Q.1 Ram invests a total sum of 2000 rupees on government bonds in 4 years. If these investments are in A.P and the sum of squares of the investments is 1200000. Find the investment made by ram in each year respectively. It is also known that he always invest more than the previous year.

Q.2 Ram invest different amounts during the year on shares. S₁, S₂, S₃……….S_m are different sums of ‘n’ amounts invested in ‘m’ years. If the amounts invested during the years are in A.P whose first terms are 1,2,3…..m and common difference are 1,3,5…..,(2m-1) respectively then find the total amount invested by Ram in ‘m’ years.

Q.3 Find the sum of the series .4 + .44 + .444……. to n terms

Q.4 If the equation px² + 2qx + r = 0 and dx² + 2ex + f = 0 have a common root, and p,q,r are in G.P.,
then in which type of progression is d/p , e/q , f/r

Q.5 Find the sum of all the terms, If the first 3 terms among 4 positive integers are in A.P and the last 3 terms are in G.P. Moreover the difference between the first and last term is 40.

Q.6 What should come at the place of question mark? 46080, 3840, 384, 48, 8, 2, ?

Q.7 The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.

Q.8 Given A = 2⁶⁵ and B = (2⁶⁴ + 2⁶³ + 2⁶² + ... + 2⁰), which of the following is true?

Q.9 If log 2, log (2x - 1) and log (2x + 3) are in A.P, then x is equal to ____

Q.10 Let α β) be the roots of x² - x + p = 0 and γ, δ) be the roots of x² - 4x + q = 0 where p and q are integers. If α, β, γ, θ) are in geometric progression then p + q is