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Class XI Revision Quiz Week 2 Day 5

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Question 1

Which is not commutative ?

Question 2

Let f: X-> yf(x) = sinx + cosx + 2√ 2 be invertible .
Then which X-> Y is not possible?

Question 3

Let f(x) =3x² +7x +c , where c is a varibale coefficient and x>7/6 . Then the value of [c] such that f(x) touches f^-1(x) is ([.] is G.I.F. )

Question 4

If f : (2,3) -> (0,1) defined by f(x) =x-[x], where [.] is greatest integer function , Find the inverse

Question 5

If f : Z->Z defined by f(x) =[x+1] ,where [.] is G.I.F.
Find the inverse

Question 6

Two bodies A and B rotate about an axis, such that angle θ_A (in radius) covered by the first body is proportional to the square of time, & θ_B (in radius) covered by the second body varies linearly. At t = 0, θ_A = θ_B = 0. If A completes its first revolution in

sec. & B needs 4π sec. to complete half revolution then; angular velocity ω_A: ω_B at t = 5 sec. are in the ratio

Question 7

A uniform circular ring of mass per unit length λ and radius R is rotating with angular velocity ω about its own axis in a gravity free space. Tension in the ring is

Question 8

A uniform rod of mass m and length

rotates in a horizontal plane with an angular velocity ω about a vertical axis passing through one end. The tension in the rod at distance x from the axis is:

Question 9

An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is θ, then :

Question 10

A rigid massless rod of length 3

has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be :

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Oct 8JEE & BITSAT