...

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TWO CONDUCTING SPHERE OF RADII a AND bHAVE CHARGES Q1 AND Q2.DISTANCE BETWEEN THE SPHERE IS R IF E1 AND E2 ARE ELECTRIC FIELD VECTORS AT ANY POINT THEN WHAT IS THE VALUE OF (EPSALION)0∫E1.E2 dv 1-K Q1 Q2/R 2-KQ1.Q1/a+kQ1.Q2 ...

\lim_{z \rightarrow \infty}\frac{\int_{1/2}^{z}{[cot^{-1}x]dx}}{\int_{1/2}^{z}{[1+\frac{1}{x}}]dx} where [.] is GINT ...

1..IF P,Q,R MAY BE PERIMETER ,CIRCUMRADIUS AND INRADIUS OF AN ARBITARY TRIANGLE THE WHICH OF THE FOLLOWING MAY NOT BE ALWAYS TRUE-- (A)P>Q+R (B) P≤Q+R (C)P/6<Q+R<6P (MULTI ANSWER) ...