Daily Maths Practice Set-38

(With Detail Solution)

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 DAILY MATHS PRACTISE SET- 38

1. In a factory, Ajay and Vijay work on the same

machine to cut diamonds but on alternate hour
basis. Ajay works for the first hour and then Vijay
works for the second hour and so on. Ajay can (a) 5 (b) 4 (c) 2 (d) 3
complete the work in 6 hour s, while Vijay
6. In  ABC and  PQR, AB = PQ and  B =  Q. The
completes it in 16 hours if they work individually.
In how much time can they complete the work if two triangles are congruent by SAS criteria, if :
they are using the machine on alternate basis?  ABC  PQR AB = PQ B =Q
(SAS)
(a) BC = QR (b) AC = PR
(c) AC = QR (d) BC = PQ
7. Anuradha invests her money in a firm where the
principal amount becomes 3 times in 10 years.
What is the yearly rate of simple interest offered
by the firm ?
(a) 8 hr 30 min (b) 5 hr
(c) 9 hr (d) 9 hr 30 min
2. In  ABC and  DEF,  A = 55º, AB = DE, AC = DF,
 E = 85º and  F = 40º. By which property are (a) 25% (b) 20% (c) 22% (d) 18%
 ABC and  DEF congruent ? 8. Study the given graph and answer the question
 ABC  DEF  A = 55º, AB = DE, AC = DF, that follows.
 E = 85º  F = 40º  ABC
 DEF The number of appeared candidates and passed
candidates (in hundreds) in test from six different
(a) SAS property (b) ASA property
institutions.
(c) RHS property (d) SSS property
3. John drives 250 km at 50 km/hr and then he
drives 350km at 70km/hr. Find his average speed
for the whole journey in km/hr.
Appeared Candidates
250 km 50 km/hr
40 Passed Candidates
Number of Candidates (in numbers)

350 km 70 km/hr
35 34
30 26
(km/hr
25 24
(a) 55 km/hr (b) 60 km/hr 20
20 16 20
(c) 58 km/hr (d) 65 km/hr 18
15 12 14
4. If y = 1  3  4 , then the value of 2y4 – 8y³ – 6y² 8
10
+ 28y – 84 is : 5
y = 1 3  4 2y4 – 8y³ – 6y² + 28y – 84 0
A B C D E
The nu mber of candidates who passed fr om
(a) 40 3 (b) 80 3 (c) 20 3 (d) 60 3 distance C and D together is approximately what
percentage (rounded off the nearest integer) of the
5. If two circles do not touch or intersect each other
total number of candidates who appeared from
and one does not lie inside the other, then find
institutions B and E together ?
the number of common tangents.
C D B
 E y
90 84 85
80 72
(a) 100% (b) 77% (c) 95% (d) 90% 65
70
9. Two trains are moving in the opposite direction 57
at the speed of 48 km/hr and 60 k m/hr 60 54
respectively. The time taken by the slower train 50
to cross a man sitting in the faster train is 12 40
seconds. What is the length of the slower train ?
30
20
10
0 x
2011 2012 2013 2014 2015 2016
(a) 480 metres (b) 720 metres What is the approximate percentage of change in
(c) 180 metres (d) 360 metres the number of per sons who have taken the
10. A shopkeeper listed the marked price of a chair insurance policy in the year 2014 to that in the
at a certain amount. If the shopkeeper declares year 2011 (correct to one decimal plane)?
a 15% discount and sold it at Rs 1445, then what
is the marked price ?

Rs 1445
(a) 33.3% (b) 26.4% (c) 35.5% (d) 23.1%
(a) Rs.1750 (b) Rs.1,800
(c) Rs.1700 (d) Rs.1,850 5– 4 5 4
15. If x = and y = , then the value of
11. A person having bought goods for Rs.400 sells half 5 4 5– 4
of it at a gain of 5%. At what gain percentage must he
sell the remainder, so as to gain 25% on the whole? x² – xy + y²
x² + xy + y² = ?
Rs. 400

5– 4 5 4 x² – xy + y²
x= y=
5 4 5– 4 x² + xy + y²
(a) 30% (b) 25% (c) 20% (d) 45%
12
12. If cotA = , then the value of sinA = ? 361 341 384 321
5 (a) (b) (c) (d)
363 343 387 323
12
cotA = sinA =? 4
5 16. If sin θ – cos θ = , then find the value of sin θ +
5
5 12 5 13 cos θ .
(a) (b) (c) (d)
13 13 12 12
4
13. What is the value of tan 6° × tan 45° × tan 84°? sin θ – cos θ = sin θ + cos θ
5
tan 6° × tan 45° × tan 84°
(a) 1 (b) tan 6° × tan 39°
(c) 3 (d) tan 6° + tan 45° + tan 84° 5 5 34 24
(a) (b) (c) (d)
14. The given bar diagram represents the number of 34 24 5 5
persons who have taken an insurance policy on 17. An iron rod with diameter 4 cm and length 12 cm
the y- axi s, and the year of purchase of the is drawn into a wire of length 12 m of uniform
insurance policy on the x-axis. thickness. Determine the thickness of the wire.
y-

x-
(a) 0.6 cm (b) 0.7 cm (c) 0.3 cm (d) 0.4 cm
18. The fourth proportional to 16 and 26 and 32 is : school D and E is how much percent less than
the number of players participating in game M
from school H and I ?
(a) 15 (b) 52 (c) 54 (d) 24
D E L
19. If tan    = 3 , tan    = 1 where    and
H I M
   are acute angles, then what is tan (6  )?
(a) 22.68 percent (b) 32.52 percent
tan     = 3 , tan    = 1    
(c) 26.22 percent (d) 43.53 percent
    tan (6  ) 23. The HCF of 222, 642 and 1062 is ____.

(a) –1 (b) 0 (c) 1 (d) 222, 642 1062 (HCF) _____

2 –1
(a) 6 (b) 8 (c) 4 (d) 2
2p 1  1 24. The table given below shows the cost price and
20. If p + 
p² – 5p +1 10 , p  0, then the value of
= 
 p  profit percentage of 5 articles.
is :

2p  
=
1
p  0, p + 1  Article Cost price Profit
p² – 5p +1 10  p 

P 450 90%
Q 250 100%
(a) 10 (b) 25 (c) 1 (d) 15
R 600 60%
21. In a division sum, the divisor is 10 times the
quotient and four times the remainder. What is S 730 70%
the dividend if the remainder is 45 ? T 400 80%
Total selling of article P and Q is what percent of
total selling price of article R, S and T ?
(a) 4123 (b) 3285 (c) 2895 (d) 5412 P Q R, S T
22. The table given below shows the number of players
participating in two games in six different schools. (a) 36.26 percent (b) 49.27 percent
(c) 35.87 percent (d) 46.38 percent
25. A and B invested their money in a business in
Games the ratio of 9 : 5. If 10% of the total profit goes for
School L M charity and A’s share is Rs 29840, what is the
total profit (in Rs. to the nearest integer)?
D 82 136
E 68 92 A B
F 56 72 A
G 78 94 Rs 29840 (Rs.
H 44 86
I 100 108 (a) Rs. 51745 (b) Rs. 55715
Number of players participating in game L from (c) Rs. 57545 (d) Rs. 51575

ANSWERS
1. (a) 4. (a) 7. (b) 10. (c) 13. (a) 16. (c) 18. (b) 20. (b) 22. (a) 24. (d)
2. (a) 5. (b) 8. (b) 11. (d) 14. (a) 17. (d) 19. (a) 21. (b) 23. (a) 25. (d)
3. (b) 6. (a) 9. (d) 12. (a) 15. (d)
 SOLUTIONS
 
2
1. (a) Eff. (y2 – 2y)2 = 6  4 3
Ajay 6 8
48 y4 – 4y3 + 4y2 = 84 + 48 3
3 (T.W.) Multiply by 2 both sides
Vijay 16
2y4 – 8y2 + 8y2 = 168 + 96 3
Ist hour work by Ajay = 8
IInd hour work by Vijay = 3 ....(iii)
2 hour work  8+3 = 11 units Multiply by 14 in equation (ii)

 
8 hour work  11×4 = 44 units
Remaining work = 48 – 44 = 4 units 14(y2 – 2y) = 14 6  4 3
Ajay's 1 hour work = 8
14y2 – 28y = 84 + 56 3 ......(iv)
4 1
4 work    hr equation (ii) – (iv)
8 2

1 2y 4  8y 3  8y 2  168  96 3
Total time = 8 hour = 8 hour 30 min
2 14y 2  28y  84  56 3
2. (a)  ABC and  DEF —  – —
2y  8y  6y  28y  84  40 3
4 3 2

A D
2y4 – 8y3 – 6y2 + 28y – 84 = 40 3
55º
55º
5. (b) Two circle do not touch or intersect.

85º 40º
B C E F

D  180º 85  40º = 55°

AB = DE
AC = DF
A  D Number of tangents = 4
6. (a)
By SAS property  ABC and  DEF are congruent.
3. (b) Average speed A P
Total Distance
= Total time

250  350 B C Q R
250 350
= 
50 70 AB = PQ
B =Q
600
= = 60 km/hr For congruent by SAS [  BC = QR]
55
(side angle side)
4. (a) y = 1 + 3  4 7. (b) P   3P
SI2P

y–1= 3 + 2 .........(i) P  R 10

2P =
 
2 100
(y – 1)2 = 3 2
Rate = 20%
y + 1 – 2y = 7 + 4 3
2 8. (b) Number of candidates who passed (C + D) = 8 +
26 = 34
y2 – 2y = 6 + 4 3 .............(ii) No. of students appeared from (B + E) = 24 + 20 =
44
 34 850 x 2  xy  y 2 x 2  y 2 1
Required % = × 100 = = 77%  x  xy  y 
44 11 2 2
x2  y2 1
9. (d) Relative speed = (48 + 60) = 180 km/hr
1
5 x2  1
= 108 × = 30 m/sec x2
18 = 1
x2  2  1
Distance = speed × time x
= 30 × 12 = 360 meter
322  1 321
10. (c) SP = 1445 = 
322  1 323
1445 100
MP = = Rs 1700 16. (c) asin  – bcos  = c
85
bsin θ + acos θ = d
11. (d) CP = 400 Rs.
a 2 + b2 = c 2 + d2
5 x 25
200 × + 200 × = 400 × d2 = a 2  b 2 – c 2
100 100 100
1000 + 200x = 10000
4
200x = 9000 sin  – cos  =
5
x = 45%
Alternate :
sin θ + cos θ = d

5%  x% 16 34 34
d = 1 1   
2 2
Average = = 25% 25 25 5
2
5% + x% = 50% 17. (d) Diameter = 4 cm
x% = 45% Radius = 2 cm
l = 12 cm
12 B
12. (a) cotA = =  ×2×2×12 =  × r2 × 1200
5 P
H = 13 4
 r2
100
P 5
sinA = =
H 13 2
r = = 0.2 cm
13. (a) tan6º × tan45º × tan84º 10
[If A + B = 90°, then tanA.tanB = 1] Thickness = 0.2 × 2 = 0.4 cm
= 1 × tan45º 18. (b) Fourth propotional of 16, 26, 32
=1×1=1
bc
14. (a) Fourth proportional =
Policy in 2014  72 a
  18
Policy in 2011  54 
26  32
= = 52
16
18 1
% change = 100 = 33 %
54 3 19. (a) tan     3 = tan60°

5 4 5 4    = 60°
15. (d) x = ,y 
5 4 5 4
tan      1 = tan45°
1
y= [xy = 1] (    ) = 45º
x
solve (i) and (ii)
1
 x   18 2  = 105°
x
6  = 315°
1 tan 6  = tan315° [IVth quadrant]
 x   322
2

x2 = tan (360° – 315º)

 = –tan45º = –1
2p 1
20. (b)
p² – 5p +1 = 10
P2 – 5P + 1 = 20P
P2 + 1 = 25P
1
P+ = 25
P
21. (b) Remainder = 45
Divisor = 45 × 4 = 180

180
Quotient =  18
10
Divident = Divisor × Quotient + Remainder
= 180 × 18 + 45
= 3240 + 45 = 3285
22. (a) No. of players in game from school (D + E) = 82
+ 68 = 150
In school (H + I) = 86 + 108
= 194
Difference = 194 – 150 = 44

44
% change = 100 = 22.68%
194
23. (a) HCF of 222, 642 and 1062
Check by option,
(a) 6 is all number is divisible by 6.
24. (c) Total S.P of P and Q
190 200
= 450 × + 250 ×
100 100
= 855 + 500 = 1355
SP of R S T
960 1241 720 = 2921

1355
% change = 100 = 46.38%
2921
25. (d) Invested money = 9 : 5
9 units = 29840
29840
1 unit =
9

29840
14 units (90%) = × 14
9

29840 100
Total profit = × 14 ×
9 90
= Rs 51575.30