DCCB Mock Test in English Series 4, DCCB Online Test Series 4

160 = (180*4*R)/100
R = 5%

Part of the book he can read in 1 minute = 1/k
Part of the book he can read in 8 minutes =8/k.

36 (6^m) = (216)^3m+4 => 6² 6^m = (6³)^3m+4 => 6^2+m = 6^9m+12 Equating powers of 6 on both sides.
m + 2 = 9m + 12 => -10 = 8m => m = -5/4

Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000

7 + 5 – (3/2 * 1/4) of 2/7 + 7/2 * 1/16
= 7 + 5 – (3/2 * 1/4) * 2/7 + 7/2 * 1/16 = 7 + 5 – 3/28 + 7/32
= 12 + 3/28 + 7/32 = 12 + (7 * 7 – 3 * 8)/224
= 12 + 25/224 = 12 25/224

65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900

Let the shares of A, B and C be a, b and c respectively.
a:b:c = 1/2:1/3:1/4
a:b:c = 6/12:4/12:3:12 = 6:4:3
Share of C = 3/13 * 1560 = Rs.360.

12/ (2 * 2) = 3 days

x Not younger_______ ↑
The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in ⁶P₆ ways.
The required number of ways = 6(6!) = 4320

100 * 100 = 10000
110 * 125 = 13750
———–
3750
10000 —— 3750
100 ——- ? => 37.5%

A’s one day’s work = 1/30
B’s one day’s work = 1/45
(A + B)’s one day’s work = 1/30 + 1/45 = 1/18
The part of the work completed in 3 days = 3 (1/18) = 1/6.

25% of x = x/4 ; 15% of 1500 = 15/100 * 1500 = 225
Given that, x/4 = 225 – 15 => x/4 = 210 => x = 840.

9/12 = 3/4 * 900 = 675
650
————-
25
1/4 ——– 25
1 ——— ? => Rs.100

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)³ – 1}]
= 12000 * 331/1000 = Rs. 3972

Speed of train relative to man = 63 – 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.

Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm – 166 cm + 106 cm
= 180 * 35 cm – 166 cm + 106 cm/35 = 180 cm – 60 /35 cm
= 180 cm – 1.71 cm = 178.29 cm.

Let the two positive numbers be 5x and 8x respectively.
8x – 5x = 15
3x = 15 => x = 5
=> Smaller number = 5x = 25.

πr² = 30  h = 6
1/3 * 30 * 6 = 60

Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = 9/54 * 60 = 10 min.

1347
7431
————
6084

X – (10/100) X = X * ?
? = 90%

Unit digit in 7¹⁰⁵ = unit digit in [(7⁴)²⁶ * 7]
But, unit digit in (7⁴)²⁶ = 1
unit digit in 7¹⁰⁵ = (1 * 7) = 7

Compound ratio of A:B:C
A:B = 3:4
B:C = 5:6
———-
A:B:C = 15:20:24
We can divide Rs.118000 in this ratio.
Share of A = 15/59 * 118000 = 30000
Share of B = 20/59 * 118000 = 40000
Share of C = 24/59 * 118000 = 48000

Let the capital be Rs. x. Then,
(x * 8 * 1)/100 – (x * 31/4 * 1/100) = 61.50
32x – 31x = 6150 * 4
x = 24,600.

(3^a+1 9^a+2 27^a) / (3^a-1 9^a 27^a+1) = [3^a+1 3^2(a+2) (3³)^a] / [3^a-1 (3²)^a (3³)^a+1] = 3^6a+5 / 3^6a+2 = 3³ = 27.

Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x² = 6912
x² = 576 = 4 * 144 = 2² * 12² (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x² = 1 : 4x = 1: 96.

lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10

Given SP = Rs. 6800
Marked price = [SP(100)]/(100 – d%) = (6800 * 100)/(100 – 15) = Rs. 8000
If SP = Rs. 8000, profit = 60%
CP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs. 5000

RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec

2C + 3T = 1300 — (1)
3C + 3T = 1200 — (2)
Subtracting 2nd from 1st, we get
-C + T = 100 => T – C = 100

Sum of the ages of 14 students
= (16 * 35) – (14 * 21) = 560 – 294 = 266
Required average = (266/14) = 19 years.

x/7 = y/9 => x:y = 7:9
7/16 * 96 = 42

Hence, x = (p + q – r)/r = (p – q + r)/q = (q + r – p)/p
=> x = (p + q – r + p – q + r + q + r – p)/(r + q + p)
=> x = (p + q + r)/(r + q + p) = 1.

Let sum = x. Then, S.I. = 2x/5, Time = 10 years.
Rate = (100 * 2x) / (x * 5 * 10) = 4%

300 = 4.75 = 4.25.3 = 2².5².3¹
Number of factors of 300 = (2 + 1)(2 + 1)(1 + 1) = 18.
There are 16 factors of 300 excluding 1 and itself.

x² + 7x – 6x + 42 = 0
x(x + 7) – 6(x + 7) = 0
(x + 7)(x – 6) = 0 => x = -7, 6

Crocodile, Turtle, Allegator and Frog are amphibians, while Chameleon is a terrestrial animal.

Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x – 8) + (7x – 8) + (9x – 8) = 56
20x = 80 => x = 4
Their present ages are 16, 28 and 36 years respectively.

(800*3*3)/100 = 72
920 + 72 = 992

Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 – 96 =Rs. 4
100 —— 4
? ——— 200 => 5000

Except 4242, all other numbers are divisible by 11.

For a number to be divisible by 4, the number formed by the last two digits of that number must be divisible by 4.
For a number to be divisible by 9, the sum of its digits must be divisible by 9.
Among the choices, choices (a) and (b) are divisible by 4 but of the first two choices, only choice (b) is divisible by 9.
Hence choice (b) is divisible by both 4 and 9.

If the interest earned is 25% more than the earlier interest then the rate of interest also should be 25% higher than the earlier rate.
Let the earlier rate of interest be x%.
Now it will be (x + 3)%
% increase = (x + 3) – x/x * 100 = 25
=> x = 12

1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 365 = 266 * 3 = 798
———–
987

S = 180/6 * 18/5 = 108 kmph

Let the monthly salaries of Ram and Shyam be Rs. r and Rs. s respectively.
10/100 r = 8/100 s
r = 4/5 s
Monthly salary of Abhinav = (1.92 lakhs)/12 = Rs. 0.16 lakhs
s = 2(0.16 lakhs) = 0.32 lakhs
r = 4/5(0.32 lakhs) = Rs. 25600

P = (P*3*R)/100
R = 33 1/3%

We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways = 6! * ⁷P₆