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A large stone of mass Me/2 is released when c.o.m of the stone is at a height h(<<Re) find the speed of stone when it is at a height h/2.Me, Re are mass and radius of earth ...

Let a,b,c,d be four integers such that ad is odd and bc is even,then ax3+bx2+cx+d = 0 has (a) at least one irrational roots (b) all three rational roots (c) all three integral roots (d) none of these ...

\hspace{-16}\bf{(1)\;\; \int\frac{x^2-1}{(x^2+1)\sqrt{1+x^4}}dx}$\\\\\\ $\bf{(2)\;\;\int\frac{x^2}{(x^4-1)\sqrt{x^4+1}}dx}$\\\\\\ $\bf{(3)\;\;\int\frac{x-1}{(x+1)\sqrt{x^3+x+1}}dx}$ ...

\hspace{-16}\bf{\int_{0}^{\frac{\pi}{2}}\frac{\sin(2nx).\sin x}{\cos x}dx\;\;, }$ Where $\bf{n\in \mathbb{N}}$ ...

Let a,b,p,q ε Q and suppose that f(x) = x2 +ax+b=0 and g(x)= x3 + px + q = 0 have a common irrational root , then (a) f(x) divides g(x) (b) g(x) ≡ x f(x) (c) g(x) ≡ (x-b-q)f(x) (d) none ...

What is the product? Please show mechanism too PhCOMe + ClCH2COOC2H5 --NaNH2→ ?? ...

For what compound A stands in the following equation? MeCOMe + CH≡CH -NaNH2→ A ...

3 CH2O + CH3CHO → Dil.Na2 Co3→ ? What is the product at a temperature of 400 C? ...

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Which of the following has the maximum acidic strength? ...

The angle of elevation of the sun, when the shadow of the pole is sqrt{3} times the height of the pole, is ...

a ray of light is coming along the line y = b from the positive direction of the x-axis and strikes a concave mirror , whose intersection with the xy-plane is a parabola y2 = 4ax . find the equation of the reflected ray and s ...

A uniform ladder of length 5m is placed against the wall as shown in the figure. If coefficient of friction mu is the same for both the walls, what is the minimum value of mu for it not to slip? *Image* ...

The equation of common tangent to the circle {{x}^{2}}+{{y}^{2}}=2 and parabola {{y}^{2}}=8x is ...

The points on the parabola {{y}^{2}}=12x , whose focal distance is 4, are ...

In a YDSE both slits produce equal intensities on the screen. A 100% transparent thin film is placed in front of one of the slits. Now the intensity of the geometrical center of system on the screen becomes 75% of the previou ...

The equilibrium constant for the reaction; {{N}_{2}}left( g ight)+{{O}_{2}}(g) ightleftharpoons 2NO(g) at temperature T is 4 imes {{10}^{-4}}. The value of {{K}_{c}} for the reaction. at the same temperature is: ...

For a car taking a turn on a horizontal surface, let N1 and N2Â be the normal reactions of the road on the inner and outer wheels respectively. ...

A house subtends a right angle at the window of an opposite house and the angle of elevation of the window; from the bottom of the first house is 60o. If the distance between the two houses be 6 meters, then the height of the ...

The parametric representation (2+{{t}^{2}},2t+1) represents ...

Calculate the oxidation number of Sulphur in Sulphuric acid ,Sulphurous acid,Hydrogen Sulphide ...

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60°with the wall, find the height of the wall. ...

If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pεR,then the value of bc+ca+ab is? ...

If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pεR,then the value of bc+ca+ab is? ...

If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pεR,then the value of bc+ca+ab is? ...

Let f(x)= ax2+bx+c ,a,b,c ε R.If f(x)takes real values for real values of x and non real values for non real of x,then (a) a=0 (b) b=0 (c) c=0 (d) nothing can be said about a,b,c ...

A parallel beam of sodium light of wavelength 6000 Λ is incident on a thin glass plate of μ= 1.5 such that angle of incidence in the plate is 600.The smallest thickness of the plate which will make it appear dark by reflect ...

If x is real,then the maximum value of y=2(a-x)[x+√(x2+b2] ...

Let a,b,c be non-zero real numbers such that 0 ∫ 1 (e-x +ex )(ax2+bx+c)dx = 0 ∫ 2 (e-x+ex)(ax2+bx+c)dx Then the quadratic equation ax2 +bx+c = 0 has (a) no root in (0,1) (b)at least one root in (1,2) (c) a double root in ...

Let a,b,c be non-zero real numbers such that 0 ∫ 1 (e-x +ex )(ax2+bx+c)dx = 0 ∫ 2 (e-x+ex)(ax2+bx+c)dx Then the quadratic equation ax2 +bx+c = 0 has (a) no root in (0,1) (b)at least one root in (1,2) (c) a double root in ...