28:I[81166,["/_next/static/immutable/chunks/2corl6wyj4669.js","/_next/static/immutable/chunks/38n271cv4vmyv.js","/_next/static/immutable/chunks/2pf73jja2520w.js"],"default"] 29:T54d,क्रमिक लाभ और हानि माना कि केतन का क्रय मूल्य x है। केतन 5% लाभ पर बेचता है, अतः महेश देता है

x \times \frac{105}{100} = 1.05 x

। महेश 24% हानि पर बेचता है, अतः डेविड देता है

1.05 x \times \frac{76}{100} = 0.798 x

।

डेविड ने वास्तव में ₹3990 चुकाए, अतः 0.798x=3990।

x = \frac{3990}{0.798} = 5000

केतन का क्रय मूल्य ₹5,000 था - इसलिए सही विकल्प (c) है।2a:T502,Population growth A 25% yearly rise multiplies the population by

\frac{5}{4}

each year. So to go back one year, multiply by

\frac{4}{5}

. 1 year ago

= 110000 \times \frac{4}{5} = 88000

2 years ago

= 88000 \times \frac{4}{5} = 70400

3 years ago

= 70400 \times \frac{4}{5} = 56320

Required difference =70400-56320=14080 - option (c).2b:T63f,जनसंख्या वृद्धि 25% की वार्षिक वृद्धि प्रति वर्ष जनसंख्या को

\frac{5}{4}

गुना कर देती है। अतः एक वर्ष पीछे जाने के लिए

\frac{4}{5}

से गुणा कीजिए। 1 वर्ष पहले

= 110000 \times \frac{4}{5} = 88000

2 वर्ष पहले

= 88000 \times \frac{4}{5} = 70400

3 वर्ष पहले

= 70400 \times \frac{4}{5} = 56320

अतः अभीष्ट अंतर =70400-56320=14080 - इसलिए सही विकल्प (c) है।2c:T484,Speed, time and delay For a fixed distance, time is inversely proportional to speed. Speed becomes

\frac{3}{4}

, so time becomes

\frac{4}{3}

of the normal time.

Let the normal time be T: extra time

= \frac{4}{3} T - T = \frac{T}{3}

\frac{T}{3} = 24 \Rightarrow T = 72

The normal journey takes 72 minutes - option (c).2d:T5ed,चाल, समय और विलंब नियत दूरी के लिए समय, चाल के व्युत्क्रमानुपाती होता है। चाल

\frac{3}{4}

हो जाती है, अतः समय सामान्य समय का

\frac{4}{3}

हो जाता है।

माना कि सामान्य समय T है: अतिरिक्त समय

= \frac{4}{3} T - T = \frac{T}{3}

।

\frac{T}{3} = 24 \Rightarrow T = 72

अतः सामान्य चाल से यात्रा में 72 मिनट लगते - इसलिए सही विकल्प (c) है।2e:T526,CI and SI difference Simple interest for 2 years is ₹42, so one year's interest is

\frac{42}{2} = 21

. For 2 years, CI - SI =43-42=1; this ₹1 is only the interest earned on the first year's interest of ₹21.

21 \times \frac{R}{100} = 1 \Rightarrow R = \frac{100}{21}

per cent per annum.

P = \frac{S I \times 100}{R \times T} = \frac{42 \times 100}{\frac{100}{21} \times 2}

= \frac{4200 \times 21}{200} = 441

The principal is ₹441 - option (a).2f:T693,चक्रवृद्धि और साधारण ब्याज का अंतर 2 वर्ष का साधारण ब्याज ₹42 है, अतः एक वर्ष का ब्याज

\frac{42}{2} = 21

है। 2 वर्ष के लिए चक्रवृद्धि ब्याज - साधारण ब्याज =43-42=1; यह ₹1 केवल पहले वर्ष के ₹21 ब्याज पर मिला ब्याज है।

21 \times \frac{R}{100} = 1 \Rightarrow R = \frac{100}{21}

प्रतिशत वार्षिक।

P = \frac{S I \times 100}{R \times T} = \frac{42 \times 100}{\frac{100}{21} \times 2}

= \frac{4200 \times 21}{200} = 441

अतः मूलधन ₹441 है - इसलिए सही विकल्प (a) है।30:T41c,Time and work Take the total work as the LCM of 16, 12 and 4, i.e. 48 units. A does

\frac{48}{16} = 3

units a day; B does

\frac{48}{12} = 4

units a day. All three together do

\frac{48}{4} = 12

units a day.

C alone does 12-(3+4)=5 units a day. Days needed by C

= \frac{48}{5}

- option (b).31:T586,समय और कार्य कुल कार्य को 16, 12 और 4 का ल.स., अर्थात् 48 इकाई मानिए। A प्रतिदिन

\frac{48}{16} = 3

इकाई करता है; B प्रतिदिन

\frac{48}{12} = 4

इकाई करता है। तीनों मिलकर प्रतिदिन

\frac{48}{4} = 12

इकाई करते हैं।

अतः C अकेला प्रतिदिन 12-(3+4)=5 इकाई करता है। C को लगने वाले दिन

= \frac{48}{5}

- इसलिए सही विकल्प (b) है।32:T47b,Ratio, income and saving Income : expenditure =6:5, and the 5 parts of expenditure are ₹4,50,000. One part

= \frac{450000}{5} = 90000

, so income

= 6 \times 90000 = 540000

. New income

= 540000 \times \frac{140}{100} = 756000

New expenditure

= 450000 \times \frac{80}{100} = 360000

Final saving =756000-360000=396000, i.e. ₹3,96,000 - option (a).33:T524,अनुपात, आय और बचत आय : व्यय =6:5 है और व्यय के 5 भाग ₹4,50,000 के बराबर हैं। एक भाग

= \frac{450000}{5} = 90000

, अतः आय

= 6 \times 90000 = 540000

। नई आय

= 540000 \times \frac{140}{100} = 756000

नया व्यय

= 450000 \times \frac{80}{100} = 360000

अंतिम बचत =756000-360000=396000, अर्थात् ₹3,96,000 - इसलिए सही विकल्प (a) है।34:T4cb,Hemisphere surface area Plating is done on the inside only, so the area needed is the curved surface of a hemisphere,

2 π r^{2}

(the flat rim disc and the outside are not plated).

2 π r^{2} = 2 \times \frac{22}{7} \times 3.5 \times 3.5

= 2 \times 22 \times 0.5 \times 3.5 = 77

, so the area is 77 sq cm. Cost

= 77 \times 4 = 308

The tin plating costs ₹308 - option (a).35:T667,अर्धगोले का पृष्ठीय क्षेत्रफल कलई केवल भीतरी भाग पर होती है, अतः अभीष्ट क्षेत्रफल अर्धगोले का वक्र पृष्ठीय क्षेत्रफल

2 π r^{2}

है (ऊपर का समतल वृत्त तथा बाहरी सतह इसमें नहीं आते)।

2 π r^{2} = 2 \times \frac{22}{7} \times 3.5 \times 3.5

= 2 \times 22 \times 0.5 \times 3.5 = 77

, अतः क्षेत्रफल 77 वर्ग cm है। लागत

= 77 \times 4 = 308

अतः कलई कराने की लागत ₹308 है - इसलिए सही विकल्प (a) है।1e:["$","$L28",null,{"mode":"exam","dropped":0,"bilingual":true,"choiceSubjects":[],"questions":[{"id":4241,"n":41,"subject":"Elementary Mathematics","stem":"Evaluate:

16 + 12 \div 3 - 3 \times 4

","stemHi":"मान ज्ञात कीजिए:

16 + 12 \div 3 - 3 \times 4

","context":null,"contextHi":null,"options":[{"key":"a","text":"10","textHi":null,"imageUrl":null},{"key":"b","text":"11","textHi":null,"imageUrl":null},{"key":"c","text":"7","textHi":null,"imageUrl":null},{"key":"d","text":"8","textHi":null,"imageUrl":null}],"correct":"d","sol":"BODMAS order\nBODMAS: finish every division and multiplication before any addition or subtraction.\n

12 \div 3 = 4

and

3 \times 4 = 12

.\n

16 + 12 \div 3 - 3 \times 4 = 16 + 4 - 12

\n=20-12=8\nSo the value is 8, and the correct option is (d).","solHi":"बोडमास क्रम\nबोडमास: जोड़ और घटाव से पहले सभी भाग तथा गुणा कर लीजिए।\n

12 \div 3 = 4

तथा

3 \times 4 = 12

।\n

16 + 12 \div 3 - 3 \times 4 = 16 + 4 - 12

\n=20-12=8\nअतः अभीष्ट मान 8 है, इसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":4242,"n":42,"subject":"Elementary Mathematics","stem":"The simple interest on a principal amount (in ₹) is ₹576 for a period of 3 years at the rate of 6% per annum. The principal amount (in ₹) is:","stemHi":"किसी मूलधन (₹ में) पर 6% वार्षिक की दर से 3 वर्ष का साधारण ब्याज ₹576 है। मूलधन (₹ में) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"3202","textHi":null,"imageUrl":null},{"key":"b","text":"3206","textHi":null,"imageUrl":null},{"key":"c","text":"3200","textHi":null,"imageUrl":null},{"key":"d","text":"3213","textHi":null,"imageUrl":null}],"correct":"c","sol":"Simple interest\nFormula:

S I = \frac{P \times R \times T}{100}

\nHere SI=576, R=6 and T=3.\n

576 = \frac{P \times 6 \times 3}{100} = \frac{18 P}{100}

P = \frac{576 \times 100}{18} = 3200

\nSo the principal is ₹3,200 - option (c).","solHi":"साधारण ब्याज\nसूत्र:

S I = \frac{P \times R \times T}{100}

\nयहाँ SI=576, R=6 तथा T=3 है।\n

576 = \frac{P \times 6 \times 3}{100} = \frac{18 P}{100}

P = \frac{576 \times 100}{18} = 3200

\nअतः मूलधन ₹3,200 है - इसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":4243,"n":43,"subject":"Elementary Mathematics","stem":"Ketan bought a shirt and sold it to Mahesh at a profit of 5%. Mahesh sold it to David at a loss of 24%. If David paid ₹3990, then the cost price (in ₹) of the shirt Ketan bought is","stemHi":"केतन ने एक कमीज़ खरीदी और उसे महेश को 5% लाभ पर बेच दिया। महेश ने उसे डेविड को 24% हानि पर बेच दिया। यदि डेविड ने ₹3990 चुकाए, तो केतन द्वारा खरीदी गई कमीज़ का क्रय मूल्य (₹ में) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"5150","textHi":null,"imageUrl":null},{"key":"b","text":"4800","textHi":null,"imageUrl":null},{"key":"c","text":"5000","textHi":null,"imageUrl":null},{"key":"d","text":"4750","textHi":null,"imageUrl":null}],"correct":"c","sol":"Successive profit and loss\nLet Ketan's cost price be x.\nKetan sells at 5% profit, so Mahesh pays

x \times \frac{105}{100} = 1.05 x

.\nMahesh sells at 24% loss, so David pays

1.05 x \times \frac{76}{100} = 0.798 x

.\n $\"figure\"/$ \nDavid actually paid ₹3990, so 0.798x=3990.\n

x = \frac{3990}{0.798} = 5000

\nKetan's cost price was ₹5,000 - option (c).","solHi":"$29","pos":2,"neg":0.25},{"id":4244,"n":44,"subject":"Elementary Mathematics","stem":"What will be the difference in population 3 years ago and 2 years ago of a town, whose current population is 110000 and which is increasing at a rate of 25% every year?","stemHi":"किसी नगर की वर्तमान जनसंख्या 110000 है और वह प्रतिवर्ष 25% की दर से बढ़ रही है। उस नगर की 3 वर्ष पहले और 2 वर्ष पहले की जनसंख्या में कितना अंतर होगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"13330","textHi":null,"imageUrl":null},{"key":"b","text":"13530","textHi":null,"imageUrl":null},{"key":"c","text":"14080","textHi":null,"imageUrl":null},{"key":"d","text":"14430","textHi":null,"imageUrl":null}],"correct":"c","sol":"$2a","solHi":"$2b","pos":2,"neg":0.25},{"id":4245,"n":45,"subject":"Elementary Mathematics","stem":"If

x

and

y

are inversely proportional, then which of the following is correct ?","stemHi":"यदि

x

और

y

व्युत्क्रमानुपाती हैं, तो निम्नलिखित में से कौन-सा सही है?","context":null,"contextHi":null,"options":[{"key":"a","text":"

\frac{x}{y} = k

","textHi":null,"imageUrl":null},{"key":"b","text":"

xy = \frac{y}{x}

","textHi":null,"imageUrl":null},{"key":"c","text":"

\frac{x}{y} = 1

","textHi":null,"imageUrl":null},{"key":"d","text":"

xy = k

","textHi":null,"imageUrl":null}],"correct":"d","sol":"Inverse proportion\nInversely proportional means

x \propto \frac{1}{y}

, i.e. one grows exactly as fast as the other shrinks.\nReplacing the proportionality sign by a constant k gives

x = \frac{k}{y}

.\nCross-multiplying, xy=k - the product stays constant.\nOption (a)

\frac{x}{y} = k

is the test for direct proportion, so it is not the answer.\nHence the correct option is (d).","solHi":"व्युत्क्रमानुपात\nव्युत्क्रमानुपाती होने का अर्थ है

x \propto \frac{1}{y}

, अर्थात् एक जितना बढ़ता है दूसरा उतना ही घटता है।\nअनुपात चिह्न के स्थान पर अचर k रखने पर

x = \frac{k}{y}

प्राप्त होता है।\nतिर्यक गुणा करने पर xy=k, अर्थात् गुणनफल अचर रहता है।\nविकल्प (a)

\frac{x}{y} = k

समानुपात (direct proportion) की शर्त है, अतः वह उत्तर नहीं है।\nइसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":4246,"n":46,"subject":"Elementary Mathematics","stem":"Lokesh travels from City A to City B. If Lokesh drives his car at

\frac{3}{4}

of his normal speed, then he reaches City B 24 minutes late. Find the time (in minutes) that Lokesh would have taken to travel from City A to City B if he drove at his normal speed.","stemHi":"लोकेश शहर A से शहर B तक यात्रा करता है। यदि लोकेश अपनी कार को अपनी सामान्य चाल के

\frac{3}{4}

पर चलाता है, तो वह शहर B पर 24 मिनट देर से पहुँचता है। ज्ञात कीजिए कि सामान्य चाल से चलने पर लोकेश को शहर A से शहर B तक जाने में कितना समय (मिनट में) लगता।","context":null,"contextHi":null,"options":[{"key":"a","text":"62","textHi":null,"imageUrl":null},{"key":"b","text":"65","textHi":null,"imageUrl":null},{"key":"c","text":"72","textHi":null,"imageUrl":null},{"key":"d","text":"70","textHi":null,"imageUrl":null}],"correct":"c","sol":"$2c","solHi":"$2d","pos":2,"neg":0.25},{"id":4247,"n":47,"subject":"Elementary Mathematics","stem":"The price (per litre) of petrol increases by 50%. By what percent should its consumption be reduced such that the expenditure on it increases by

11 %

only ?","stemHi":"पेट्रोल का मूल्य (प्रति लीटर) 50% बढ़ जाता है। उसकी खपत में कितने प्रतिशत की कमी की जानी चाहिए ताकि उस पर होने वाला व्यय केवल

11 %

ही बढ़े?","context":null,"contextHi":null,"options":[{"key":"a","text":"36%","textHi":null,"imageUrl":null},{"key":"b","text":"26%","textHi":null,"imageUrl":null},{"key":"c","text":"80%","textHi":null,"imageUrl":null},{"key":"d","text":"74%","textHi":null,"imageUrl":null}],"correct":"b","sol":"Price, consumption, expenditure\nExpenditure = price × consumption, so fix easy numbers: price =100, consumption =100, expenditure =10000.\nPrice rises by 50%, so the new price is 150.\nExpenditure is allowed to rise by 11% only: new expenditure

= 10000 \times \frac{111}{100} = 11100

.\nNew consumption

= \frac{11100}{150} = 74

\n $\"figure\"/$ \nFall in consumption =100-74=26 out of 100, i.e. 26% - option (b).\nNote that 74% is the consumption that remains, not the cut, which is why (d) is the trap here.","solHi":"मूल्य, खपत और व्यय\nव्यय = मूल्य × खपत, अतः सुविधाजनक मान लीजिए: मूल्य =100, खपत =100, व्यय =10000।\nमूल्य 50% बढ़ता है, अतः नया मूल्य 150 है।\nव्यय केवल 11% बढ़ना चाहिए: नया व्यय

= 10000 \times \frac{111}{100} = 11100

।\nनई खपत

= \frac{11100}{150} = 74

\n $\"figure\"/$ \nखपत में कमी =100-74=26 (प्रति 100), अर्थात् 26% - इसलिए सही विकल्प (b) है।\nध्यान दीजिए कि 74% शेष बची खपत है, कमी नहीं; इसी कारण (d) यहाँ भ्रम पैदा करता है।","pos":2,"neg":0.25},{"id":4248,"n":48,"subject":"Elementary Mathematics","stem":"The average weight of Shivam, Rupesh and Mandar is 46 kg . If the average weight of Shivam and Rupesh be 39 kg and that of Rupesh and Mandar be 48 kg , then the weight of Rupesh (in kg ) is:","stemHi":"शिवम, रूपेश और मंदार का औसत भार 46 kg है। यदि शिवम और रूपेश का औसत भार 39 kg हो तथा रूपेश और मंदार का औसत भार 48 kg हो, तो रूपेश का भार (kg में) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"36","textHi":null,"imageUrl":null},{"key":"b","text":"56","textHi":null,"imageUrl":null},{"key":"c","text":"46","textHi":null,"imageUrl":null},{"key":"d","text":"51","textHi":null,"imageUrl":null}],"correct":"a","sol":"Average of weights\nTurn every average into a total: total = average

\times

number of people.\n

S + R + M = 46 \times 3 = 138

S + R = 39 \times 2 = 78

, so M=138-78=60.\n

R + M = 48 \times 2 = 96

, so R=96-60=36.\nRupesh weighs 36 kg - option (a).","solHi":"भार का औसत\nप्रत्येक औसत को योग में बदलिए: योग = औसत

\times

व्यक्तियों की संख्या।\n

S + R + M = 46 \times 3 = 138

S + R = 39 \times 2 = 78

, अतः M=138-78=60।\n

R + M = 48 \times 2 = 96

, अतः R=96-60=36।\nअतः रूपेश का भार 36 kg है - इसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":4249,"n":49,"subject":"Elementary Mathematics","stem":"What is the single per cent discount equivalent to two successive discounts of 18.5% and 11.5% ?","stemHi":"18.5% और 11.5% की दो क्रमिक छूटों के तुल्य एकल प्रतिशत छूट क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"30%","textHi":null,"imageUrl":null},{"key":"b","text":"27%","textHi":null,"imageUrl":null},{"key":"c","text":"27.8725%","textHi":null,"imageUrl":null},{"key":"d","text":"

32.1275 %

","textHi":null,"imageUrl":null}],"correct":"c","sol":"Successive discounts\nFor two successive discounts a and b, the single equivalent discount is

a + b - \frac{a b}{100}

.\nHere a=18.5 and b=11.5.\n

= 18.5 + 11.5 - \frac{18.5 \times 11.5}{100}

= 30 - \frac{212.75}{100} = 30 - 2.1275

\n=27.8725\nThe single equivalent discount is 27.8725% - option (c). Simply adding the two discounts gives 30%, which is why (a) is wrong.","solHi":"क्रमिक छूट\nदो क्रमिक छूटों a और b के लिए तुल्य एकल छूट

a + b - \frac{a b}{100}

होती है।\nयहाँ a=18.5 तथा b=11.5 है।\n

= 18.5 + 11.5 - \frac{18.5 \times 11.5}{100}

= 30 - \frac{212.75}{100} = 30 - 2.1275

\n=27.8725\nअतः तुल्य एकल छूट 27.8725% है - इसलिए सही विकल्प (c) है। दोनों छूटों को सीधे जोड़ने पर 30% आता है, इसी कारण (a) गलत है।","pos":2,"neg":0.25},{"id":4250,"n":50,"subject":"Elementary Mathematics","stem":"A man sold an article for ₹217, there by gaining

8.5 %

. The cost of the article (in ₹) was:","stemHi":"एक व्यक्ति ने एक वस्तु ₹217 में बेची और इस प्रकार

8.5 %

का लाभ अर्जित किया। वस्तु का क्रय मूल्य (₹ में) था:","context":null,"contextHi":null,"options":[{"key":"a","text":"198","textHi":null,"imageUrl":null},{"key":"b","text":"238","textHi":null,"imageUrl":null},{"key":"c","text":"235","textHi":null,"imageUrl":null},{"key":"d","text":"200","textHi":null,"imageUrl":null}],"correct":"d","sol":"Cost price from gain\nA gain of 8.5% is always measured on the cost price, so

S P = C P \times \frac{108.5}{100}

.\n

217 = C P \times \frac{108.5}{100}

C P = \frac{217 \times 100}{108.5}

\nCP=200\nThe article cost ₹200 - option (d).","solHi":"लाभ से क्रय मूल्य\n8.5% का लाभ सदैव क्रय मूल्य पर लिया जाता है, अतः

S P = C P \times \frac{108.5}{100}

।\n

217 = C P \times \frac{108.5}{100}

C P = \frac{217 \times 100}{108.5}

\nCP=200\nअतः वस्तु का क्रय मूल्य ₹200 था - इसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":4251,"n":51,"subject":"Elementary Mathematics","stem":"Find the value of\n[(19 × 8) × {7 ÷ 7 × (16 − 12)/4}]","stemHi":"निम्नलिखित का मान ज्ञात कीजिए\n[(19 × 8) × {7 ÷ 7 × (16 − 12)/4}]","context":null,"contextHi":null,"options":[{"key":"a","text":"146","textHi":null,"imageUrl":null},{"key":"b","text":"170","textHi":null,"imageUrl":null},{"key":"c","text":"152","textHi":null,"imageUrl":null},{"key":"d","text":"155","textHi":null,"imageUrl":null}],"correct":"c","sol":"Nested brackets, BODMAS\nStart with the innermost bracket: 16-12=4.\nSo

\frac{16 - 12}{4} = \frac{4}{4} = 1

.\nCurly bracket next:

7 \div 7 \times 1 = 1 \times 1 = 1

.\nRound bracket:

19 \times 8 = 152

.\nWhole expression

= 152 \times 1 = 152

- option (c).","solHi":"कोष्ठक और बोडमास\nसबसे भीतरी कोष्ठक से आरंभ कीजिए: 16-12=4।\nअतः

\frac{16 - 12}{4} = \frac{4}{4} = 1

।\nअब मझले कोष्ठक में:

7 \div 7 \times 1 = 1 \times 1 = 1

।\nगोल कोष्ठक:

19 \times 8 = 152

।\nअतः पूरा व्यंजक

= 152 \times 1 = 152

- इसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":4252,"n":52,"subject":"Elementary Mathematics","stem":"If 4% of x = 48, then x is equal to:","stemHi":"यदि x का 4% = 48 है, तो x बराबर है:","context":null,"contextHi":null,"options":[{"key":"a","text":"2400","textHi":null,"imageUrl":null},{"key":"b","text":"2500","textHi":null,"imageUrl":null},{"key":"c","text":"1300","textHi":null,"imageUrl":null},{"key":"d","text":"1200","textHi":null,"imageUrl":null}],"correct":"d","sol":"Percentage of a number\n"4% of x" means

\frac{4}{100} \times x

.\n

\frac{4 x}{100} = 48

\n4x=4800\nx=1200\nSo x=1200 - option (d).","solHi":"संख्या का प्रतिशत\n"x का 4%" का अर्थ है

\frac{4}{100} \times x

।\n

\frac{4 x}{100} = 48

\n4x=4800\nx=1200\nअतः x=1200 - इसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":4253,"n":53,"subject":"Elementary Mathematics","stem":"The value of 50 − 7 × [2 + 5 × {16 − 2(6 − 5) × 8} ÷ 31] is:","stemHi":"50 − 7 × [2 + 5 × {16 − 2(6 − 5) × 8} ÷ 31] का मान है:","context":null,"contextHi":null,"options":[{"key":"a","text":"36","textHi":null,"imageUrl":null},{"key":"b","text":"40","textHi":null,"imageUrl":null},{"key":"c","text":"35","textHi":null,"imageUrl":null},{"key":"d","text":"34","textHi":null,"imageUrl":null}],"correct":"a","sol":"Nested brackets, BODMAS\nOpen the brackets from the inside out.\nInnermost round bracket: 6-5=1.\nCurly bracket:

16 - 2 \times 1 \times 8 = 16 - 16 = 0

.\nSquare bracket:

2 + 5 \times 0 \div 31 = 2 + 0 = 2

.\nFinally

50 - 7 \times 2 = 50 - 14 = 36

.\nSo the value is 36 - option (a). Because the curly bracket is exactly 0, the

\div 31

never changes anything.","solHi":"कोष्ठक और बोडमास\nकोष्ठकों को भीतर से बाहर की ओर हल कीजिए।\nसबसे भीतरी गोल कोष्ठक: 6-5=1।\nमझला कोष्ठक:

16 - 2 \times 1 \times 8 = 16 - 16 = 0

।\nवर्ग कोष्ठक:

2 + 5 \times 0 \div 31 = 2 + 0 = 2

।\nअंत में

50 - 7 \times 2 = 50 - 14 = 36

।\nअतः अभीष्ट मान 36 है - इसलिए सही विकल्प (a) है। मझला कोष्ठक ठीक 0 है, इसलिए

\div 31

से कोई अंतर नहीं पड़ता।","pos":2,"neg":0.25},{"id":4254,"n":54,"subject":"Elementary Mathematics","stem":"Evaluate:

16 + 12 \div 4 - 3 \times 4

","stemHi":"मान ज्ञात कीजिए:

16 + 12 \div 4 - 3 \times 4

","context":null,"contextHi":null,"options":[{"key":"a","text":"9","textHi":null,"imageUrl":null},{"key":"b","text":"10","textHi":null,"imageUrl":null},{"key":"c","text":"7","textHi":null,"imageUrl":null},{"key":"d","text":"6","textHi":null,"imageUrl":null}],"correct":"c","sol":"BODMAS order\nBODMAS: division and multiplication come before addition and subtraction.\n

12 \div 4 = 3

and

3 \times 4 = 12

.\n

16 + 12 \div 4 - 3 \times 4 = 16 + 3 - 12

\n=19-12=7\nSo the value is 7 - option (c).","solHi":"बोडमास क्रम\nबोडमास: भाग और गुणा, जोड़ तथा घटाव से पहले किए जाते हैं।\n

12 \div 4 = 3

तथा

3 \times 4 = 12

।\n

16 + 12 \div 4 - 3 \times 4 = 16 + 3 - 12

\n=19-12=7\nअतः अभीष्ट मान 7 है - इसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":4255,"n":55,"subject":"Elementary Mathematics","stem":"The average of 19 consecutive natural numbers is 41 . What is the smallest number among these numbers?","stemHi":"19 क्रमागत प्राकृत संख्याओं का औसत 41 है। इन संख्याओं में सबसे छोटी संख्या कौन-सी है?","context":null,"contextHi":null,"options":[{"key":"a","text":"30","textHi":null,"imageUrl":null},{"key":"b","text":"32","textHi":null,"imageUrl":null},{"key":"c","text":"31","textHi":null,"imageUrl":null},{"key":"d","text":"33","textHi":null,"imageUrl":null}],"correct":"b","sol":"Average of consecutive numbers\nFor an odd count of consecutive numbers the average is exactly the middle term.\nWith 19 terms the middle one is the 10th, so the 10th number is 41.\nThe 1st term is 9 steps before the 10th.\n $\"figure\"/$ \nSmallest =41-9=32\nSo the smallest number is 32 - option (b).","solHi":"क्रमागत संख्याओं का औसत\nविषम संख्या में ली गई क्रमागत संख्याओं का औसत ठीक मध्य पद होता है।\n19 पद होने पर मध्य पद 10वाँ है, अतः 10वीं संख्या 41 है।\nपहला पद 10वें पद से 9 कदम पीछे है।\n $\"figure\"/$ \nसबसे छोटी संख्या =41-9=32\nअतः सबसे छोटी संख्या 32 है - इसलिए सही विकल्प (b) है।","pos":2,"neg":0.25},{"id":4256,"n":56,"subject":"Elementary Mathematics","stem":"If at same rate of interest, in 2 years, the simple interest is ₹42 and compound interest is ₹43, then what is the principal (in ₹) ?","stemHi":"यदि समान ब्याज दर पर 2 वर्षों में साधारण ब्याज ₹42 और चक्रवृद्धि ब्याज ₹43 है, तो मूलधन (₹ में) क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"441","textHi":null,"imageUrl":null},{"key":"b","text":"434","textHi":null,"imageUrl":null},{"key":"c","text":"436","textHi":null,"imageUrl":null},{"key":"d","text":"445","textHi":null,"imageUrl":null}],"correct":"a","sol":"$2e","solHi":"$2f","pos":2,"neg":0.25},{"id":4257,"n":57,"subject":"Elementary Mathematics","stem":"A can finish a work in 16 days, and

B

can do the same work in 12 days. With the help of C, they complete the work in 4 days. In how many days can C alone do the same work ?","stemHi":"A एक कार्य को 16 दिनों में पूरा कर सकता है और

B

उसी कार्य को 12 दिनों में कर सकता है। C की सहायता से वे उस कार्य को 4 दिनों में पूरा कर लेते हैं। C अकेला उसी कार्य को कितने दिनों में कर सकता है?","context":null,"contextHi":null,"options":[{"key":"a","text":"

\frac{48}{7}

","textHi":null,"imageUrl":null},{"key":"b","text":"

\frac{48}{5}

","textHi":null,"imageUrl":null},{"key":"c","text":"

\frac{38}{7}

","textHi":null,"imageUrl":null},{"key":"d","text":"

\frac{43}{7}

","textHi":null,"imageUrl":null}],"correct":"b","sol":"$30","solHi":"$31","pos":2,"neg":0.25},{"id":4258,"n":58,"subject":"Elementary Mathematics","stem":"The ratio of income and expenditure is

6 : 5

. Income increases by 40% and expenditure decreases by

20 %

. If the initial expenditure is ₹4,50,000. Find the final saving (in ₹).","stemHi":"आय और व्यय का अनुपात

6 : 5

है। आय 40% बढ़ जाती है और व्यय

20 %

घट जाता है। यदि प्रारंभिक व्यय ₹4,50,000 है, तो अंतिम बचत (₹ में) ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"

3, 96, 000

","textHi":null,"imageUrl":null},{"key":"b","text":"

3, 84, 000

","textHi":null,"imageUrl":null},{"key":"c","text":"

3, 90, 000

","textHi":null,"imageUrl":null},{"key":"d","text":"

3, 69, 000

","textHi":null,"imageUrl":null}],"correct":"a","sol":"$32","solHi":"$33","pos":2,"neg":0.25},{"id":4259,"n":59,"subject":"Elementary Mathematics","stem":"A hemispherical bowl made of brass has an inner radius 3.5 cm . Find the cost of tin plating it on the inside at the rate of ₹4 per

{cm}^{2}

","stemHi":"पीतल से बने एक अर्धगोलाकार कटोरे की आंतरिक त्रिज्या 3.5 cm है। ₹4 प्रति

{cm}^{2}

की दर से उसके भीतरी भाग पर कलई कराने की लागत ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"₹308","textHi":null,"imageUrl":null},{"key":"b","text":"₹318","textHi":null,"imageUrl":null},{"key":"c","text":"₹328","textHi":null,"imageUrl":null},{"key":"d","text":"₹348","textHi":null,"imageUrl":null}],"correct":"a","sol":"$34","solHi":"$35","pos":2,"neg":0.25},{"id":4260,"n":60,"subject":"Elementary Mathematics","stem":"A man goes to Ahmedabad from Kolkata at a speed of 4 km/hr and returns to Kolkata at speed of 12 km/hr, through same route. What is his average speed (in km/hr) of the entire journey ?","stemHi":"एक व्यक्ति कोलकाता से अहमदाबाद 4 km/hr की चाल से जाता है और उसी मार्ग से 12 km/hr की चाल से कोलकाता लौटता है। पूरी यात्रा में उसकी औसत चाल (km/hr में) क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"10","textHi":null,"imageUrl":null},{"key":"b","text":"6","textHi":null,"imageUrl":null},{"key":"c","text":"9","textHi":null,"imageUrl":null},{"key":"d","text":"7","textHi":null,"imageUrl":null}],"correct":"b","sol":"Average speed both ways\nThe two legs cover the same distance, so the average speed is the harmonic mean, not the ordinary mean.\nFormula: average speed

= \frac{2 x y}{x + y}

= \frac{2 \times 4 \times 12}{4 + 12} = \frac{96}{16}

\n=6\nThe average speed is 6 km/hr - option (b).\nThe ordinary average

\frac{4 + 12}{2} = 8

is wrong because far more time is spent on the slow leg.","solHi":"आने-जाने की औसत चाल\nदोनों चरणों में दूरी समान है, अतः औसत चाल हरात्मक माध्य होती है, साधारण माध्य नहीं।\nसूत्र: औसत चाल

= \frac{2 x y}{x + y}

= \frac{2 \times 4 \times 12}{4 + 12} = \frac{96}{16}

\n=6\nअतः औसत चाल 6 km/hr है - इसलिए सही विकल्प (b) है।\nसाधारण औसत

\frac{4 + 12}{2} = 8

गलत है, क्योंकि धीमी चाल वाले चरण में कहीं अधिक समय लगता है।","pos":2,"neg":0.25}],"test":{"slug":"ssc-gd-constable--19-feb-2025-shift-1-maths","title":"SSC GD Constable 19 February 2025 Shift-1 — Elementary Mathematics Sectional Test","examName":"SSC GD","paperLabel":"19 February 2025 · Shift 1","sectionSubject":"Elementary Mathematics","durationMinutes":15,"format":"sectional_test"}}]