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- Question
Find the sum of the Arithmetic Series upto 36 terms 2, 5, 8, 11,...
Options- A. 3924
- B. 1962
- C. 1684
- D. 1452
- Correct Answer
- 1962
ExplanationArithmetic Series ::
An Arithmetic Series is a series of numbers in which each term increases by a constant amount.
How to find the sum of the Arithmetic Sequence or Series for the given Series ::
When the series contains a large amount of numbers, its impractical to add manually. You can quickly find the sum of any arithmetic sequence by multiplying the average of the first and last term by the number of terms in the sequence.
That is given by Where n = number of terms, a1 = first term, an = last term
Here Last term is given by where d = common difference
Now given Arithmetic Series is
2, 5, 8, 11,...
Here a1 = 2, d = 3, n = 36
Now,
Now, Sum to 36 terms is given by
Therefore, Sum to 36 terms of the series 2, 5, 8, 11,... is 1962.
- 1. In a two-digit number, the digit at the unit's place is 1 less than twice the digit at the ten's place. If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is
Options- A. 47
- B. 59
- C. 23
- D. 35 Discuss
- 2. If a number is multiplied by three-forth of itself. The value thus obtained is 10800. What is that number?
Options- A. 210
- B. 180
- C. 120
- D. 160 Discuss
- 3. A can beat B by 5 meters in 100 m and B can beat C by 15 meters in 200 m race. A can beat C in 400 m race by:
Options- A. 50.5 m
- B. 48.5 m
- C. 45.5 m
- D. 42.5 m Discuss
- 4. A train is running at the rate 40 kmph. A man also is going in the same direction parallel to the train at the speed of 25 kmph. If the train crosses the man in 48 sec, the length of the train is?
Options- A. 50 meters
- B. 100 meters
- C. 150 meters
- D. 200 meters Discuss
- 5. If H is the orthocentre of ? ABC, then the orthocentre of ? HBC is (fig. given) :
Options- A. N
- B. M
- C. A
- D. L Discuss
- 6. A person observed that he required 30 s time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30m/min, than the radius of the circular ground is (take ? = 22/7)
Options- A. 10.5 m
- B. 3.5 m
- C. 5.5 m
- D. 7.5 m Discuss
- 7. A and B are two events such that P(A) = 0.3 and P ( A?B) = 0.8. If A and B are independent, then P (B) is
Options- A. 2/3
- B. 3/8
- C. 2/7
- D. 4/7 Discuss
- 8. If two diameters of a circle intersect each other at right angles, then the quadrilateral formed by joining here end points is a :
Options- A. Rhombus
- B. Rectangle
- C. Square
- D. Parallelogram Discuss
- 9. What is the least number must be added to 1057 to get a number exactly divisible by 23?
Options- A. 1
- B. 3
- C. 2
- D. 4 Discuss
- 10. A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speed is?
Options- A. 4:1
- B. 1.4
- C. 2:1
- D. 1:2 Discuss
More questions
Correct Answer: 47
Explanation:
let us assume the ten's digit number be x and unit's place digit be y.
Then two digit Original Number = 10x + y
According to question ? y = 2x - 1 ................(1)
When digits are interchanged then new number = 10y + x
If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20,
New Number - Original Number = Original number - 20
? 10y + x - (10x + y) = 10x + y - 20
? 10y + x - 10x - y - 10x - y = - 20
? 8y - 19x = - 20
? 19x - 8y = 20 ...................(2)
Put the value of y from equation (1) in above equation (2).
? 19x - 8(2x - 1) = 20
? 19x - 16x - 8 = 20
? 7x = 20 + 8
? 7x = 28
? x = 28/7
? x = 4
Put the value of y in equation (1)
From (i) y = 2 x 4 -1 = y = 7
? original number = 10x + y =10 x 4 + 7 = 47.
Correct Answer: 120
Explanation:
Let the number be N
According to the question N x ( N x 3)/4 = 10800
? 3N2 / 4 = 10800
? N2 = (10800 x 4) / 3= 14400
N = ?14400 = 120
Correct Answer: 48.5 m
Explanation:
? A runs 100 m while B runs 95 m
? A runs 400 m while B runs 95 x 400 / 100 = 380 m
Again, B runs 200 m while C runs 185 m
? B runs 380 m while C runs 185 x 200 / 380 = 3515 / 10 = 351.5 m
Hence, A runs 400 m while C runs 351.5 m
So, A can beat C by (400 ? 351.5) = 48.5 m
Correct Answer: 200 meters
Explanation:
? Relative speed of the train = (40 - 25) km/hr = 15 x (5/18) = 25/6 m/sec
? Length of the train = (48 x 25) / 6 = 200 meters .
Correct Answer: M
Explanation:
From above given triangle , It is clear that the altitudes AL, BM and CN of ?ABC intersect at H. Then H is the orthocentre of ?ABC.
In ?ABC, HL ? BC and BN ? CH.
Thus, the two altitudes HL and BN of ?HBC, intersects at A.
Hence the orthocentre of ?HBC is M .
Correct Answer: 3.5 m
Explanation:
Let the radius of circular field = r m.
Speed of person in m/s = 30/60 = 1/2m/s
According to the question,
[(2?r) /(1/2)] - [(2r)/(1/2)] = 30
? 4?r - 4r = 30
? [4 x (22/7) - 4]r =30
? (125 - 4)r = 30
? (8.5)r = 30
? r = 30/8.5 = 3.5 m
Correct Answer:
Explanation:
Let P(B) = x
Given, P(A?B) = 0.8 and P(A) = 0.3
? P(A) + P(B) - P(A?B) = 0.8
? P(A) + P(B) - P(A) P(B) = 0.8 {?A and B are independent}
? 0.3 + x - 0.3x = 0.8
? 0.7x = 0.5
? x = 5/7
Correct Answer: Square
Explanation:
From given figure , we have
In quadrilateral ABCD , we can see that
Diagonal AB = Diagonal CD ......... ( ? )
AO = OB ......... ( ? )
DO = CO ......... ( ? )
?DOB = 90° ......... ( ? )
From ( ? ) , ( ? ) , ( ? ) and ( ? ) , we get
From above , it is clear that In quadrilateral ABCD , diagonals are equal and they bisect each other at 90° .
? Quadrilateral ABCD is square.
Correct Answer: 1
Explanation:
Correct Answer: 4:1
Explanation:
Let x km . be covered in y hrs.
then, 1st speed = (x / y) km/hr.
2nd speed = [(x/2) / 2y)] km/hr.
= (x/4y) km/hr.
? Ratio of speed = x/y : x/4y = 1 :1/4 = 4: 1
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