5326

Mathematics Integration Level: Misc Level

Integrate by using substitution method

\int_{0}^{\frac{\pi}{2}}\sqrt{Cosx}Sin^{3}xdx




5325

Mathematics Integration Level: Misc Level

Integrate by using substitution method

\int_{0}^{1}\frac{x}{1+x^4}dx




5324

Mathematics Integration Level: Misc Level

Integrate by using substitution method

\int_{0}^{a}\frac{dx}{\sqrt{ax-x^{2}}}dx




5323

Mathematics Integration Level: Misc Level

Integrate by using substitution method

\int_{0}^{1}\frac{x}{\sqrt{1+x^{2}}}dx




5322

Mathematics Integration Level: Misc Level

Integrate by using substitution method

\int_{0}^{\frac{\pi}{2}}\frac{Sinx}{\sqrt{1+Cosx}}dx




5321

Mathematics Integration Level: Misc Level

Integrate by using substitution method

\int_{a}^{b}\frac{logx}{x}dx




5320

Mathematics Integration Level: Misc Level

Integrate by using substitution method

\int_{0}^{\frac{\pi}{2}}\frac{Cosx}{3+4Sinx}dx




5319

Mathematics Integration Level: Misc Level

Integrate by using substitution method

\int_{0}^{1}xe^{x^{2}}dx




5318

Physics Current Electricity Level: Misc Level

In Fig the ideal batteries have emfs E1 =150 V and E2 =50 V and the resistances are R1 =3.0 Q and R2=2.0 Q. If the potential at P is defined to be 150 V, What is the potential at  Q?




5314

Physics Current Electricity Level: Misc Level

A Parallel -plate capacitor has a plate area of 126 square centimeters and a plate separation of 0.58 mm, Half the area between the plates is filled with Teflon . The other half is filled with air. 

a.when 20 V is applied, the charge on this capacitor is ---

b. The maximum voltage that can be applied to the capacitor is --  




5313

Physics Current Electricity Level: Misc Level

A charge of 5.0 \eta C is placed at the origin and another charge of -9.4 \eta C is  placed at x =26.0 cm.

a. where on the x -axis is the resulting electric potential ( voltage) is equal to zero volts?




5312

Physics Modern Physics Level: Misc Level

An alpha particle , starting from rest, acquired a speed of 1.38 x 104 m/s while moving through an electric potential difference.

a. The magnitude of the electrical potential was ---

b.  the final energy of the alpha particle, in electron volts, was ---eV.




5311

Physics Electrostatics Level: Misc Level

A 10 -cm diameter metal sphere produces an electric field of 5,000 N/c towards the sphere at a point 25 cm the surface of the sphere. 

a. The charge on the sphere i is--

b. the voltage at the center of the sphere is --




5310

Physics Electrostatics Level: Misc Level

Two point charges are placed on the x-y plane at the coordinates:q1 =+4 \eta C at ( 15 cm) and q2 =-6 \eta C  at  ( - 10 cm, 10 )

a. The voltage at the origin is ---

b. the force on a +3 \eta C placed at the origin is ---




5309

Physics Circular Motion Level: Misc Level

An object is moving in a circular path of radius 1 m with a uniform speed of 1.0 x 106 m/s. The acceleration of the object has a magnitude of:

(a) 1.0 x 10 3 m/s2

(b) 0

(c) 1.0 x106 m/s2

(d) 1.0 x10 12 m/s2


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