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- Question
- If the m th term of an Arithmetic Progression (AP) is 1/n and n th term is 1/m, then find the sum of mn terms.
Options- A. (mn-1)/4
- B. (mn+1)/4
- C. (mn+1)/2
- D. (mn-1)/2
- Correct Answer
- (mn+1)/2
Explanationlet us assume a be the first term and d the common difference.
According to Question,
mth term of an Arithmetic Progression (AP) is 1/n
Use the Arithmetic Progression formula for mth term,
? a + ( m - 1 ) x d = tm
? a + ( m - 1 ) x d = 1/n
? a + md - d = 1/n .......................(1)
Use the Arithmetic Progression formula for nth term,
? a + ( n - 1 ) x d = tn
? a + ( n - 1 ) x d = 1/m
? a + nd - d = 1/m.........................(2)
Subtracts Equation (1) from Equation (2) , we will get
? a + nd - d - (a + md - d) = 1/m - 1/n
? a + nd - d - (a + md - d) = 1/m - 1/n
? a + nd - d - a - md + d = 1/m - 1/n
? nd - md = 1/m - 1/n
? d(n - m) = 1/m - 1/n
? d(n - m) = (n - m)/mn
? d = 1/mn.......................................(3)
Put the value of d in Equation (1), we will get,
? a + md - d = 1/n
? a + ( m x 1/mn ) - 1/mn = 1/n
? a + 1/n - 1/mn = 1/n
? a = 1/n - 1/n + 1/mn
? a = 1/mn.....................................(4)
Now according to question,
Sum of mn terms = mn/2(2a + ( mn - 1) x d)
Smn = mn/2(2a + ( mn - 1) x d)
Put the value of a and d in above equation, we will get,
Smn = mn/2 [ 2 x 1/mn + ( mn - 1) x 1/mn ]
Smn = mn/2 [2/mn + 1 - 1/mn ]
Smn = mn/2 [ 1 + 1/mn ]
Smn = mn/2 [ ( mn + 1 )/mn ]
Smn = mn/2 (1 + mn)/mn
Smn = 1/2 (1 + mn)
Smn = (1 + mn)/2 = (mn + 1)/2 - 1. The product of two consecutive odd numbers is 19043. Which is the smaller one?
Options- A. 137
- B. 131
- C. 133
- D. 129 Discuss
- 2. The angle of elevation of the top of a hill from each of the vertices A, B, C of a horizontal triangle is ?. The height of the hill is :
Options- A. b tan ? cosec B
- B. a tan ? cosec A 2
- C. c tan ? cosec C 2
- D. None of these Discuss
- 3. From a point on a circular tract 5 Km long A, B and C started running in the same direction at the same time with speeds of 2 1? 2 Km/h, 3 Km/h and 2 Km/h. respectively. Then on the starting point all three will meet again after :
Options- A. 30 hours
- B. 6 hours
- C. 10 hours
- D. 15 hours Discuss
- 4. The radius of the wheel of a vehicle is 70 cm. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle is?
Options- A. 29.46 km/hr.
- B. 31.68 km/hr.
- C. 36.25 km/hr.
- D. 32.72 km/hr. Discuss
- 5. A library has two books each having three copies and three other books each having two copies. In how many ways can all these books be arranged in a shelf so that copies of the same book are not separated?
Options- A. 120
- B. 180
- C. 160
- D. 140 Discuss
- 6. Find the LCM of 1/3, 2/9, 5/6 and 4/27.
Options- A. 1/54
- B. 10/27
- C. 20/3
- D. 3/20 Discuss
- 7. A runs 1 3? 8 times as fast as B. If A gives B a start of 120 m and they reach the goal at the same time, the goal is at a distance of:
Options- A. 360 m
- B. 440 m
- C. 460 m
- D. 380 m Discuss
- 8. 124.35 % 8096 =?
Options- A. 2000
- B. 10000
- C. 1000
- D. 12000 Discuss
- 9. Given that log 10 2 = 0.3010 the value of log 10 5 is?
Options- A. 0.3241
- B. 0.6911
- C. 0.6990
- D. 0.7525 Discuss
- 10. In a month of 31 days, third Thursday falls on 16th. What will be the last day of the month?
Options- A. 5th Friday
- B. 4th Saterday
- C. 5th Wednesday
- D. 5th Thirsday Discuss
More questions
Correct Answer: 137
Explanation:
Let the two consecutive numbers are N and N+2
According to the question
N (N + 2) = 19043
? N2 + 2N - 19043 = 0
? N2 + 139N - 137N - 19043= 0
? N( N + 139) - 137 ( N - 137 ) = 0
? N( N + 139) ( N - 137) = 0
? N = 137 and N = - 139
? N = 137
Correct Answer: a tan ? cosec A 2
Explanation:
Correct Answer: 10 hours
Explanation:
A will reach at starting point in 5 * 2 / 5 = 2 hours ;
B will reach at starting point in 5 / 3 hours ;
C will reach at starting point in 5 / 2 hours ;
Then, on the starting point all three will meet after the L.C.M. of 2, 5 / 3, 5 / 2, 10 / 1 = 10 hours.
Correct Answer: 31.68 km/hr.
Explanation:
Circumference = 2?r
= 2 x (22 / 7) x 70 cm
= 440 cm
Distance travelled in 10 revolutions = 440 x 10 cm
= 4400 cm
= 44 m
? Speed = distance / time
= 44 / 5 m/sec
= (44 / 5) x (18 / 5) km/hr
= 31.68 km/hr
Correct Answer: 120
Explanation:
Regarding all copies of the same book as one book, we have only 5 books. These 5 books can be arranged in 5! ways. But all copies of the same book being identical can be arranged in only one way.
? Required number = 5! x 1! x 1! x 1! x 1! = 120
Correct Answer: 20/3
Explanation:
We known that,
LCM of fractions = (LCM of numerators) / (HCF of denominators)
? Required LCM = (LCM of 1, 2, 5, and 4) / (HCF of 3, 9, 6 and 27)
? = 20/3
Correct Answer: 440 m
Explanation:
The speed of A and B are in the ratio 11 : 8.
Let, speeds be 11s and 8s (in m/sec).
Let, race be of P meter.
Then, time taken by A to run P meter is same as that of B to run (P - 120) meter.
? P / 11 = (P - 120) / 8
? P / 11 = (P - 120 / 8
? 8P = 11 x (P - 120 )
? 8P = 11P - 120 x 11
? 11P - 8P = 120 x 11
? 3P = 11 × 120
? P = 440.
Correct Answer: 10000
Explanation:
? = 124.35% of 8096
= (8096 x 124.35)/100 = 1006737.6/100
= 10067.376 = 10000
Correct Answer: 0.6990
Explanation:
log105 = log10(10/2)
= log1010 - log102
= 1-0.3010
= 0.6990
Correct Answer: 5th Friday
Explanation:
Friday will fall on 3, 10, 17, 24, 31
So, it will be 5th Friday on 31 st
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