-
1) Prove that ∫x3 2ax-x2 dx=7πa5/8. 2) Integrate: [ x4/(1-x4)] *cos-1(2x/(1+x2). Upper limit=1/ 3 ;Lower limit=-1/ 3 . 3) Integrate::: 2-x2/[(1+x) 1-x2 ].Upper limit=1;Lower limit=0. 4) Integrate:::: log(1+tanx) from 0 to ...
-
Let f(x) be a non constant twice differentiable function defined on (-∞,∞) such that f(x)=f(1-x) and f'(1/4)=0.Then a) f''(x) vanishes at least twice on [0,1] b) f'(1/2)=0 c) ∫(frm -1/2 to 1/2)f(x+1/2)sinxdx=0 d) ∫(fr ...
-
evaluate *Image* answer given is π2. ...
-
Integrate: 1) [(x-1) x4+2x3-x2+2x+1 ]/x2(x+1) 2) (x2-1)/(x3 2x4-2x2+1 ) ...
-
if α,β are two different values of θ lying between 0 and 2Πwhich satisfy the equation 6 cos θ + 8 sin θ = 9,then find the value of sin(α + β). ...
-
If sin α + sin β = a and cos α + cos β = b,then prove that sin(α + β) = (2ab/a2 + b2) ...
-
If angle θ is divided into two parts such that the tangent of one part is λ times the tangent of the other, and α is their difference,show that sinθ = (λ+1/λ-1)sinα ...
-
If f(x)=∫xa 1/f(x) dx (x>0) and ∫1a 1/f(x) dx= 2 ,then f(50) is: ...
-
The minimum value of mod of(sinA + cosA + tanA + secA + cotA + cosecA) is 2 2 -k.Find k ...
-
If x2-x+1=0 and the two roots of the equation are α and β;then find the value of α2013+β2013. ...
-
A block of mass m is attached to one end of a long elastic rope. The other end of the elastic rope is fixed to the roof of a building. Initially the block is in contact with the roof at the point where the rope is fixed and i ...
-
A block of mass m is attached to one end of a long elastic rope. The other end of the elastic rope is fixed to the roof of a building. Initially the block is in contact with the roof at the point where the rope is fixed and i ...
-
*Image* Two rods Ab and BC are light and of length 1 m each. θ=φ=30° at an instant. ω = 1 rad/sec . End C remains in contact with the horizontal. Find- Angular velocity of Rod BC Velocity of Block Angular accn of Rod BC A ...
-
*Image* ...
-
\hspace{-16}$If $\bf{\mathbb{S} = \sum_{r=4}^{1000000}\frac{1}{r^{\frac{1}{3}}}}.$ Then value of $\bf{\left[\mathbb{S}\right] = }$\\\\\\ where $\bf{[x] = }$ Greatest Integer function ...
-
A particle located at x=o at time t=0 starts moving along the positive X-direction with a velocity v that varies with time is? explain ...
-
A cannon ball is fired with a velocity v such that it makes an angle θ with the horizontal. At the highest point,the cannon ball splits into two parts of equal masses. One of the parts retraces the initial path of the ball. ...
-
A motorcyclist starts from the bottom of a slope of angle 45° to cross a valley. The width of the valley 90m and length of the slope is 80 2 m. What is the minimum value of u (initial velocity)? ...
-
A cannon ball is fired with a velocity v such that it makes an angle θ with the horizontal. At the highest point,the cannon ball splits into two parts of equal masses. One of the parts retraces the initial path of the ball. ...
-
A rod of length 10 m. is travelling on a smooth,level,horizontal surface.Beyond a point A,the floor ceases to be smooth and the coefficient of friction is k=0.1.The rod is travelling such that it is moving towards the point A ...
-
A particle is projected from the bottom of an inclined plane at an angle θ with the surface of the incline.The angle of the inclined plane is 45.For what value of θ will the particle retrace it's path after collision with t ...
-
if a x x x x b x x = f(x)-xf/(x). x x c x x x x d then f(x)=? ...
-
An intelligent trader travels from 1 place to another with 3 sacks carrying 30 coconuts each.No sack can hold more than 30 coconuts each.On the way he passes through 30 checkpoints and on each checkpoint he has to give 1 coco ...
-
If R be the range of a projectile on horizontal plane, and H1 and H2 be the maximum heights for its two possible trajectories,find the relation between the given parameters. ...
-
The velocity of a train increases at a constant rate α from zero to v and then remains constant for an interval and finally decreases to zero at a constant rate β. If x be the total distance covered,find the total time take ...
-
If a) x1 + x2 + ...................+x1007 =(2014)2 b) x1 /(x1 +1)=x2 /(x2 +3)=.....................=x1007 /(x1007 +2013) then x253 =? ...
-
If a) x1 + x2 + ...................+x1007 =(2014)2 b) x1 /(x1 +1)=x2 /(x2 +3)=.....................=x1007 /(x1007 +2013) then x253 =? ...
-
*Image* ...
-
Find the numebr of solutions of the equation- 8[x2 - x] + 4[x]=13+12[sinx],where [.]denotes the G.I.F. ...
-
\hspace{-16}\mathbb{I}$f $\bf{x_{i}\; \big(i=1,2,3,.....,48\big)}$ are the Roots of the equation $\bf{\mathbb{P}(x)=18x^4+3x+2006}$\\\\ Then Find value of $\bf{\sum_{i=1}^{48}\frac{x_{i}}{1+x_{i}}=}$ ...
