To complete a certain work A alone would take m times as many days as B and C together; B would take n times as many days as A and C together; C alone would take p times as many days as A and B together. Show that the number of days in which each do it alone are as . Prove also .

Solve the equation
 

Solve
 
 

Prove that

Prove if a, b, c are unequal and in harmonic progression, then
 

Prove if a, b, c are in harmonic progression, then
 

If the sum of m terms of an arithmetic progression is equal to sum of either the next n terms or the next p terms, prove that
 

Prove that

Eliminate x, y, z from the equations
 
 
 
 

A geometric and harmonic progression have the same p^th, q^th, r^th terms a, b, c respectively. Show that

Solve the equation  

Solve the equations
 

Solve the equation
 

Find the value of

A waterman rows a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. Find the rate of the stream.

If α, β are roots of  and γ, δ are roots of  , show that .

Statement 1 -
Statement 2 -

a) Statement 1 is false, Statement 2 is true

b) Statement 1 is true, Statement 2 is true. Statement 2 is correct explanation of Statement1

c) Statement 1 is true, Statement 2 is true. Statement 2 is not a correct explanation of Statement1

d) Statement 1 is true, Statement 2 is false

In the binomial expansion of , the sum of 5^th and 6^th terms is zero. Then    equals

a)

b)

c)

d)

The sum of the series   is

a)

b)

c) 0

d)

If the coefficient in powers of x of the function  is
 , then  is

a)

b)

c)

d)

The value of  is

a)

b)

c)

d)

The coefficient of the   and  terms in the binomial expansion of  are in arithmetic progression then m and r satisfy the relation

a)

b)

c)

d)

If the coefficient of  in  equals the coefficient of  in  , then a and b satisfy the relation

a)

b)  1

c)

d)