The Uttar Pradesh (UP) Lekhpal Exam was held on 13th Sep 2015, Here we provides you UPSSSC Lekhpal 2015 Questions and Answers Key of all Sets with PDF download. UP Lekhpal Answer Key 2015 Download 13th Sept Exam Paper Solution. UPSSSC Chakbandi Lekhpal Exam 2015 Answer Key and Expected Cut Off Marks. Official answer key or previous question papers when searched online, cannot be found. Like all other government exams, they do not provide question papers and answer keys in the official website.
Lekhpal cut off marks2015 (expected)
General – 52 Marks
OBC – 50 Marks
SC – 45 Marks
ST – 40 Marks
Search for UP Lekhpal Answer key 2015.
Click on the link (if declared officially)
Select set of question papers.
Download the page for answer sheet.
up rajaswa lekhpal answer key
up rajaswa lekhpal answer key 2015
1: If the circumference of a circle is 18.6 cm more than its diameter, then what is the diameter of the circle ?
2πr = 18.6 + 2r
2πr - 2r = 18.6
2r (π - 1) = 18.6
2r = 186/10 X 7/15
r = 186/10 X 7/15 X 1/2
=> 1302/300
D = 2 X 1302/300 = 8.68
2: The HCF and LCM of two numbers are 12 and 2448 respectively. If the difference of the numbers is 60, then the sum of the numbers is ?
difference of numbers = 60
We know that,
LCM x HCF of two numbers = Multiplication of both numbers
Let a and b are two numbers, Then
a X b = LCF X HCF
a X b = 12 X 2448 = 29376 — eqn. (1)
a – b = 60 ; given in question
as, (a – b)2 = a2 + b2 – 2ab and
as (a + b)2 = a2 + b2 + 2ab
(a + b)2 = (a – b)2 + 4ab
(a + b)2 = 60X60 + 4X29376
(a + b)2 = 121104
(a + b) = √(121104)
(a + b) = 348
Sum of two numbers = 348
3: The prices of a scooter and a moped are in the ratio9:5. If a scooter costs Rs. 4200 more than a moped, then the price of the moped is ?
Now,
(x+4200) : x = 9 : 5
9x = 5(x +4200)
9x = 5x + 21,000
4x = 21,000
x = 21,000/5 => 5250.
4: The sum of three numbers is 392. If the ratio of first number to second number is 2:3 and the ratio of second number to third number is 5:8, then the third number is ?
A:B = 2:3 and B:C = 5:8 = ( 5 x 3/5) : ( 8 x 3/5) = 3 : 24/5
Hence, A:B:C = 2:3:24/5 => 10:15:24
C = 392 x 24/49 => 192
5: The perimeter of a triangular field is 540 meters and the ratio of its sides is 5:12:13. What will be the area of this field ?
6: The perimeter of a top surface of a rectangular table is 28 m and its area is 48 m^2. What is the length of the hypotenuse of the table ?
Formula-
The perimeter of the rectangular table = 2 (l + b)
Then, 2(l + b) = 28
l + b = 28/2
l + b = 14 ……………………………………………….. (1)
Area of surface of the rectangular table = 48 m2
Then, lb = 48
l = 48/b
Put the value of l = 48/b in equation (1),
Then, 48/b + b = 14
(48 + b2) /b = 14
48 + b2 = 14b
b2 – 14b + 48 = 0
b2 – 8b – 6b + 48 = 0
b (b – 8) – 6 (b – 8) = 0
(b – 8) (b – 6) = 0
b – 8 = 0 & b – 6 = 0
b = 8 & b = 6
Then, l = 48/6 = 8
l = 8 cm & b = 6 m
Hypotenuse of the rectangular surface of the table = (82 + 62)1/2
= (64 + 36)1/2
= (100)1/2
= 10 m
Then, the hypotenuse of the table is 10 m.
Hence, the answer is (3) 10 m.
7: The perimeter of a triangle is 30 cm and its area is 30 cm2. If the length of the largest side of the triangle is 13 cm, then what is the smallest side of the triangle ?
the area of a triangle = 30 cm2
Then, ab/2 = 30
ab = 30 x 2
ab = 60 cm
a = 60/b
The a + b + 13 = 30
a + b = 30 – 13
a + b = 17 ………….. (1)
Put the value of a = 60/b in equation (1),
60/b + b = 17
60 + b2 = 17 b
b2 – 17 b + 60 = 0
b2 – 12b – 5 b+ 60
b (b – 12) – 5 (b – 12) = 0
(b – 12) (b – 5) = 0
b – 12 = 0 & b – 5 = 0
b = 12 and b = 5
Then, the sides of the triangle are 5, 7 and 13.
Then, the smallest side of the triangle is 5.
8: The radius of the wheel is 21 cm. How many rounds will it take to cover the distance of 792 metres ?
Then, the circumference of the wheel = (2 x 22 x 21)/7
= 2 x 22 x 3
= 132 cm
The distance covered by wheel in a round = 132 cm
Total distance covered by the wheel = 792 m
1 m = 100 cm
Therefore, 792 m = 792 x 100 = 79200 cm
Then, the number of rounds of the wheel to cover the distance 79200 cm = 79200/132
= 600
9: A man is twice as fast as a woman and a woman is twice as fast as a boy. If all of them i.e, a man, a woman and a boy can finish a work together is 4 days, in how many days will a boy do it alone ?
10: In a mixture of 60 litres, the ratio of acid and water is 2:1. What amount of water must be added to make the ration of acid and water as 1:2 ?
Total quantity of mixture = 60 litres
Then, the of acid in the mixture = 60 x 2/3
= 40 litres
The, quantity of water in the mixture = 60 x 1/3
= 20 litres
If water 60 litres added, then the ratio will be 1:2
Then, the new ratio of acid and water = 40 : (20+40)
= 40 : 80
= 1:2
11: In ΔABC, If ∠A = 90o, a = 25 cm, b = 7 cm, then what is the value of tan B ?
C = (252 – 72)1/2
C = (625 – 49)1/2
C = (576)1/2
C = 24 cm
Then, the value of tan B = 7/24
12: If the interest on a sum of money be 1 paisa per rupee per month, what is the rate per cent per annum ?
Ans: b
Let the rate of interest be R%.
Simple Interest = Principal x Time x Rate/100
Then, 1/100 = 1 x 1 x R/100 x 12
1 = R/12
R = 12%
Then, the rate percent of per annum is 10%.
13: The standard deviation of a set of 50 observations is 8. If each observation is multiplied by 2, then the value of standard deviation will be ?
14: For what value of x will the mode of the following data be 27 ?
25, 26, 27, 23, 27, 26, 24, x, 27, 26, 25, 25
15: The sum of mean and median of 1, 6, 8, 3, 2 is ?
= 20/5 = 4
The median if 1, 6, 8, 3, 2 = 8
Then, the sum of mean and median = 8 + 4 = 12.
16: A man traveled 2/11 of his journey by train, 17/22 by car and walked the remaining 1 kilometer. How far did he go ?
A man traveled 2/11 of his journey by train,
Then, the journey traveled by the train = (2/11)x
17/22 by car,
Then, the journey traveled by the car = (17/22)x
Total journey traveled by the train and car = X (2/11 + 17/22)
= X(4 + 17)/22
= (21/22)X
Remaining journey = X – 21X/22
= (22X – 21X)/22
= X/22
Then, X/22 = 1
X = 22 km
Then, the total distance of the journey is 22 km.
17: While computing mean of grouped data, we assume the frequencies are ?
18: What least fraction must be subtracted from the square root of 930.25 so that the result is a whole number ?
30.5 = 30 + .5
= 30 + 1/2
If 1/2 subtracted from the number 30 + 1/2, then the remaining number will be whole number is 30.
Then, 30 + 1/2 – 1/2
= 30
30 is a whole number
19: 300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution ?
Total quantity of the solution = 300 gm
40% sugar,
Then, the quantity of sugar in the solution = 300 x 40/100
= 120 gm
Therefore, the quantity of water in the solution = 300 – 120
= 180 gm
Then, 180 + 120 + X = (300 + X)/2 + 180
120 + X = (300 + X)/2
By cross multiplication,
2 x 120 + 2 x X = 300 + X
240 + 2 X = 300 + X
2 X – X = 300 – 240
X = 60 gm
Short Trick –
(300 + X)/2 = 180
300 + X = 180 x 2
300 + X = 360
X = 360 – 300
X = 60 gm
20: The difference between a number obtained by increasing a certain number by 8% and than obtained by diminishing it by 3% is 407. The original number is ?
According to the question,
108 X/100 – 97 X/100 = 407
(108 X – 97 X)/100 = 407
11 X/100 = 407
11 X = 407 x 100
X = 407 x 100/11
X = 37 x 100
X = 3700
Then, the original number is 3700.
21: Which fraction should be added to the sum of 5 3/4, 4 4/5 and 7 3/8 to make the result a whole number ?
= (23 x 10 + 24 x 8 + 59 x 5)/40
= (230 + 192 + 295)/40
= 717/40 = 17 + 37/40
Let the added X to make whole number.
Then, 37/40 + X = 1
(37 + 40X )/40 = 1
37 + 40 X = 40
40X = 40 – 37
X = 3/40
UP Lekhpal Cut off marks
Lekhpal cut off marks2015 (expected)
General – 52 Marks
OBC – 50 Marks
SC – 45 Marks
ST – 40 Marks
UP Lekhpal Answer Key 2015:
Visit the Official website from the link given below.Search for UP Lekhpal Answer key 2015.
Click on the link (if declared officially)
Select set of question papers.
Download the page for answer sheet.
up rajaswa lekhpal answer key
up rajaswa lekhpal answer key 2015
1: If the circumference of a circle is 18.6 cm more than its diameter, then what is the diameter of the circle ?
- 8.68 cm
- 8.84 cm
- 7.54 cm
- 7.84 cm
2πr = 18.6 + 2r
2πr - 2r = 18.6
2r (π - 1) = 18.6
2r = 186/10 X 7/15
r = 186/10 X 7/15 X 1/2
=> 1302/300
D = 2 X 1302/300 = 8.68
2: The HCF and LCM of two numbers are 12 and 2448 respectively. If the difference of the numbers is 60, then the sum of the numbers is ?
- 248
- 204
- 348
- 284
difference of numbers = 60
We know that,
LCM x HCF of two numbers = Multiplication of both numbers
Let a and b are two numbers, Then
a X b = LCF X HCF
a X b = 12 X 2448 = 29376 — eqn. (1)
a – b = 60 ; given in question
as, (a – b)2 = a2 + b2 – 2ab and
as (a + b)2 = a2 + b2 + 2ab
(a + b)2 = (a – b)2 + 4ab
(a + b)2 = 60X60 + 4X29376
(a + b)2 = 121104
(a + b) = √(121104)
(a + b) = 348
Sum of two numbers = 348
3: The prices of a scooter and a moped are in the ratio9:5. If a scooter costs Rs. 4200 more than a moped, then the price of the moped is ?
- Rs. 5700
- Rs. 6300
- Rs. 3350
- Rs. 5250
Now,
(x+4200) : x = 9 : 5
9x = 5(x +4200)
9x = 5x + 21,000
4x = 21,000
x = 21,000/5 => 5250.
4: The sum of three numbers is 392. If the ratio of first number to second number is 2:3 and the ratio of second number to third number is 5:8, then the third number is ?
- 176
- 192
- 162
- 120
A:B = 2:3 and B:C = 5:8 = ( 5 x 3/5) : ( 8 x 3/5) = 3 : 24/5
Hence, A:B:C = 2:3:24/5 => 10:15:24
C = 392 x 24/49 => 192
5: The perimeter of a triangular field is 540 meters and the ratio of its sides is 5:12:13. What will be the area of this field ?
- 9320 sq.metre
- 9450 sq.metre
- 9560 sq.metre
- 9720 sq.metre
6: The perimeter of a top surface of a rectangular table is 28 m and its area is 48 m^2. What is the length of the hypotenuse of the table ?
- 12.5 m
- 5 m
- 10 m
- 12 m
Formula-
The perimeter of the rectangular table = 2 (l + b)
Then, 2(l + b) = 28
l + b = 28/2
l + b = 14 ……………………………………………….. (1)
Area of surface of the rectangular table = 48 m2
Then, lb = 48
l = 48/b
Put the value of l = 48/b in equation (1),
Then, 48/b + b = 14
(48 + b2) /b = 14
48 + b2 = 14b
b2 – 14b + 48 = 0
b2 – 8b – 6b + 48 = 0
b (b – 8) – 6 (b – 8) = 0
(b – 8) (b – 6) = 0
b – 8 = 0 & b – 6 = 0
b = 8 & b = 6
Then, l = 48/6 = 8
l = 8 cm & b = 6 m
Hypotenuse of the rectangular surface of the table = (82 + 62)1/2
= (64 + 36)1/2
= (100)1/2
= 10 m
Then, the hypotenuse of the table is 10 m.
Hence, the answer is (3) 10 m.
7: The perimeter of a triangle is 30 cm and its area is 30 cm2. If the length of the largest side of the triangle is 13 cm, then what is the smallest side of the triangle ?
- 5 cm
- 6 cm
- 4 cm
- 3 cm
the area of a triangle = 30 cm2
Then, ab/2 = 30
ab = 30 x 2
ab = 60 cm
a = 60/b
The a + b + 13 = 30
a + b = 30 – 13
a + b = 17 ………….. (1)
Put the value of a = 60/b in equation (1),
60/b + b = 17
60 + b2 = 17 b
b2 – 17 b + 60 = 0
b2 – 12b – 5 b+ 60
b (b – 12) – 5 (b – 12) = 0
(b – 12) (b – 5) = 0
b – 12 = 0 & b – 5 = 0
b = 12 and b = 5
Then, the sides of the triangle are 5, 7 and 13.
Then, the smallest side of the triangle is 5.
8: The radius of the wheel is 21 cm. How many rounds will it take to cover the distance of 792 metres ?
- 400
- 600
- 200
- 300
Then, the circumference of the wheel = (2 x 22 x 21)/7
= 2 x 22 x 3
= 132 cm
The distance covered by wheel in a round = 132 cm
Total distance covered by the wheel = 792 m
1 m = 100 cm
Therefore, 792 m = 792 x 100 = 79200 cm
Then, the number of rounds of the wheel to cover the distance 79200 cm = 79200/132
= 600
9: A man is twice as fast as a woman and a woman is twice as fast as a boy. If all of them i.e, a man, a woman and a boy can finish a work together is 4 days, in how many days will a boy do it alone ?
- 28 days
- 7 days
- 21 days
- 14 days
10: In a mixture of 60 litres, the ratio of acid and water is 2:1. What amount of water must be added to make the ration of acid and water as 1:2 ?
- 60 litres
- 72 litres
- 44 litres
- 52 litres
Total quantity of mixture = 60 litres
Then, the of acid in the mixture = 60 x 2/3
= 40 litres
The, quantity of water in the mixture = 60 x 1/3
= 20 litres
If water 60 litres added, then the ratio will be 1:2
Then, the new ratio of acid and water = 40 : (20+40)
= 40 : 80
= 1:2
11: In ΔABC, If ∠A = 90o, a = 25 cm, b = 7 cm, then what is the value of tan B ?
- 24/7
- 24/25
- 7/25
- 7/24
C = (252 – 72)1/2
C = (625 – 49)1/2
C = (576)1/2
C = 24 cm
Then, the value of tan B = 7/24
12: If the interest on a sum of money be 1 paisa per rupee per month, what is the rate per cent per annum ?
Ans: b
- 10 1/2%
- 12%
- 10%
- 15%
Let the rate of interest be R%.
Simple Interest = Principal x Time x Rate/100
Then, 1/100 = 1 x 1 x R/100 x 12
1 = R/12
R = 12%
Then, the rate percent of per annum is 10%.
13: The standard deviation of a set of 50 observations is 8. If each observation is multiplied by 2, then the value of standard deviation will be ?
- 8
- 16
- 2
- 4
14: For what value of x will the mode of the following data be 27 ?
25, 26, 27, 23, 27, 26, 24, x, 27, 26, 25, 25
- 26
- 27
- 24
- 25
15: The sum of mean and median of 1, 6, 8, 3, 2 is ?
- 10
- 12
- 6
- 7
= 20/5 = 4
The median if 1, 6, 8, 3, 2 = 8
Then, the sum of mean and median = 8 + 4 = 12.
16: A man traveled 2/11 of his journey by train, 17/22 by car and walked the remaining 1 kilometer. How far did he go ?
- 24 km
- 33 km
- 27 km
- 22 km
A man traveled 2/11 of his journey by train,
Then, the journey traveled by the train = (2/11)x
17/22 by car,
Then, the journey traveled by the car = (17/22)x
Total journey traveled by the train and car = X (2/11 + 17/22)
= X(4 + 17)/22
= (21/22)X
Remaining journey = X – 21X/22
= (22X – 21X)/22
= X/22
Then, X/22 = 1
X = 22 km
Then, the total distance of the journey is 22 km.
17: While computing mean of grouped data, we assume the frequencies are ?
- centred at the upper limit of the classes
- centred at the lower limits of the classes
- evenly distributed over all the classes
- centres at the class markes of the classes
18: What least fraction must be subtracted from the square root of 930.25 so that the result is a whole number ?
- 1/6
- 4/3
- 2/3
- 1/2
30.5 = 30 + .5
= 30 + 1/2
If 1/2 subtracted from the number 30 + 1/2, then the remaining number will be whole number is 30.
Then, 30 + 1/2 – 1/2
= 30
30 is a whole number
19: 300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution ?
- 60 gm
- 25 gm
- 45 gm
- 40 gm
Total quantity of the solution = 300 gm
40% sugar,
Then, the quantity of sugar in the solution = 300 x 40/100
= 120 gm
Therefore, the quantity of water in the solution = 300 – 120
= 180 gm
Then, 180 + 120 + X = (300 + X)/2 + 180
120 + X = (300 + X)/2
By cross multiplication,
2 x 120 + 2 x X = 300 + X
240 + 2 X = 300 + X
2 X – X = 300 – 240
X = 60 gm
Short Trick –
(300 + X)/2 = 180
300 + X = 180 x 2
300 + X = 360
X = 360 – 300
X = 60 gm
20: The difference between a number obtained by increasing a certain number by 8% and than obtained by diminishing it by 3% is 407. The original number is ?
- 3700
- 3400
- 3500
- 3600
According to the question,
108 X/100 – 97 X/100 = 407
(108 X – 97 X)/100 = 407
11 X/100 = 407
11 X = 407 x 100
X = 407 x 100/11
X = 37 x 100
X = 3700
Then, the original number is 3700.
21: Which fraction should be added to the sum of 5 3/4, 4 4/5 and 7 3/8 to make the result a whole number ?
- 1/40
- 3/40
- 1/10
- 1/20
= (23 x 10 + 24 x 8 + 59 x 5)/40
= (230 + 192 + 295)/40
= 717/40 = 17 + 37/40
Let the added X to make whole number.
Then, 37/40 + X = 1
(37 + 40X )/40 = 1
37 + 40 X = 40
40X = 40 – 37
X = 3/40
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