SSC CGL 20th August Shift 3 - QA
AB is a chord of a circle with centre O and P is any point on the circle. If ∠APB = 122°, then what is the measure of ∠OAB?
- A.
32°
- B.
15°
- C.
22°
- D.
28°
Answer: Option A
Explanation :
Workspace:
In triangle PQR, points E and F are on sides PQ and PR respectively such that EF is parallel to QR. If PE = 2 cm and EQ = 3 cm, then area(△PQR) : area(△PEF) is equal to:
- A.
3 : 2
- B.
25 : 4
- C.
5 : 2
- D.
9 : 4
Answer: Option B
Explanation :
△PQR and △PEF are similar triangles.
⇒ =
⇒ =
⇒ =
⇒ =
⇒ Area of triangle PQR : Area of triangle PEF = 25:4
Hence, the correct answer is Option B
Workspace:
The average weight of a certain number of students in a class is 55.5 kg. If 4 students with average weight 60 kg join the class, then the average weight of all students in the class increases by 360 g. The number of students in the class, initially, is:
- A.
46
- B.
31
- C.
41
- D.
36
Answer: Option A
Explanation :
Let the initial number of students = n
Average of the weight of 'n' students = 55.55
Sum of the weight of 'n' students = 55.55n
Sum of the weight of 4 students = 60 x 4 = 240 kg
According to the problem,
= 55.55 +
= 55.55 + 0.36
= 55.86
55.55n + 240 = 55.86n + 223.44
0.36n = 16.56
n = 46
The initial number of students = n = 46
Hence, the correct answer is Option A
Workspace:
The area of a triangular plot having sides 12 m, 35 m and 37 m is equal to the area of a rectangular field whose sides are in the ratio 7 : 3. The perimeter (in m) of the field is:
- A.
20
- B.
20
- C.
24
- D.
24
Answer: Option A
Explanation :
Perimeter of triangular plot = 12 + 35 + 37 = 84 m
Half of the perimeter = s = 42 m
Area of the triangular plot =
=
= 210 cm2
The area of a triangular plot is equal to the area of a rectangular field.
Area of a rectangular field = 210 cm2
Sides of rectangular filed are in the ratio 7 : 3.
Let the sides of the rectangular field are 7p and 3p respectively.
7p x 3p = 210
p2 = 10
p =
Perimeter of the rectangular field = 2(7p + 3p)
= 20p
= 20 cm
Hence, the correct answer is Option A
Workspace:
Two circles of radius 15 cm and 37 cm intersect each other at the points A and B. If the length of common chord is 24 cm, what is the distance (in cm) between the centres of the circles?
- A.
44
- B.
45
- C.
42
- D.
40
Answer: Option A
Explanation :
From triangle AHG,
AH2 + GH2 = AG2
AH2 + 122 = 152
AH2 + 144 = 225
AH2 = 81
AH = 9 cm
From triangle CHG,
CH2 + GH2 = CG2
CH2 + 122 = 372
CH2 + 144 = 1369
CH2 = 1225
CH = 35 cm
Distance between two circles = AC = AH + CH = 9 + 35 = 44 cm
Hence, the correct answer is Option A
Workspace:
If x - y = 4 and x3 - y3 = 316, y > 0 then the value of x4 - y4 is:
- A.
2500
- B.
2320
- C.
2401
- D.
2482
Answer: Option B
Explanation :
x - y = 4 ...(1)
(x - y)3 = 64
x3 - y3 - 3xy(x - y) = 64
316 - 3xy(4) = 64
12xy = 252
xy = 21 ...(2)
x - y = 4
(x - y)2 = 42
x2 + y2 - 2xy = 16
x2 + y2 - 2(21) = 16
x2 + y2 = 58 ...(3)
(x + y)2 = x2 + y2 + 2xy
(x + y)2 = 58 + 2(21)
(x + y)2 = 100
x + y = 10 ...(4)
x4 - y4 = (x2 + y2)(x2 - y2 )
= (x2 + y2 ) (x + y) (x - y)
= (58) (10) (4)
= 2320
Hence, the correct answer is Option B
Workspace:
The number 823p2q is exactly divisible by 7, 11 and 13. What is the value of (p - q)?
- A.
8
- B.
5
- C.
11
- D.
3
Answer: Option B
Explanation :
Workspace:
In the table, production and sale (in 1000 tonnes) of a certain product of a company over 5 years is given. Study the table and answer the question.
- A.
2016, 2018
- B.
2019
- C.
2015, 2016
- D.
2015, 2019
Answer: Option D
Explanation :
In 2015, percentage of sales of the production = × 100 = 80%
In 2016, percentage of sales of the production = × 100 = 92.14%
In 2017, percentage of sales of the production = × 100 = 75.86%
In 2018, percentage of sales of the production = × 100 = 96.67%
In 2019, percentage of sales of the production = × 100 = 86.87%
∴ In 2015 and 2019, sale is 80% or more but less than 90% of the production.
Hence, the correct answer is Option D
Workspace:
The value of is:
- A.
- B.
-
- C.
- D.
-
Answer: Option A
Explanation :
=
=
=
=
=
Hence, the correct answer is Option A
Workspace:
Study the following table and answer the question:
Percentage of marks obtained by six students A, B, C, D, E and in five subjects.
What are the average marks of students B, C, D and F in Math?
- A.
125.5
- B.
82.5
- C.
123.75
- D.
120.75
Answer: Option C
Explanation :
The average marks of students B, C, D and F in Math =
=
=
=
= 123.75
Hence, the correct answer is Option C
Workspace:
Hari suffered a loss of 8% by selling an article. If he had sold it for ₹300 more, he would have made a profit of 4%. Find his CP (in ₹).
- A.
2400
- B.
2250
- C.
2575
- D.
2500
Answer: Option D
Explanation :
Let the cost price of article = 100C
Hari suffered a loss of 8% by selling an article.
Selling price of the article = × 100C = 92C
If he had sold it for ₹300 more, he would have made a profit of 4%.
92C + 300 = × 100C
92C + 300 = 104C
12C = 300
C = 25
The cost price of article = ₹2500
Hence, the correct answer is Option D
Workspace:
Two numbers are in the ratio 2 : 3. If 5 is subtracted from the first number and six is added to the second number, then the ratio becomes 5 : 12. What would the ratio become when eight is added to each number?
- A.
19 : 14
- B.
14 : 19
- C.
11 : 14
- D.
14 : 11
Answer: Option B
Explanation :
Two numbers are in the ratio 2 : 3.
Let the two numbers are 2p and 3p respectively.
According to the problem,
=
24p - 60 = 15p + 30
9p = 90
p = 10
Required ratio = = = =
Hence, the correct answer is Option B
Workspace:
Price of a one gram gold coin decreased by 10% on its initial price on Monday and increased by 20% on Tuesday and again increased by 8% on Wednesday, and 5% increase on Thursday. If the final price on Thursday is ₹5511.24, then the initial price (in ₹) of one gram gold coin on Monday was?
- A.
4000
- B.
4250
- C.
4500
- D.
5000
Answer: Option C
Explanation :
Let the initial price of one gram gold coin on Monday was 'P'.
According to the problem,
P × × × × = 5511.24
P × × × 108 × = 551124
P × × × 27 × = 551124
P = 4500
The initial price of one gram gold coin on Monday was ₹4500.
Hence, the correct answer is Option C
Workspace:
A boat goes 30 km upstream in 3 hours and downstream in 1 hour. How much time (in hours) will this boat take to cover 60 km in still water?
- A.
6
- B.
3
- C.
2
- D.
5
Answer: Option B
Explanation :
Let the speed of the boat in still water = m
Speed of the stream = s
Upstream speed = m - s
= m - s
m - s = 10............(1)
Downstream speed = m + s
= m + s
m + s = 30...........(2)
Adding (1) and (2),
2m = 40
m = 20
Speed of the boat in still water = 20 km/h
Time required for the boat to cover 60 km in still water = = 3 hours
Hence, the correct answer is Option B
Workspace:
Simplify the following expression:
8 ÷ 4 of 2 − 15 ÷ 2 of 5 − 6 ÷ 5 × (−7 + 5) of 2
- A.
-
- B.
31
- C.
7
- D.
4
Answer: Option D
Explanation :
8 ÷ 4 of 2 − 15 ÷ 2 of 5 − 6 ÷ 5 × (−7 + 5) of 2
= 8 ÷ 4 of 2 − 15 ÷ 2 of 5 − 6 ÷ 5 × (−2) of 2
= 8 ÷ 8 − 15 ÷ 10 − 6 ÷ 5 × (−4)
= - - × (-4)
= 1 - +
=
=
= 4
Hence, the correct answer is Option D
Workspace:
Table shows District-wise data of number of primary school teachers posted in schools ofa city.
Study the table and answer the question.
In which district(s) is the number of female teachers Exceed the number of male teachers by more than 500?
- A.
West and South
- B.
East and North
- C.
North and South
- D.
East and West
Answer: Option B
Explanation :
Difference between number of female teachers and male teachers respectively in East district = 2375 - 1650 = 725
Difference between number of female teachers and male teachers respectively in North district = 2651 - 1075 = 1576
Difference between number of female teachers and male teachers respectively in West district = 1520 - 1280 = 240
Difference between number of female teachers and male teachers respectively in Central district = 859 - 690 = 169
In East and North districts, number of female teachers Exceed the number of male teachers by more than 500.
Hence, the correct answer is Option B
Workspace:
Study the following table and answer the question:
Percentage of marks obtained by six students A, B, C, D, E and F in five subjects.
The total marks obtained by student F in English, Science and Hindi is approximately what percent of the total marks obtained by student A in English, Mathematics, Science and Hindi?
(Correct to one decimal place)
- A.
50.2
- B.
49.3
- C.
48.4
- D.
45.5
Answer: Option B
Explanation :
The total marks obtained by student F in English, Science and Hindi = × 50 + × 80 + × 75 = 36 + 52 + 45 = 133
The total marks obtained by student A in English, Mathematics, Science and Hindi = × 50 + × 150 + × 80 + × 75 = 35 + 135 + 52 + 48 = 270
Required percentage = × 100
= 49.259%
= 49.3% (approximately)
Hence, the correct answer is Option B
Workspace:
loan is to be returned in two equal yearly instalments. If the rate of interest is 10% p.a.. compounded annually and each instalment is ₹6534, then the total interest charged (in ₹) is:
- A.
1642
- B.
1579
- C.
1728
- D.
1867
Answer: Option C
Explanation :
Workspace:
What is the coefficient of x in the expansion of (3x - 4)3?
- A.
108
- B.
-108
- C.
144
- D.
-144
Answer: Option C
Explanation :
Workspace:
The value of sin2 60° cos2 45° + 2 tan2 60° - cosec2 30° is equal to
- A.
- B.
- C.
-
- D.
-
Answer: Option B
Explanation :
sin2 60° cos2 45° + 2 tan2 60° - cosec2 30° = ∙ + 2 - (2)2
= ∙ + 2(3) - 4
= + 6 - 4
= + 2
=
=
Hence, the correct answer is Option B
Workspace:
The side of an equilateral △ABC is 3 cm. P is a point on side BC such that BP : PC = 1 : 2. The length (in cm) of AP is:
- A.
6
- B.
7
- C.
7
- D.
6
Answer: Option B
Explanation :
Workspace:
The marked price of an article is ₹5320. It is subject to two successive discounts, the first being 15%, and the second at a rate of 20% of the first. What is the selling price (to nearest ₹) of the article?
- A.
₹4522
- B.
₹4127
- C.
₹4000
- D.
₹4386
Answer: Option D
Explanation :
The marked price of an article is ₹5320.
First discount = 15%
Price of the article after 15% discount = × 5320 = ₹4522
Second discount = 20% of 15% = × 15% = 3%
Selling price of the article after 3% discount = × 4522 = ₹4386.34
= ₹4386 (approximately)
Hence, the correct answer is Option D
Workspace:
The value of sec4 θ(1 - sin4 θ) - 2tan2 θ is:
- A.
- B.
1
- C.
-1
- D.
0
Answer: Option B
Explanation :
sec4 θ(1 - sin4 θ) - 2 tan2 θ = sec4 θ - sec4 θ sin4 θ - 2 tan2 θ
= sec4 θ - - 2 tan2 θ
= sec4 θ - tan4 θ - 2 tan2 θ
= (sec2 θ + tan2 θ) (sec2 θ - tan2 θ) - 2 tan2 θ
= (sec2 θ + tan2 θ) (1) - 2 tan2 θ
= sec2 θ + tan2 θ - 2 tan2 θ
= sec2 θ - tan2 θ
= 1
Hence, the correct answer is Option B
Workspace:
If x + y + z = 3, xy + yz + zx = -12x + y + z = 3, xy + yz + zx = −12 and xyz = -16xyz = −16, then the value of is :
- A.
9
- B.
8
- C.
10
- D.
11
Answer: Option C
Explanation :
x + y + z = 3
x + y = 3 - zx + y = 3 − z ........(1)
(x + y)3 = (3 - z)3
x3 + y3 + 3xy(x + y) = 27 - z3 - 3.3.z(3 - z)
x3 + y3 + 3xy(3 - z) = 27 - z3 - 9z(x + y) [From (1)]
x3 + y3 + 9xy - 3xyz = 27 - z3 - 9xz - 9yz
x3 + y3 + z3 = 27 - 9xy - 9xz - 9yz + 3xyz
x3 + y3 + z3 = 27 - 9(xy + yz + zx) + 3xyz
x3 + y3 + z3 = 27 - 9(-12) + 3(-16)
x3 + y3 + z3 = 27 + 108 - 48
x3 + y3 + z3 = 87 .........(2)
=
=
= 10
Hence, the correct answer is Option C
Workspace:
A can do a piece of work in 2 days, and B can dofive times the same work in 15 days when they work for ten hours a day. If they work together, then how many hours in addition to a days’ work will they require to complete the work?
- A.
2
- B.
0
- C.
3
- D.
1
Answer: Option A
Explanation :
Workspace: