Write the correct answer
0 of 24 Questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 24 Questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score 

Your score 

The sum of four consecutive numbers in an A.P. is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7 : 15. Find the numbers.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let the four consecutive numbers be
..(1)
when
Four numbers are 2, 6, 10, 14
If \(\dfrac{1}{a},\dfrac{1}{b},\dfrac{1}{c} \) are in A.P., show that :
(i) \(\dfrac{b+c}{a},\dfrac{c+a}{b},\dfrac{a+b}{c} \) are in A.P.
(iii) \(bc, ca, ab \) are in A.P.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(i) are in A.P.
We know that, if a, b, c are in AP, then b – a = c – b
If, are in AP
Then,
If are in AP
Then,
Let us take LCM
Now let us consider LHS:
Multiply both numerator and denominator by ‘c’ we get ,
Now let us consider RSS:
Multiply both numerator and denominator by ‘a’ we get,
(ii) are in A.P.
We know that if ,
Consider LHS:
Upon simplification we get,
Now,
we know,
are in AP
So,
or
Hence, given terms are in AP.
If pth, qth and rth terms of an A.P. are a, b and c respectively, then show that :
(a) a(q – r) + b(r – p) + c(p – q) = 0
(b) (a – b)r + (b – c)p + (c – a)q = 0
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(a)
term …(1)
term …(2)
term …(3)
(b)
The sums of \(x \) terms of three A.Ps are \(S_1,S_2 \) and \(S_3 \). The first term of each is unity and the common differences are 1, 2 and 3 respectively . Prove that \(S _1 + S_3 = 2S_2\).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(RHS)
If mth term of an A.P. is \(\dfrac{1}{n} \) and the \(n^{th} \) term is \(\dfrac{1}{m} \), show that the sum of its mn terms is \(\dfrac{1}{2}\ (mn+1) \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
term ….(1)
term …(2)
In eqn (1)
If \(S_1,S_2,S_3 \) be the sums of \(n,2n \) and \(3n \) terms respectively of an A.P., prove that \(S_3=3(S_2S_1) \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Prove that no matter what the real numbers a and b are, the sequence with nth term a + nb is always an A.P. What is the common difference? What is the sum of the first 20 terms ?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
nth term
term
which is constant. Hence the sequence is an AP and the common difference is
A contractor employed 150 labourers to finish a piece of work in a certain number of days. 4 workers went away the second day, 4 more workers went away the third day and so on. If it took 8 more days to finish the work, find the number of days in which the work was completed.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
AP …. term
work done
term
not possible so
The students of a school decided to beautify the school on the annual day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at interval of every 2m. The flags are stored in the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag completing this jobs and returning back to collect her books ? What is the maximum distance she travelled carrying a flag?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
For placing second flag and return his interval position
For placing flag and return his interval position
Maximum distance = Distance travelled by Ruchi during placing the flag in her left position or flag in her right position
Kartik repays his total loan of Rs. 1,18,000 by paying every month starting with the first instalment of 1000. He increases the instalment by Rs 100 every month. What amount will be paid by him in the 30th instalment? What amount of loan does he still have to pay after the 30th instalment?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Amount of first installment = 1000
Increase in amount of each installment
Amount of loan to be still paid after paying the both installment
A contractor on construction job specifies a penalty for delay of completion beyond a certain date as follows : Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day etc. the penalty for each succeeding day being Rs 50 more than for the preceding day. How much money the contractor has to pay as penalty if he has delayed the work by 30 days ?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(a, b\) and \(c \) be the sums of first \(p, q\) and \(r \) terms respectively of an AP, show that \(\dfrac{a}{p}(qr)+\dfrac{b}{q}(rp)+\dfrac{c}{r}(pq)=0 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Sum of first p, q and r terms of an AP. Are a , b and c respectively. Prove that
let the first term of AP be A and common difference be d.
sum of the first p terms is
….(1)
sum of the first q terms is …(2)
sum of the first r terms is …(3)
now
In November 2009, the number of visitors to a zoo increased daily by 20. If a total of 12300 people visited the zoo in that month, find the number of visitors on 1st November 2009.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Number of visitors
A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top (see figure). If the top and bottom rungs are 2.5 m apart, what is the length of the wood required for the rungs?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The gap between two consecutive rungs is 25 cm and top and bottam rungs are 2.5 m i.e 250 cm apart
Number of rungs
Find the sum of the first 31 terms of an A.P. whose nth term is given by \(3+\dfrac{2}{3}n \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
A sum of Rs 2700 is to be used to give eight cash prizes to students of a school for their overall acedemic performatnce. If each prize is Rs. 25 more than its preceding prize find the value of each of the prizes.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let first cash prize
Next 7 cash prize
A/Q
value of first prize
value of second prize
value of third prize
value of fourth prize
value of fifth prize
value of sixth prize
value of seventh prize
value of eighth prize
In an A.P., prove that \(a_{m+n} + a_{mn} = 2a_m\), where \(a_a \) denotes nth term of the A.P.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
…(1)
…(2)
…(3)
Adding (1) and (2)
A spiral is made up of successive semicircles, with centres alternatively at A and B, starting with centre at A of radii 0.5 cm, 1.5 cm, 2 cm. as shown in the figure. What is the total length of such spiral made up of thirteen consecutive semicircles? (Take \(\pi=\dfrac{22}{7} \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Length of first semicircle
Length of second semicircle
Length of third semicircle
A manufacturer of T.V. sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find
(a) The production in the first year
(b) The production in the 10th year
(c) The total production in first 7 years
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let production in the first year
…(1)
…(2)
Subtracting (1) from (2) we get
(i) Production in the first year
(ii) Production in the 10th year
(ii) Production in the 7 year
The houses of a row are numbered consecutively from 1 to 49. There is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the number of the houses following it. Find this value of x.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
A woman takes up a job of Rs 8000 per month with an annual increment of Rs 100. What will she earn over a period of 10 years ?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Annual salary in 1st year
Annual salary in 2nd year
years
228 logs are to be stacked in a store in the following manner: 30 logs in the bottom, 28 in the next row, then 26 and so on. In how many rows can these 228 logs be stacekd? How many logs are there in the last row?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If the last row be , number of logs in the last row
Since the number of logs cannot be negative the no. of rows should be 12
Let row
logs
Neera saves Rs 1600 during the first year, Rs 2100 in the second year, Rs 2600 in the third year. If she continues her savings in this pattern, in how many years will she save Rs 38500?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
First year
Second year
Hence she will save in years
If \(m \) times the \(m^{th} \) term of an A.P. is equal to \(n \) times its \( n^{th}\) term, show that the \((m+n)^{th}\) term of the A.P. is zero \((m\ne n) \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Rejecting the non trivial case of we assume that and are different.
The LHS of this equation denotes the term of the AP which is zero.