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Q: The potential drop V0 (in VOLTS) across a resistor varies as V0 = 2 i3/2 where ' i ' is the current in mA. Find the resistance of above device when V0 = 16 V. Q: A conducting sphere of radius ' a ' has charge Q on it. It i ...

Prove that if n>2,then there exists a prime p satisfying n>p>n! ...

This is a dig from the old threads of TargetIIT which was unsolved. Let f be a continuous function in [a,b]. Prove that there exists c \in \left(a,b \right) such that \int_{a}^{c}{f(x)dx}=\left(b-c \right)f(c) . ...

Two balls at height H1 and H2 are thrown with velocity V. they are having same mass and charge. the ball with height H1 falls at a distance L from the initial height. find the height of the second ball at the instant when the ...

Find the charge on 2μF capacitor in steady state : *Image* ...

A body starts sliding down from the top of an inclined plane. The upper half of the inclined plane AB is smooth and the lower half BC is rough. The block just comes to rest at the bottom. Find the coefficient of friction betw ...

The least positive integer n for which ( 1+i/1-i )n= 2/π sin-1( 1+x2/2x ) x≥0 ...

A book contains pages numbered from 1 to 50. 4 leaves (i. e., 8 pages) were torn off the book. What is the probability that the sum of the page numbers is 68? ...

find the sum to infinity....1/2.4+1.3/2.4.6+1.3.5/2.4.6.8 ....... ...

*Image* A thick shell with inner radius R and outer radius 3R has a uniform charge density σ coulomb/meter cube it has a spherical cavity of radius R as shown in the fig. above, please find the electric field at the center o ...

\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{1}{\sin^2 x.\sin\left(x+\frac{\pi}{6}\right)}dx=$ ...

A resistor of resistance R and temp. coeff. of resistivity=α is connected in parallel with a resistor of resistance 3R and temp. coeff. of resistivity=2α.Find equivalent α. ...

A body of mass 2 kg is projected at an angle of 60° to the horizontal with a speed of 20 m/s. The work done by gravity by the time it makes 30° to the horizontal (g=10m/s)? ...

The distance 'x' moved by a body under the action of a force varies with time 't' as x=3t^2 + 4t +5, where 'x' is expressed in metre and 't' in second. If the work done by force in the first 2 seconds is 60 J, kinetic energy ...

prove this... The angle between the two focal radii in a parabola y2 = 4ax is double the angle between the tangents drawn from their end points. ...

1. Let f be defined on [0,1] be a twice differentiable function such that, \left|f''(x) \right|\leq 1 for all x \in \left[0,1 \right] . If f(0)=f(1) , then show that, \left|f'(x)\right|<1 for all x \in \left[0,1 \right] . ...

In mathematics, the Gamma function (represented by the capitalized Greek letter Γ) is an extension of the factorial function to real and complex numbers. For a complex number z with positive real part the Gamma function is d ...

show that the semi-latus rectum of the parabola y2 = 4ax is the harmonic mean between the segments of any focal chord. ...

find greatest integer of the following 1/ 2 +1/ 3 +1/ 4 +.............+1/ 80 ...

if a + 2b + c = 4 then find the max(ab + bc + ac) ...

\hspace{-16}$Calculate value of \\\\\\ $\mathbf{(1)::I_{1}=\int_{0}^{\pi}\frac{\sin x}{7+4\cos 2x+\cos^2 2x}dx}$\\\\\\ $\mathbf{(2)::I_{2}=\int_{0}^{\pi}\frac{x.\sin x}{7+4\cos 2x+\cos^2 2x}dx}$\\\\ \hspace{-16}$Ans\; :: $I_{ ...

\hspace{-16}\int\frac{x^2}{\left(1+\sin 2x\right)}dx ...

sorry for multiple posting ...

Please post a detailed explanatory solution to the following. *Image* Thanks ...

Solve 1 +x2 +y2 +x2 y2 + xy dy/dx = 0 ...

Q. Let f(x) and g(x) be differentiable functions such that f'(x)g(x)\neq f(x)g'(x) for any real x. Show that between any two real solutions of f(x)=0 , there is atleast one real solution of g(x)=0 . ...

the argument of (1- i 3 ) is (1+ i 3 ) A) 60° B) 120° C) 210° D) 240° i got the answer as 240° but the book ans says it is 60°.... 'am baffled!! ...

\hspace{-16}$If $\mathbf{f(x)}$ is a defined function in such a way such that\\\\\\ $\mathbf{f(x+1)=\frac{f(x).\cos\left(\frac{\pi}{67}\right)+\sin\left(\frac{\pi}{67}\right)}{\cos\left(\frac{\pi}{67}\right)-f(x).\sin\left(\f ...

*Image* ...

Integrate: 1) ∫ 1/sinx+sec x dx Please show me the steps also. ...