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1.) The area of a triangle is 90 square meter and its base is 8 times its height. What is the perimeter of the triangle?
एक त्रिभुज का क्षेत्रफल 90 वर्ग मीटर है और इसका आधार इसकी ऊंचाई का 8 गुना है।त्रिभुज की परिधि क्या है?
1.) 30m
2.) 60m
3.) 45m
4.) 50m
5.) Can't be determine.
Sol:
Length of the other side is not known, hence can't be determine.
2.) A man can row 8 kmh-1 in still water. If the river is running at 2 kmh-1, it takes 4 hrs more upstream than to go downstream for the same distance. Then the distance is given by-
एक आदमी शांत जल में 8 किमी प्रति घंटा की गति से चलता है। यदि नदी 2 किमी प्रति घंटे से बह रही हो तो नाव धारा के अनुकूल जाने की तुलना में धारा के प्रतिकूल जाने में 4 घंटे अधिक लेती है। तो दी गयी दूरी क्या होगी ?
1.) 30km
2.) 60km
3.) 45km
4.) 50km
5.) Can't be determine.
Sol:
Let the distance be x.
⇒
∴ 2x = 120 => x = 60 km.
3.) If the difference between CI and SI on a certain sum of money for three years at 5% per annum is Rs 61, what is the sum (in Rs)?
यदि किसी निश्चित राशि पर 5% प्रतिवर्ष की दर से तीन वर्षों का चक्रवृद्धि ब्याज और साधारण ब्याज में अंतर 61 रुपये है तो राशि क्या है ?
1.) 8000
2.) 6000
3.) 4500
4.) 5000
5.) None of these
Sol:
Difference between CI and SI for 3 years = 
= 8000 Rs.
4.) A person lends Rs. 1540 for five years and Rs. 1800 for four years. If he gets Rs. 1788 as interest on both amounts, what is the rate of interest?
एक व्यक्ति 5 वर्षो के लिए 1540 रुपए और 4 वर्षों के लिए 1800 रु. उधार देता है। यदि वह दोनों मूलधनों से कुल 1788 रु. प्राप्त करता है ,तो ब्याज की दर क्या है ?
1.) 10%
2.) 12%
3.) 15%
4.) 18%
5.) 20%
Sol:
Let the interest rate be r%.
∴ 
7700r + 7200r = 178800
∴ r =
= 12
= 12
5.) A basket contains eight white and ten black balls. Two ball are drawn without any replacement. What is the probability that one ball is white and the other ball is black?
एक बास्केट में आठ सफेद और दस काली गेंदें हैं। दो गेंद बिना किसी प्रतिस्थापन के निकाली जाती है। क्या संभावना है ली एक गेंद सफेद और एक गेंद काली हो ?
1.) 100/153
2.) 88/153
3.) 150/153
4.) 80/153
5.) 53/153
Sol:
Two balls can be drawn from 18 balls in 18C2 Ways, i.e. 153 ways. One white from 8 white balls can be drawn in 8C1 = 8 ways and one black ball from 10 black can be drawn in 10C1 = 10 ways.
∴ n(S) = 153, n(E) = 8 x 10 = 80
∴ P(E) = 
6.) The average weight of a group of 53 girls was calculated as 58 kgs. It was later discovered that the weight of one of the girls was read as 65 kgs., whereas her actual weight was 45 kgs. What is the actual average weight of the group of 53 girls? (rounded off to two digits after decimal)
53 लड़कियों के एक समूह का औसत वजन 58 किलोग्राम था। बाद में यह पाया गया की एक लड़की के वज़न को 65 किग्रा आँका गया जबकि उसका वज़न 45 किग्रा था। 53 लड़कियों के समूह का वास्तविक औसत वजन क्या है?(दशमलव के बाद दो अंक तक )
1.) 57.35
2.) 57.62
3.) 57.97
4.) 56.58
5.) 58.56
Sol:
Actual weight of 53 girls = 53 x 58 + 45 – 65
= 3074 + 45 – 65 = 3054 kg.
∴ Required actual average weight = 
= 57.62kg.
= 57.62kg.
7.) A person 'X' can do a piece of work in 75 days and 'Y' can do the same piece of work in 45 days. They work together for 15 days and then 'X' leaves. In how many days will' Y' finish the work?
एक व्यक्ति 'X' किसी कार्य को 75 दिनों में कर सकता है और 'Y' उसी कार्य को 45 दिनों में करता है। वे दोनों मिलकर किसी कार्य को 15 दिन तक करते है इसके बाद X कार्य छोड़ देता है ,कितने दिनों में Y कार्य को
समाप्त कर लेगा ?
1.) 15
2.) 17
3.) 19
4.) 21
5.) 23
Sol:
X's one day's work = 1/75
and Y's one day's work = 1/45
∴ (X + Y)'s one day's work = 
and (X + Y)'s 15 day's work
= [
] x 15 = 
] x 15 =
∴ Remaining work = 1 – 
= 
=
∴ Y will do the rest of the work in 45 x 
= 21 days
= 21 days
8.) Aanya is two years older than Vibhu who is twice as old as Anu. If the total of the ages of Aanya, Vibhu and Anu be 27, the how old is Vibhu?
आन्या , विभु से 2 वर्ष बड़ी है जो अनु की आयु की दोगुनी आयु का है। यदि आन्या ,विभु और अनु की आयु का कुल 27 है तो विभु की आयु क्या है ?
1.) 5
2.) 8
3.) 10
4.) 12
5.) 15
Sol:
Let Anu is x years old then age of Vibhu and Aanya is 2x and 2x+2 years respectively.
According to question-
2x + 2x + 2 + x = 27
x = 5 , Hence age of Vibhu = 2 x 5 = 10 years
9.) Smallest side of a right angled triangle is 8 cm less than the side of a square of perimeter 56 cm. second largest side of this triangle is 4 cm less than the length of rectangle of area 96 cm2 and breadth 8cm. What is the largest side of the triangle?
एक समकोण त्रिभुज की सबसे छोटी भुजा 8 सेमी छोटी है उस वर्ग की भुजा से जिसका परिमाप 56 सेमी है। इस त्रिभुज की दूसरी सबसे बड़ी भुजा 4 सेमी कम है आयताकार की लम्बाई से जिसका क्षेत्रफल 96 समी2 है और चौड़ाई 8 सेमी हो, त्रिभुज की सबसे लम्बी भुजा क्या है?
1.) 5
2.) 8
3.) 10
4.) 12
5.) 15
Sol:
56 = 4a, 14 = a
P = 14 - 8 = 6, 96 = 8 × l
l = 12, b = 12 - 4 = 8
10.) A property tax increase was proposed by a municipal corporation and it was observed that 40% of the property owners favored it while 30% of the non-owners of property favored it. If 70% of voters are owners, what is the probability that a voters selected at random would be the one favoring the increment?
संपत्ति कर में वृद्धि के लिय नगर निगम ने एक प्रस्ताव रखा और पाया संपत्ति धारक में से 40% पक्ष में है और गैर संपत्ति धारक में से 30% पक्ष में है। यदि मतदाताओं का 70% संपत्ति धारक है, क्या प्रायकिता है कि यदि एक मतदाता चुना जाये तो वह वृद्धि के पक्ष में हो?
1.) 0.37
2.) 0.52
3.) 0.68
4.) 0.42
5.) 0.15
Sol:
Answers :
Q.1) 5
Q.2) 2
Q.3) 1
Q.4) 2
Q.5) 4
Q.6) 2
Q.7) 4
Q.8) 3
Q.9) 3
Q.10) 1
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