Class XI Revision Quiz Week 3 Day 4

The sum of the series where Ci represents the binomial coefficients is

Find the solution of the given series
C(50,1)+2C(50,2)+3C(50,3)+...+50(C(50,50))

Air of density  is blowing across the horizontal wings of an aeroplane in such a way that its speeds above and below the wings are 150 ms^-1 and
100 ms^-1, respectively. The pressure difference between the upper and lower sides of the wings, is :

Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angle of contact θ and the height h upto which water rises change. These changes are :

A thin tube sealed at both ends is 100 cm long. It lies horizontally, the middle 20 cm containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced?

(Given : cross section of the tube can be assumed to be uniform)

A copper wire of length 1 .0 m and a steel wire of length 0 .5 m having equal cross-sectional areas are joined and to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm. If the young’s moduli of copper and steel are respectively  and  the total extension of the composite wire is :

A body of mass ‘m’ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is 1 cm. If the angular velocity is doubled, the elongation in the spring is 5 cm. The original length of the spring is :