HSC Arts इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Compute the sum of first n terms of the following series:
8 + 88 + 888 + 8888 + ...

Compute the sum of first n terms of the following series:
6 + 66 + 666 + 6666 + ...

Compute the sum of first n terms of 1 + (1 + 4) + (1 + 4 + 4²) + (1 + 4 + 4² + 4³) + ...

Find the general term and sum to n terms of the sequence `1, 4/3, 7/9, 10/27, ......`

Find the value of n, if the sum to n terms of the series `sqrt(3) + sqrt(75) + sqrt(243) + ......` is `435 sqrt(3)`

Show that the sum of (m + n)^th and (m − n)^th term of an AP. is equal to twice the m^th term

A man repays an amount of Rs.3250 by paying Rs.20 in the first month and then increases the payment by Rs.15 per month. How long will it take him to clear the amount?

In a race, 20 balls are placed in a line at intervals of 4 meters, with the first ball 24 meters away from the starting point. A contestant is required to bring the balls back to the starting place one at a time. How far would the contestant run to bring back all balls?

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2^nd hour, 4^th hour and n^th hour?

What will Rs.500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

In a certain town, a viral disease caused severe health hazards upon its people disturbing their normal life. It was found that on each day, the virus which caused the disease spread in Geometric Progression. The amount of infectious virus particle gets doubled each day, being 5 particles on the first day. Find the day when the infectious virus particles just grow over 1,50,000 units?

Choose the correct alternative:
If ⁿC₁₀ > ⁿC_r for all possible r, then a value of n is

Choose the correct alternative:
The sum up to n terms of the series `sqrt(2) + sqrt(8) + sqrt(18) + sqrt(32) + ...` is

Find the combined equation of the straight lines whose separate equations are x − 2y − 3 = 0 and x + y + 5 = 0

Show that 4x² + 4xy + y² − 6x − 3y − 4 = 0 represents a pair of parallel lines

Show that 2x² + 3xy − 2y² + 3x + y + 1 = 0 represents a pair of perpendicular lines

Show that the equation 2x² − xy − 3y² − 6x + 19y − 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is tan⁻¹(5)

Prove that the equation to the straight lines through the origin, each of which makes an angle α with the straight line y = x is x² – 2xy sec 2α + y² = 0

Find the equation of the pair of straight lines passing through the point (1, 3) and perpendicular to the lines 2x − 3y + 1 = 0 and 5x + y − 3 = 0

Find the separate equation of the following pair of straight lines
3x² + 2xy – y² = 0