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Mathematics — Set 11

10 Questions with Answers & Explanations

Set 11 of 14

1

यदि २० वटा संख्याको औसत शून्य छ भने कति संख्या शून्य भन्दा ठूला हुनुपर्छ ? (The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?)

Options

A

0

B

1

C

10

D

19

Correct Answer

19

Explanation

To maintain an average of zero, the sum must be zero. One very large negative number can balance out 19 positive numbers.

2

रोकिएको समय नगन्दा बसको गति ५४ किलोमिटर प्रतिघण्टा छ, रोकिएको समय गन्ने हो भने बसको गति ४५ किलोमिटर प्रतिघण्टा छ भने बस एक घण्टामा कति समय रोकिएको रहेछ। (Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?)

Options

A

6

B

10

C

12

D

20

Correct Answer

10

Explanation

रोकिएको समय प्रति घण्टा = [(चालको फरक) / (विना अवरोधको चाल)] × ६० मिनेट = [(५४ - ४५) / ५४] × ६० = ९/५४ × ६० = १० मिनेट।

3

तलका मध्ये कति ओटा संख्यालाई १३२ ले निःशेष भाग जान्छ ? How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336

Options

A

4

B

5

C

6

D

7

Correct Answer

4

Explanation

A number is divisible by 132 if it is divisible by 3, 4, and 11. Among the given numbers, 264, 396, 792, and 6336 are divisible by 132. Thus, there are 4 such numbers.

4

एउटा मानिसले कुनै यात्रामा पहिलो १६० किलोमिटर ६४ किलोमिटर प्रति घण्टा र अर्को १६० किलोमिटर ८० प्रति घण्टाका दरले पार गर्‍यो भने पहिलो ३२० किलोमिटर यात्राको औषत गति कति थियो ? (A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:)

Options

A

35.55 km/hr

B

36 km/hr

C

1.11 km/hr

D

71 km/hr

Correct Answer

71 km/hr

Explanation

बराबर दूरी पार गर्दा औषत गतिको सूत्र २xy/(x+y) प्रयोग गरिन्छ। (२*६४*८०)/(६४+८०) = ७१.११ किलोमिटर/घण्टा हुन्छ, जसलाई विकल्प अनुसार ७१ मानिएको छ।

5

कुनै सङ्ख्याले एक चौथाईको एक तिहाई १५ हुन्छ भने उक्त सङ्ख्याको दश भागको तीन भाग कति हो ? If one-third of one-fourth of a number is 15, then three-tenth of that number is:

Options

A

35

B

36

C

45

D

54

Correct Answer

54

Explanation

(1/3) * (1/4) * X = 15 implies X = 15 * 12 = 180. Three-tenth of 180 is (3/10) * 180 = 54.

6

कम्पनी Y को तलकामध्ये कुन वर्षमा अघिल्लो वर्षको तुलनामा उत्पादनमा अधिकतम वृद्धि वा गिरावट छ ? For which of the following years, the percentage rise/fall in production from the previous year is the maximum for Company Y?

Context: तल दिइएको स्तम्भ चित्रमा तीन ओटा कम्पनी X, Y, Z ले दिइएका वर्षहरुमा उत्पादन गरेको कागज ( लाख टन ) मा प्रस्तुत गरिएको छ : The bar graph given below shows the data of the production of paper (in lakh tonnes) by three different companies X, Y and Z over the years. Production of Paper (in lakh tonnes) by Three Companies X, Y and Z over the Years. बाँयाबाट क्रमशः X, Y, Z का स्तम्भ हुन्।

Questions

A

1997

B

1998

C

1999

D

2000

Correct Answer

1997

Explanation

कम्पनी Y को लागि प्रतिशत वृद्धि: १९९७ मा ((३५-२५)/२५)*१०० = ४०%, १९९८ मा ०%, १९९९ मा ((४०-३५)/३५)*१०० = १४.२८%, २००० मा ((५०-४०)/४०)*१०० = २५%। त्यसैले १९९७ मा अधिकतम वृद्धि भएको छ।

7

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is:

Options

A

12π cm³

B

15π cm³

C

16π cm³

D

20π cm³

Correct Answer

16π cm³

Explanation

When rotated about the 3 cm side, the height (h) is 3 cm and the radius (r) is 4 cm. Volume = (1/3) * π * r² * h = (1/3) * π * 4² * 3 = 16π cm³.

8

एउटा किराना पसलेले पाँच महिनामा क्रमशः Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 को सामान बिक्री गर्‍यो भने सबै महिनाको औसत रु. ६५०० कायम गर्न छैटौं महिनामा कतिको सामान बेच्नु पर्ला ? / A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

Options

A

Rs. 4991

B

Rs. 5991

C

Rs. 6001

D

Rs. 6991

Correct Answer

Rs. 4991

Explanation

The total sale required for 6 months to have an average of 6500 is 6500 * 6 = 39,000. Sum of sales for the first 5 months = 6435 + 6927 + 6855 + 7230 + 6562 = 34,009. Required sale in the 6th month = 39,000 - 34,009 = 4,991.

9

A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.

Options

A

Rs. 1900

B

Rs. 2660

C

Rs. 2800

D

Rs. 2840

Correct Answer

Rs. 2660

Explanation

Effective capital ratio A:B:C = (6500*6):(8400*5):(10000*3) = 39:42:30. Working partner A gets 5% of 7400 = 370. Remaining profit 7030 is shared in ratio 39:42:30. B's share = (42/111) * 7030 = Rs. 2660.

10

एउटा डुङ्गा स्थिर पानीमा १३ किलोमिटर प्रतिघण्टाको दरले कुद्छ, यदि नदीको वहाव ४ किलोमिटर प्रतिघण्टा छ भने उक्त डुङ्गाले पानीको बहावतिर ६८ किलोमिटर यात्रा गर्न कति समय लाग्छ होला ? / A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

Options

A

2 hours

B

3 hours

C

4 hours

D

5 hours

Correct Answer

4 hours

Explanation

Downstream speed = Still water speed + Stream speed = 13 + 4 = 17 km/hr. Time = Distance / Speed = 68 / 17 = 4 hours.

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