26:I[81166,["/_next/static/immutable/chunks/2corl6wyj4669.js","/_next/static/immutable/chunks/38n271cv4vmyv.js","/_next/static/immutable/chunks/2pf73jja2520w.js"],"default"] 27:T4d5,Surds, square root value The value of

\sqrt{35}

is given, so change the required surd into a form that contains

\sqrt{35}

. Multiply the numerator and the denominator inside the root by 5:

\sqrt{\frac{7}{5}} = \sqrt{\frac{7 \times 5}{5 \times 5}} = \frac{\sqrt{35}}{5}

Substituting

\sqrt{35} = 5.916

= \frac{5.916}{5} = 1.1832

Hence, option (a) is the most appropriate answer.28:T5ac,करणी, वर्गमूल का मान

\sqrt{35}

का मान दिया गया है, अतः अभीष्ट करणी को ऐसे रूप में बदलिए जिसमें

\sqrt{35}

आ जाए। मूल चिह्न के अंदर अंश तथा हर दोनों को 5 से गुणा कीजिए:

\sqrt{\frac{7}{5}} = \sqrt{\frac{7 \times 5}{5 \times 5}} = \frac{\sqrt{35}}{5}

\sqrt{35} = 5.916

रखने पर:

= \frac{5.916}{5} = 1.1832

इसलिए सही विकल्प (a) है।29:Tb9e,Rationalisation, algebraic identity Rationalise x by multiplying the numerator and the denominator by

\sqrt{3} + \sqrt{2}

x = \frac{{(\sqrt{3} + \sqrt{2})}^{2}}{{(\sqrt{3})}^{2} - {(\sqrt{2})}^{2}} = \frac{3 + 2 + 2 \sqrt{6}}{3 - 2} = 5 + 2 \sqrt{6}

In the same way

y = \frac{{(\sqrt{3} - \sqrt{2})}^{2}}{3 - 2} = 5 - 2 \sqrt{6}

. So x+y=10 and

x y = {(5)}^{2} - {(2 \sqrt{6})}^{2} = 25 - 24 = 1

Identity:

x^{2} + y^{2} = {(x + y)}^{2} - 2 x y

= {(10)}^{2} - 2 \times 1 = 100 - 2 = 98

Hence, option (b) is the most appropriate answer.2a:Tc2a,परिमेयकरण, बीजीय सर्वसमिका x के अंश तथा हर को

\sqrt{3} + \sqrt{2}

से गुणा करके परिमेय कीजिए:

x = \frac{{(\sqrt{3} + \sqrt{2})}^{2}}{{(\sqrt{3})}^{2} - {(\sqrt{2})}^{2}} = \frac{3 + 2 + 2 \sqrt{6}}{3 - 2} = 5 + 2 \sqrt{6}

इसी प्रकार

y = \frac{{(\sqrt{3} - \sqrt{2})}^{2}}{3 - 2} = 5 - 2 \sqrt{6}

। अतः x+y=10 तथा

x y = {(5)}^{2} - {(2 \sqrt{6})}^{2} = 25 - 24 = 1

।

सर्वसमिका:

x^{2} + y^{2} = {(x + y)}^{2} - 2 x y

= {(10)}^{2} - 2 \times 1 = 100 - 2 = 98

इसलिए सही विकल्प (b) है।2b:T454,Profit percentage Profit is the excess of the selling price over the cost price, and the profit percentage is always taken on the cost price. Formula: profit %

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

Here CP = ₹800 and SP = ₹960, so the profit =960-800=160, i.e. ₹160. Profit %

= \frac{160}{800} \times 100 = \frac{1}{5} \times 100 = 20

. Hence the profit percentage is

20 %

, so option (c) is correct.2c:T567,लाभ प्रतिशत लाभ विक्रय मूल्य का क्रय मूल्य से आधिक्य होता है तथा लाभ प्रतिशत सदैव क्रय मूल्य पर ज्ञात किया जाता है। सूत्र: लाभ %

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

।

यहाँ CP = ₹800 तथा SP = ₹960 है, अतः लाभ =960-800=160, अर्थात् ₹160। लाभ %

= \frac{160}{800} \times 100 = \frac{1}{5} \times 100 = 20

। अतः लाभ प्रतिशत

20 %

है, इसलिए सही विकल्प (c) है।2d:T6c6,Successive discounts Two successive discounts act one after the other, so take a convenient marked price of ₹100 and apply them in turn.

After the first discount of

30 %

100 \times \frac{70}{100} = 70

. After the second discount of

20 %

70 \times \frac{80}{100} = 56

. The price falls from ₹100 to ₹56, so the total fall is ₹44 on ₹100, that is

44 %

. The formula gives the same value:

a + b - \frac{a b}{100} = 30 + 20 - \frac{30 \times 20}{100} = 44

. Hence the single equivalent discount is

44 %

, so option (d) is correct.2e:T814,क्रमिक छूट क्रमिक छूट एक के बाद एक लगती है, अतः अंकित मूल्य ₹100 मानकर दोनों छूटें बारी-बारी से लगाइए।

30 %

की पहली छूट के बाद:

100 \times \frac{70}{100} = 70

।

20 %

की दूसरी छूट के बाद:

70 \times \frac{80}{100} = 56

। मूल्य ₹100 से घटकर ₹56 रह जाता है, अर्थात् ₹100 पर कुल कमी ₹44 है, जो

44 %

हुई। सूत्र से भी यही मान मिलता है:

a + b - \frac{a b}{100} = 30 + 20 - \frac{30 \times 20}{100} = 44

। अतः तुल्य एकल छूट

44 %

है, इसलिए सही विकल्प (d) है।2f:T487,Mixture and alligation Two solutions of different strengths are mixed about the mean strength, and alligation gives the mixing ratio at once. Rule: (quantity of the weaker solution) : (quantity of the stronger solution) = (stronger − mean) : (mean − weaker).

Here the two strengths are

20 %

and

60 %

, and the mean strength wanted is

50 %

. Ratio =(60-50):(50-20)=10:30=1:3. Hence the

20 %

solution and the

60 %

solution must be mixed in the ratio 1:3, so option (d) is correct.30:T721,मिश्रण एवं मिश्रानुपात भिन्न सांद्रता वाले दो घोल माध्य सांद्रता के सापेक्ष मिलाए जाते हैं और मिश्रानुपात (एलिगेशन) से मिश्रण का अनुपात तुरंत प्राप्त हो जाता है। नियम: (कम सांद्रता वाले घोल की मात्रा) : (अधिक सांद्रता वाले घोल की मात्रा) = (अधिक सांद्रता − माध्य) : (माध्य − कम सांद्रता)।

यहाँ दोनों सांद्रताएँ

20 %

तथा

60 %

हैं और अभीष्ट माध्य सांद्रता

50 %

है। अनुपात =(60-50):(50-20)=10:30=1:3। अतः

20 %

घोल तथा

60 %

घोल को 1:3 के अनुपात में मिलाना होगा, इसलिए सही विकल्प (d) है।31:T700,Simple interest rate Simple interest is

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

, so the rate is

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

. Here P=8500, SI=2805 and T=4 years.

R = \frac{2805 \times 100}{8500 \times 4} = \frac{280500}{34000}

\frac{280500}{34000} = 8.25

, so the rate comes to about

8.25 %

per annum. Among the four choices only

8.38 %

lies this close: at

7.25 %

8.75 %

9.25 %

the four-year interest would be ₹2,465, ₹2,975 or ₹3,145, all far from ₹2,805. Hence option (b) is the most appropriate answer.32:T87b,साधारण ब्याज की दर साधारण ब्याज

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

होता है, अतः दर

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

। यहाँ P=8500, SI=2805 तथा T=4 वर्ष है।

R = \frac{2805 \times 100}{8500 \times 4} = \frac{280500}{34000}

।

\frac{280500}{34000} = 8.25

, अर्थात् दर लगभग

8.25 %

वार्षिक प्राप्त होती है। चारों विकल्पों में केवल

8.38 %

ही इतना निकट है:

7.25 %

8.75 %

अथवा

9.25 %

दर पर चार वर्ष का ब्याज क्रमशः ₹2,465, ₹2,975 तथा ₹3,145 होता, जो ₹2,805 से बहुत दूर है। अतः सर्वाधिक उपयुक्त विकल्प (b) है।33:T44b,Surface area of hemisphere Only the outer curved surface of a hemispherical bowl is polished, and its area is

2 π r^{2}

With r=7 cm: area

= 2 \times \frac{22}{7} \times 7 \times 7

= 2 \times 22 \times 7 = 308

square cm. Cost of polishing

= 308 \times 0.50 = 154

. Hence the polishing costs ₹154, so option (a) is correct.34:T597,अर्धगोले का पृष्ठीय क्षेत्रफल अर्धगोलाकार कटोरे की केवल बाह्य वक्र सतह पर पॉलिश होती है, जिसका क्षेत्रफल

2 π r^{2}

होता है।

r=7 cm रखने पर: क्षेत्रफल

= 2 \times \frac{22}{7} \times 7 \times 7

।

= 2 \times 22 \times 7 = 308

वर्ग cm। पॉलिश की लागत

= 308 \times 0.50 = 154

। अतः पॉलिश करने की लागत ₹154 है, इसलिए सही विकल्प (a) है।35:T4e6,Interior angle sum The interior angles of any polygon of n sides add up to

(n - 2) \times 180^{\circ}

Here the panel is a decagon, so n=10 and the sum

= (10 - 2) \times 180^{\circ}

= 8 \times 180^{\circ} = 1440^{\circ}

. Hence the total of all interior angles is

1440^{\circ}

, so option (c) is correct.36:T5d6,अंतःकोणों का योग n भुजाओं वाले किसी भी बहुभुज के अंतःकोणों का योग

(n - 2) \times 180^{\circ}

होता है।

यहाँ पैनल दस भुजाओं वाला है, अतः n=10 और योग

= (10 - 2) \times 180^{\circ}

।

= 8 \times 180^{\circ} = 1440^{\circ}

। अतः सभी अंतःकोणों का योग

1440^{\circ}

है, इसलिए सही विकल्प (c) है।37:T42d,Sides of regular polygon At every vertex of a polygon the interior angle and the exterior angle together make a straight angle.

Exterior angle

= 180^{\circ} - 160^{\circ} = 20^{\circ}

. In a regular polygon all exterior angles are equal and add up to

360^{\circ}

, so

n = \frac{360}{20}

. n=18. Hence the polygon has 18 sides, so option (c) is correct.38:T5cc,Volume of cone and sphere Equal volumes of material mean that the volume of the cone equals the volume of the sphere.

Volume of the cone

= \frac{1}{3} π r^{2} h

and volume of the sphere

= \frac{4}{3} π r^{3}

. So

\frac{1}{3} π r^{2} h = \frac{4}{3} π r^{3}

. Cancelling

\frac{1}{3} π r^{2}

from both sides gives h=4r. Hence the height of the cone is 4r, so option (c) is correct.39:T714,शंकु एवं गोले का आयतन सामग्री का आयतन समान होने का अर्थ है कि शंकु का आयतन गोले के आयतन के बराबर है।

शंकु का आयतन

= \frac{1}{3} π r^{2} h

तथा गोले का आयतन

= \frac{4}{3} π r^{3}

। अतः

\frac{1}{3} π r^{2} h = \frac{4}{3} π r^{3}

। दोनों पक्षों से

\frac{1}{3} π r^{2}

निरस्त करने पर h=4r प्राप्त होता है। अतः शंकु की ऊँचाई 4r है, इसलिए सही विकल्प (c) है।3a:T61d,Melting and recasting Melting changes the shape but not the amount of metal, so the volume of the big ball equals the total volume of the 125 small balls.

\frac{4}{3} π R^{3} = 125 \times \frac{4}{3} π r^{3}

, which gives

R^{3} = 125 r^{3}

. With R=10:

1000 = 125 r^{3}

, so

r^{3} = 8

r = \sqrt[3]{8} = 2

. Hence the radius of each smaller ball is 2 m, so option (b) is correct.3b:T775,पिघलाकर पुनर्निर्माण पिघलाने से आकार बदलता है, धातु की मात्रा नहीं; अतः बड़ी गेंद का आयतन 125 छोटी गेंदों के कुल आयतन के बराबर है।

\frac{4}{3} π R^{3} = 125 \times \frac{4}{3} π r^{3}

, जिससे

R^{3} = 125 r^{3}

प्राप्त होता है। R=10 रखने पर:

1000 = 125 r^{3}

, अतः

r^{3} = 8

।

r = \sqrt[3]{8} = 2

। अतः प्रत्येक छोटी गेंद की त्रिज्या 2 m है, इसलिए सही विकल्प (b) है।3c:T51d,Recurring decimal to fraction In

0.272727 \dots

the block '27' repeats from the very first decimal place, so it is a pure recurring decimal with a two-digit period. Rule: a pure recurring decimal equals the repeating block divided by as many 9s as there are digits in that block. So

0.27 = \frac{27}{99}

\frac{27}{99} = \frac{27 \div 9}{99 \div 9} = \frac{3}{11}

. A check confirms it:

3 \div 11 = 0.272727 \dots

Hence the required fraction is

\frac{3}{11}

, so option (c) is correct.3d:T6ad,आवर्ती दशमलव का भिन्न रूप

0.272727 \dots

में '27' समूह पहले ही दशमलव स्थान से दोहराया जा रहा है, अतः यह दो अंकों के आवर्त वाला शुद्ध आवर्ती दशमलव है। नियम: शुद्ध आवर्ती दशमलव का मान = आवर्ती अंक-समूह ÷ उतने ही 9, जितने अंक उस समूह में हों। अतः

0.27 = \frac{27}{99}

।

\frac{27}{99} = \frac{27 \div 9}{99 \div 9} = \frac{3}{11}

। जाँच से भी यही मिलता है:

3 \div 11 = 0.272727 \dots

अतः अभीष्ट भिन्न

\frac{3}{11}

है, इसलिए सही विकल्प (c) है।3e:T483,Slab-wise fare and ratio The fare is charged in two slabs, so work out each part separately and then add.

First 50 km at ₹18 per km:

50 \times 18 = 900

. The remaining 125-50=75 km at ₹14 per km:

75 \times 14 = 1050

. Total fare =900+1050=1950, that is ₹1,950. The ratio 2:3 has 2+3=5 parts, so B's share is

\frac{3}{5}

of the total fare. B pays

\frac{3}{5} \times 1950 = 1170

. Hence passenger B paid ₹1,170, so option (c) is correct.3f:T68e,स्लैब किराया एवं अनुपात किराया दो स्लैब में लिया जाता है, अतः दोनों भागों का किराया अलग-अलग ज्ञात करके जोड़िए।

प्रथम 50 km का किराया ₹18 प्रति km की दर से:

50 \times 18 = 900

। शेष 125-50=75 km का किराया ₹14 प्रति km की दर से:

75 \times 14 = 1050

। कुल किराया =900+1050=1950, अर्थात् ₹1,950। अनुपात 2:3 में कुल 2+3=5 भाग हैं, अतः B का हिस्सा कुल किराए का

\frac{3}{5}

है। B ने दिया

\frac{3}{5} \times 1950 = 1170

। अतः यात्री B ने ₹1,170 का भुगतान किया, इसलिए सही विकल्प (c) है।40:T816,Double angle formula

\tan θ = \frac{5}{12}

means the side opposite

θ

is 5 units and the side adjacent to it is 12 units.

Hypotenuse

= \sqrt{5^{2} + 12^{2}} = \sqrt{169} = 13

, the familiar triplet (5,12,13). So

\sin θ = \frac{5}{13}

and

\cos θ = \frac{12}{13}

. Identity:

\sin 2 θ = 2 \sin θ \cos θ

\sin 2 θ = 2 \times \frac{5}{13} \times \frac{12}{13} = \frac{120}{169}

. Hence

\sin 2 θ = \frac{120}{169}

, so option (d) is correct.41:T8f6,द्विगुण कोण सूत्र

\tan θ = \frac{5}{12}

का अर्थ है कि

θ

के सम्मुख भुजा 5 इकाई तथा आसन्न भुजा 12 इकाई है।

कर्ण

= \sqrt{5^{2} + 12^{2}} = \sqrt{169} = 13

, जो सुपरिचित त्रिक (5,12,13) है। अतः

\sin θ = \frac{5}{13}

तथा

\cos θ = \frac{12}{13}

। सर्वसमिका:

\sin 2 θ = 2 \sin θ \cos θ

।

\sin 2 θ = 2 \times \frac{5}{13} \times \frac{12}{13} = \frac{120}{169}

। अतः

\sin 2 θ = \frac{120}{169}

है, इसलिए सही विकल्प (d) है।42:T6bd,Trigonometric identity Treat 2A as one single angle and use the identity

\sin^{2} 2 A + \cos^{2} 2 A = 1

\sin^{2} 2 A = 1 - {(\frac{12}{13})}^{2} = 1 - \frac{144}{169} = \frac{25}{169}

\sin 2 A = \sqrt{\frac{25}{169}} = \frac{5}{13}

, the positive value being taken as 2A is acute here. The triplet (5,12,13) shows the same thing: with adjacent side 12 and hypotenuse 13, the opposite side is 5. Hence

\sin 2 A = \frac{5}{13}

, so option (d) is correct.43:T829,त्रिकोणमितीय सर्वसमिका 2A को एक ही कोण मानकर सर्वसमिका

\sin^{2} 2 A + \cos^{2} 2 A = 1

का प्रयोग कीजिए।

\sin^{2} 2 A = 1 - {(\frac{12}{13})}^{2} = 1 - \frac{144}{169} = \frac{25}{169}

।

\sin 2 A = \sqrt{\frac{25}{169}} = \frac{5}{13}

, यहाँ 2A न्यून कोण होने के कारण धनात्मक मान लिया गया है। त्रिक (5,12,13) से भी यही स्पष्ट होता है: आसन्न भुजा 12 तथा कर्ण 13 होने पर सम्मुख भुजा 5 होती है। अतः

\sin 2 A = \frac{5}{13}

है, इसलिए सही विकल्प (d) है।1c:["$","$L26",null,{"mode":"practice","dropped":0,"bilingual":true,"choiceSubjects":[],"questions":[{"id":7051,"n":51,"subject":"Quantitative Aptitude","stem":"The average of 12 numbers is 35 . If one number is excluded, the average becomes 33. Find the excluded number.","stemHi":"12 संख्याओं का औसत 35 है। यदि एक संख्या हटा दी जाए, तो औसत 33 हो जाता है। हटाई गई संख्या ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"55","textHi":null,"imageUrl":null},{"key":"b","text":"57","textHi":null,"imageUrl":null},{"key":"c","text":"59","textHi":null,"imageUrl":null},{"key":"d","text":"61","textHi":null,"imageUrl":null}],"correct":"b","sol":"Average, excluded number\nFormula: Sum = Average

\times

Number of terms.\nSum of the 12 numbers

= 35 \times 12 = 420

\nAfter one number is removed, 11 numbers are left, so their sum

= 33 \times 11 = 363

\n $\"figure\"/$ \nExcluded number =420-363=57\nHence, option (b) is the most appropriate answer.","solHi":"औसत, हटाई गई संख्या\nसूत्र: योग = औसत

\times

पदों की संख्या।\n12 संख्याओं का योग

= 35 \times 12 = 420

\nएक संख्या हटाने पर 11 संख्याएँ शेष रहती हैं, अतः उनका योग

= 33 \times 11 = 363

\n $\"figure\"/$ \nहटाई गई संख्या =420-363=57\nइसलिए सही विकल्प (b) है।","pos":2,"neg":0.5},{"id":7052,"n":52,"subject":"Quantitative Aptitude","stem":"If

\sqrt{35} = 5.916

, find the value of

\sqrt{\frac{7}{5}}

.","stemHi":"यदि

\sqrt{35} = 5.916

, तो

\sqrt{\frac{7}{5}}

का मान ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"1.1832","textHi":null,"imageUrl":null},{"key":"b","text":"1.2832","textHi":null,"imageUrl":null},{"key":"c","text":"1.0832","textHi":null,"imageUrl":null},{"key":"d","text":"1.1916","textHi":null,"imageUrl":null}],"correct":"a","sol":"$27","solHi":"$28","pos":2,"neg":0.5},{"id":7053,"n":53,"subject":"Quantitative Aptitude","stem":"If

x = \frac{(\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2})}, y = \frac{(\sqrt{3} - \sqrt{2})}{(\sqrt{3} + \sqrt{2})}

.\nfind the value of

(x^{2} + y^{2})

.","stemHi":"यदि

x = \frac{(\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2})}, y = \frac{(\sqrt{3} - \sqrt{2})}{(\sqrt{3} + \sqrt{2})}

।\nतो

(x^{2} + y^{2})

का मान ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"96","textHi":null,"imageUrl":null},{"key":"b","text":"98","textHi":null,"imageUrl":null},{"key":"c","text":"100","textHi":null,"imageUrl":null},{"key":"d","text":"102","textHi":null,"imageUrl":null}],"correct":"b","sol":"$29","solHi":"$2a","pos":2,"neg":0.5},{"id":7054,"n":54,"subject":"Quantitative Aptitude","stem":"

P, Q

, and R invest money in a business in the ratio

3 : 5 : 7

. If the total profit at the end of the year is ₹45,000, find Q's share.","stemHi":"

P, Q

, तथा R एक व्यवसाय में

3 : 5 : 7

के अनुपात में धन निवेश करते हैं। यदि वर्ष के अंत में कुल लाभ ₹45,000 है, तो Q का हिस्सा ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"₹9,000","textHi":null,"imageUrl":null},{"key":"b","text":"₹15,000","textHi":null,"imageUrl":null},{"key":"c","text":"₹21,000","textHi":null,"imageUrl":null},{"key":"d","text":"₹12,000","textHi":null,"imageUrl":null}],"correct":"b","sol":"Partnership, profit sharing\nWhen the money stays invested for the same time, the profit is divided in the ratio of the investments.\nRatio =3:5:7, so the total number of equal parts =3+5+7=15.\nValue of one part

= \frac{45000}{15} = 3000

\n $\"figure\"/$ \nQ's share

= 5 \times 3000 = 15000

\nSo Q gets ₹15,000.\nHence, option (b) is the most appropriate answer.","solHi":"साझेदारी, लाभ विभाजन\nजब धन समान अवधि तक लगा रहता है, तब लाभ निवेश के अनुपात में बाँटा जाता है।\nअनुपात =3:5:7, अतः बराबर भागों की कुल संख्या =3+5+7=15।\nएक भाग का मान

= \frac{45000}{15} = 3000

\n $\"figure\"/$ \nQ का हिस्सा

= 5 \times 3000 = 15000

\nअतः Q को ₹15,000 मिलते हैं।\nइसलिए सही विकल्प (b) है।","pos":2,"neg":0.5},{"id":7055,"n":55,"subject":"Quantitative Aptitude","stem":"X, Y, and Z invest money in the ratio

4 : 5 : 6

. If the total profit is ₹60,000, find X's share.","stemHi":"X, Y तथा Z,

4 : 5 : 6

के अनुपात में धन निवेश करते हैं। यदि कुल लाभ ₹60,000 है, तो X का हिस्सा ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"₹16,000","textHi":null,"imageUrl":null},{"key":"b","text":"₹20,000","textHi":null,"imageUrl":null},{"key":"c","text":"₹24,000","textHi":null,"imageUrl":null},{"key":"d","text":"₹18,000","textHi":null,"imageUrl":null}],"correct":"a","sol":"Partnership, profit sharing\nThe profit is shared in the ratio of the investments 4:5:6.\nTotal number of equal parts =4+5+6=15\nValue of one part

= \frac{60000}{15} = 4000

\n $\"figure\"/$ \nX's share

= 4 \times 4000 = 16000

\nSo X gets ₹16,000.\nHence, option (a) is the most appropriate answer.","solHi":"साझेदारी, लाभ विभाजन\nलाभ निवेश के अनुपात 4:5:6 में बाँटा जाता है।\nबराबर भागों की कुल संख्या =4+5+6=15\nएक भाग का मान

= \frac{60000}{15} = 4000

\n $\"figure\"/$ \nX का हिस्सा

= 4 \times 4000 = 16000

\nअतः X को ₹16,000 मिलते हैं।\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.5},{"id":7056,"n":56,"subject":"Quantitative Aptitude","stem":"If

P : Q = 3 : 4

and

Q : R = 5 : 6

, then what is

P : Q : R

?","stemHi":"यदि

P : Q = 3 : 4

तथा

Q : R = 5 : 6

, तो

P : Q : R

क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"

15 : 20 : 24

","textHi":null,"imageUrl":null},{"key":"b","text":"3 : 4 : 6","textHi":null,"imageUrl":null},{"key":"c","text":"15 : 20 : 22","textHi":null,"imageUrl":null},{"key":"d","text":"12 : 20 : 24","textHi":null,"imageUrl":null}],"correct":"a","sol":"Combining two ratios\nQ is common to both ratios, so make the number standing for Q the same in each of them.\nIn P:Q=3:4 the value of Q is 4, and in Q:R=5:6 it is 5; the LCM of 4 and 5 is 20.\nMultiply each term of the first ratio by 5: P:Q=15:20\nMultiply each term of the second ratio by 4: Q:R=20:24\n $\"figure\"/$ \nNow Q is 20 in both, so they can be joined: P:Q:R=15:20:24.\nHence, option (a) is the most appropriate answer.","solHi":"दो अनुपातों का संयोजन\nQ दोनों अनुपातों में उभयनिष्ठ है, अतः Q के लिए आने वाली संख्या को दोनों में समान बनाइए।\nP:Q=3:4 में Q का मान 4 है तथा Q:R=5:6 में 5 है; 4 और 5 का ल.स. 20 है।\nपहले अनुपात के प्रत्येक पद को 5 से गुणा कीजिए: P:Q=15:20\nदूसरे अनुपात के प्रत्येक पद को 4 से गुणा कीजिए: Q:R=20:24\n $\"figure\"/$ \nअब दोनों में Q का मान 20 है, अतः इन्हें जोड़ा जा सकता है: P:Q:R=15:20:24।\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.5},{"id":7057,"n":57,"subject":"Quantitative Aptitude","stem":"If the average of

11, 14, x

, and 23 is 18 , find the value of x.","stemHi":"यदि

11, 14, x

तथा 23 का औसत 18 है, तो x का मान ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"22","textHi":null,"imageUrl":null},{"key":"b","text":"20","textHi":null,"imageUrl":null},{"key":"c","text":"24","textHi":null,"imageUrl":null},{"key":"d","text":"26","textHi":null,"imageUrl":null}],"correct":"c","sol":"Average, missing term\nFormula: Average

= \frac{sum of the terms}{number of terms}

\frac{11 + 14 + x + 23}{4} = 18

48 + x = 18 \times 4 = 72

\nx=72-48=24\nHence, option (c) is the most appropriate answer.","solHi":"औसत, अज्ञात पद\nसूत्र: औसत

= \frac{पदों का योग}{पदों की संख्या}

\frac{11 + 14 + x + 23}{4} = 18

48 + x = 18 \times 4 = 72

\nx=72-48=24\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.5},{"id":7058,"n":58,"subject":"Quantitative Aptitude","stem":"The average of four numbers is 30 . The average of the first and second is 25 , and that of the third and fourth is 35 . What is the second number if the first is 20?","stemHi":"चार संख्याओं का औसत 30 है। पहली तथा दूसरी संख्या का औसत 25 है और तीसरी तथा चौथी संख्या का औसत 35 है। यदि पहली संख्या 20 है, तो दूसरी संख्या क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"25","textHi":null,"imageUrl":null},{"key":"b","text":"28","textHi":null,"imageUrl":null},{"key":"c","text":"30","textHi":null,"imageUrl":null},{"key":"d","text":"32","textHi":null,"imageUrl":null}],"correct":"c","sol":"Average of grouped numbers\nSum of all four numbers

= 30 \times 4 = 120

\nSum of the first and the second

= 25 \times 2 = 50

\nSum of the third and the fourth

= 35 \times 2 = 70

, and 50+70=120, so the data are consistent.\n $\"figure\"/$ \nThe first number is 20, so the second number =50-20=30.\nHence, option (c) is the most appropriate answer.","solHi":"समूहबद्ध संख्याओं का औसत\nचारों संख्याओं का योग

= 30 \times 4 = 120

\nपहली तथा दूसरी संख्या का योग

= 25 \times 2 = 50

\nतीसरी तथा चौथी संख्या का योग

= 35 \times 2 = 70

तथा 50+70=120, अतः आँकड़े परस्पर संगत हैं।\n $\"figure\"/$ \nपहली संख्या 20 है, अतः दूसरी संख्या =50-20=30।\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.5},{"id":7059,"n":59,"subject":"Quantitative Aptitude","stem":"A student scored 84 marks in a test. If this was 70% of the total, what were the maximum marks?","stemHi":"एक विद्यार्थी ने एक परीक्षा में 84 अंक प्राप्त किए। यदि यह कुल अंकों का 70% था, तो अधिकतम अंक कितने थे?","context":null,"contextHi":null,"options":[{"key":"a","text":"110","textHi":null,"imageUrl":null},{"key":"b","text":"120","textHi":null,"imageUrl":null},{"key":"c","text":"130","textHi":null,"imageUrl":null},{"key":"d","text":"140","textHi":null,"imageUrl":null}],"correct":"b","sol":"Percentage, finding the whole\n84 marks stand for 70% of the maximum marks.\n

\frac{70}{100} \times Maximum = 84

\nMaximum

= \frac{84 \times 100}{70} = 120

\nSo the paper carried 120 maximum marks.\nHence, option (b) is the most appropriate answer.","solHi":"प्रतिशत, कुल मान ज्ञात करना\n84 अंक, अधिकतम अंकों के 70% को दर्शाते हैं।\n

\frac{70}{100} \times अधिकतम अंक = 84

\nअधिकतम अंक

= \frac{84 \times 100}{70} = 120

\nअतः प्रश्न-पत्र के अधिकतम अंक 120 थे।\nइसलिए सही विकल्प (b) है।","pos":2,"neg":0.5},{"id":7060,"n":60,"subject":"Quantitative Aptitude","stem":"A shopkeeper buys an article for Rs. 400 and sells it for Rs. 500. What is the profit percentage?","stemHi":"एक दुकानदार एक वस्तु Rs. 400 में खरीदता है और उसे Rs. 500 में बेचता है। लाभ प्रतिशत क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"20%","textHi":null,"imageUrl":null},{"key":"b","text":"

22.5 %

","textHi":null,"imageUrl":null},{"key":"c","text":"25%","textHi":null,"imageUrl":null},{"key":"d","text":"30%","textHi":null,"imageUrl":null}],"correct":"c","sol":"Profit percentage\nCost price =400 and selling price =500, so Profit =500-400=100.\nProfit percentage is always taken on the cost price, not on the selling price.\nFormula: Profit

% = \frac{Profit}{Cost price} \times 100

= \frac{100}{400} \times 100 = 25

\nSo the profit is 25%.\nHence, option (c) is the most appropriate answer.","solHi":"लाभ प्रतिशत\nक्रय मूल्य =400 तथा विक्रय मूल्य =500, अतः लाभ =500-400=100।\nलाभ प्रतिशत सदैव क्रय मूल्य पर निकाला जाता है, विक्रय मूल्य पर नहीं।\nसूत्र: लाभ

% = \frac{लाभ}{क्रय मूल्य} \times 100

= \frac{100}{400} \times 100 = 25

\nअतः लाभ 25% है।\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.5},{"id":7061,"n":61,"subject":"Quantitative Aptitude","stem":"An item bought for Rs. 800 is sold at Rs. 960 . Find the profit percentage.","stemHi":"Rs. 800 में खरीदी गई एक वस्तु Rs. 960 में बेची जाती है। लाभ प्रतिशत ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"15%","textHi":null,"imageUrl":null},{"key":"b","text":"18%","textHi":null,"imageUrl":null},{"key":"c","text":"

20 %

","textHi":null,"imageUrl":null},{"key":"d","text":"25%","textHi":null,"imageUrl":null}],"correct":"c","sol":"$2b","solHi":"$2c","pos":2,"neg":0.5},{"id":7062,"n":62,"subject":"Quantitative Aptitude","stem":"A shopkeeper provides two consecutive discounts of

30 %

and

20 %

on an item. Calculate the single discount rate that is equivalent to these successive discounts.","stemHi":"एक दुकानदार किसी वस्तु पर

30 %

और

20 %

की दो क्रमिक छूट देता है। इन क्रमिक छूटों के तुल्य एकल छूट दर की गणना कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"40%","textHi":null,"imageUrl":null},{"key":"b","text":"

50 %

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

46 %

","textHi":null,"imageUrl":null},{"key":"d","text":"44%","textHi":null,"imageUrl":null}],"correct":"d","sol":"$2d","solHi":"$2e","pos":2,"neg":0.5},{"id":7063,"n":63,"subject":"Quantitative Aptitude","stem":"In what ratio must a

20 %

salt solution be mixed with a 60% salt solution to obtain a

50 %

salt solution ?","stemHi":"

20 %

नमक के घोल को 60% नमक के घोल के साथ किस अनुपात में मिलाया जाए कि

50 %

नमक का घोल प्राप्त हो?","context":null,"contextHi":null,"options":[{"key":"a","text":"

1 : 2

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

2 : 3

","textHi":null,"imageUrl":null},{"key":"c","text":"3 : 1","textHi":null,"imageUrl":null},{"key":"d","text":"

1 : 3

","textHi":null,"imageUrl":null}],"correct":"d","sol":"$2f","solHi":"$30","pos":2,"neg":0.5},{"id":7064,"n":64,"subject":"Quantitative Aptitude","stem":"A sum of Rs. 8,500 earns Rs. 2,805 as simple interest in 4 years. Find the rate of interest.","stemHi":"Rs. 8,500 की राशि पर 4 वर्षों में Rs. 2,805 साधारण ब्याज प्राप्त होता है। ब्याज की दर ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"

7.25 %

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

8.38 %

","textHi":null,"imageUrl":null},{"key":"c","text":"8.75 %","textHi":null,"imageUrl":null},{"key":"d","text":"

9.25 %

","textHi":null,"imageUrl":null}],"correct":"b","sol":"$31","solHi":"$32","pos":2,"neg":0.5},{"id":7065,"n":65,"subject":"Quantitative Aptitude","stem":"A workshop manufactures hemispherical steel bowls of radius 7 cm . If polishing costs

₹ 0.50

per square cm , find the cost of polishing the outer surface of one bowl.","stemHi":"एक कार्यशाला में 7 cm त्रिज्या के अर्धगोलाकार इस्पात के कटोरे बनाए जाते हैं। यदि पॉलिश करने की लागत

₹ 0.50

प्रति वर्ग cm है, तो एक कटोरे की बाह्य सतह पर पॉलिश करने की लागत ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"₹154","textHi":null,"imageUrl":null},{"key":"b","text":"₹148","textHi":null,"imageUrl":null},{"key":"c","text":"₹158","textHi":null,"imageUrl":null},{"key":"d","text":"₹162","textHi":null,"imageUrl":null}],"correct":"a","sol":"$33","solHi":"$34","pos":2,"neg":0.5},{"id":7066,"n":66,"subject":"Quantitative Aptitude","stem":"A satellite has solar panels shaped as regular polygons with 10 sides. What is the total of all internal angles ?","stemHi":"एक उपग्रह में सौर पैनल 10 भुजाओं वाले सम बहुभुज के आकार के हैं। इसके सभी अंतःकोणों का योग कितना होगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"1800°","textHi":null,"imageUrl":null},{"key":"b","text":"1620°","textHi":null,"imageUrl":null},{"key":"c","text":"1440°","textHi":null,"imageUrl":null},{"key":"d","text":"1260°","textHi":null,"imageUrl":null}],"correct":"c","sol":"$35","solHi":"$36","pos":2,"neg":0.5},{"id":7067,"n":67,"subject":"Quantitative Aptitude","stem":"A biochip's cover is designed as a regular polygon such that each interior angle is

160^{\circ}

. Find the number of sides.","stemHi":"एक बायोचिप का आवरण ऐसे सम बहुभुज के रूप में बनाया गया है जिसका प्रत्येक अंतःकोण

160^{\circ}

है। भुजाओं की संख्या ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"20","textHi":null,"imageUrl":null},{"key":"b","text":"22","textHi":null,"imageUrl":null},{"key":"c","text":"18","textHi":null,"imageUrl":null},{"key":"d","text":"24","textHi":null,"imageUrl":null}],"correct":"c","sol":"$37","solHi":"सम बहुभुज की भुजाएँ\nबहुभुज के प्रत्येक शीर्ष पर अंतःकोण तथा बाह्यकोण मिलकर एक ऋजु कोण बनाते हैं।\n $\"figure\"/$ \nबाह्यकोण

= 180^{\circ} - 160^{\circ} = 20^{\circ}

।\nसम बहुभुज के सभी बाह्यकोण बराबर होते हैं तथा उनका योग

360^{\circ}

होता है, अतः

n = \frac{360}{20}

।\nn=18।\nअतः बहुभुज में 18 भुजाएँ हैं, इसलिए सही विकल्प (c) है।","pos":2,"neg":0.5},{"id":7068,"n":68,"subject":"Quantitative Aptitude","stem":"A solid cone and a solid sphere are made from the same volume of material. Both have the same radius

r

. What is the height of the cone in terms of

r

?","stemHi":"एक ठोस शंकु तथा एक ठोस गोला समान आयतन की सामग्री से बनाए गए हैं। दोनों की त्रिज्या

r

समान है।

r

के पदों में शंकु की ऊँचाई क्या होगी?","context":null,"contextHi":null,"options":[{"key":"a","text":"

2 r

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

3 r

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

4 r

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

\frac{4}{3} r

","textHi":null,"imageUrl":null}],"correct":"c","sol":"$38","solHi":"$39","pos":2,"neg":0.5},{"id":7069,"n":69,"subject":"Quantitative Aptitude","stem":"A large spherical metallic ball with a radius of 10 meters is melted down and recast into 125 identical smaller spherical balls. Assuming no metal is wasted in the process, what is the radius of each smaller ball ?","stemHi":"10 मीटर त्रिज्या वाली एक बड़ी गोलाकार धात्विक गेंद को पिघलाकर 125 एक समान छोटी गोलाकार गेंदें बनाई जाती हैं। यह मानते हुए कि इस प्रक्रिया में कोई धातु व्यर्थ नहीं होती, प्रत्येक छोटी गेंद की त्रिज्या कितनी होगी?","context":null,"contextHi":null,"options":[{"key":"a","text":"1 m","textHi":null,"imageUrl":null},{"key":"b","text":"2 m","textHi":null,"imageUrl":null},{"key":"c","text":"2.5 m","textHi":null,"imageUrl":null},{"key":"d","text":"5 m","textHi":null,"imageUrl":null}],"correct":"b","sol":"$3a","solHi":"$3b","pos":2,"neg":0.5},{"id":7070,"n":70,"subject":"Quantitative Aptitude","stem":"A digital scale measures the weight of a chemical compound as

0.272727 \dots

grams. A chemist requires this value in a fractional form for a stoichiometric calculation. What is the correct fraction?","stemHi":"एक डिजिटल तराजू किसी रासायनिक यौगिक का भार

0.272727 \dots

ग्राम मापता है। एक रसायनज्ञ को स्टॉइकियोमीट्रिक गणना के लिए यह मान भिन्न के रूप में चाहिए। सही भिन्न कौन-सी है?","context":null,"contextHi":null,"options":[{"key":"a","text":"

\frac{27}{100}

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

\frac{3}{10}

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

\frac{3}{11}

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

\frac{2}{9}

","textHi":null,"imageUrl":null}],"correct":"c","sol":"$3c","solHi":"$3d","pos":2,"neg":0.5},{"id":7071,"n":71,"subject":"Quantitative Aptitude","stem":"A taxi service charges ₹18 per km for the first 50 km and ₹14 per km thereafter. A specific trip covered a total distance of 125 km . If the total fare was split between passenger A and passenger B in the ratio 2 : 3, what amount did passenger

B

pay?","stemHi":"एक टैक्सी सेवा पहले 50 km के लिए ₹18 प्रति km तथा उसके बाद ₹14 प्रति km शुल्क लेती है। एक विशेष यात्रा में कुल 125 km की दूरी तय की गई। यदि कुल किराया यात्री A तथा यात्री B के बीच 2 : 3 के अनुपात में बाँटा गया, तो यात्री

B

ने कितनी राशि का भुगतान किया?","context":null,"contextHi":null,"options":[{"key":"a","text":"₹780","textHi":null,"imageUrl":null},{"key":"b","text":"₹1050","textHi":null,"imageUrl":null},{"key":"c","text":"₹1170","textHi":null,"imageUrl":null},{"key":"d","text":"₹1350","textHi":null,"imageUrl":null}],"correct":"c","sol":"$3e","solHi":"$3f","pos":2,"neg":0.5},{"id":7072,"n":72,"subject":"Quantitative Aptitude","stem":"A signal tower forms an elevation such that

\tan θ = \frac{5}{12}

. Compute

\sin 2 θ

.","stemHi":"एक सिग्नल टॉवर ऐसा उन्नयन कोण बनाता है कि

\tan θ = \frac{5}{12}

।

\sin 2 θ

का मान ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"

\frac{26}{10}

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

\frac{10}{26}

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

\frac{169}{120}

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

\frac{120}{169}

","textHi":null,"imageUrl":null}],"correct":"d","sol":"$40","solHi":"$41","pos":2,"neg":0.5},{"id":7073,"n":73,"subject":"Quantitative Aptitude","stem":"If

x : y = 5 : 6

and

y : z = 3 : 7

, find

x : z

.","stemHi":"यदि

x : y = 5 : 6

और

y : z = 3 : 7

, तो

x : z

ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"5:7","textHi":null,"imageUrl":null},{"key":"b","text":"5 : 14","textHi":null,"imageUrl":null},{"key":"c","text":"9 : 17","textHi":null,"imageUrl":null},{"key":"d","text":"

10 : 21

","textHi":null,"imageUrl":null}],"correct":"b","sol":"Combining ratios\ny occurs in both ratios, so make its value the same in each before joining them.\nGiven x:y=5:6 and y:z=3:7.\nMultiply the second ratio throughout by 2 so that y becomes 6: y:z=6:14.\n $\"figure\"/$ \nNow the chain gives x:y:z=5:6:14.\nHence x:z=5:14, so option (b) is correct.","solHi":"अनुपातों का संयोजन\ny दोनों अनुपातों में आता है, अतः उन्हें जोड़ने से पहले दोनों में y का मान समान कीजिए।\nदिया है x:y=5:6 तथा y:z=3:7।\nदूसरे अनुपात को 2 से गुणा कीजिए जिससे y का मान 6 हो जाए: y:z=6:14।\n $\"figure\"/$ \nअब शृंखला से x:y:z=5:6:14 प्राप्त होता है।\nअतः x:z=5:14 है, इसलिए सही विकल्प (b) है।","pos":2,"neg":0.5},{"id":7074,"n":74,"subject":"Quantitative Aptitude","stem":"What simple interest rate will cause a sum of money to double in 12 years?","stemHi":"साधारण ब्याज की कौन-सी दर पर कोई धनराशि 12 वर्षों में दोगुनी हो जाएगी?","context":null,"contextHi":null,"options":[{"key":"a","text":"

6.25 %

","textHi":null,"imageUrl":null},{"key":"b","text":"8.33%","textHi":null,"imageUrl":null},{"key":"c","text":"

9.09 %

","textHi":null,"imageUrl":null},{"key":"d","text":"12.5%","textHi":null,"imageUrl":null}],"correct":"b","sol":"Sum doubling at simple interest\nIf a sum doubles, the interest earned is equal to the sum itself, that is SI=P.\nFormula:

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

.\nSubstituting SI=P and T=12:

P = \frac{P \times R \times 12}{100}

.\nCancelling P from both sides: 100=12R, so

R = \frac{100}{12}

.\nR=8.33 approximately.\nHence the required rate is about

8.33 %

per annum, so option (b) is correct.","solHi":"साधारण ब्याज पर राशि दोगुनी\nयदि कोई राशि दोगुनी हो जाती है, तो अर्जित ब्याज उस राशि के बराबर होता है, अर्थात् SI=P।\nसूत्र:

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

।\nSI=P तथा T=12 रखने पर:

P = \frac{P \times R \times 12}{100}

।\nदोनों पक्षों से P निरस्त करने पर: 100=12R, अतः

R = \frac{100}{12}

।\nR=8.33 (लगभग)।\nअतः अभीष्ट दर लगभग

8.33 %

वार्षिक है, इसलिए सही विकल्प (b) है।","pos":2,"neg":0.5},{"id":7075,"n":75,"subject":"Quantitative Aptitude","stem":"If

\cos 2 A = \frac{12}{13}

, what is

\sin 2 A

?","stemHi":"यदि

\cos 2 A = \frac{12}{13}

, तो

\sin 2 A

का मान क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"

\frac{169}{25}

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

\frac{13}{5}

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

\frac{25}{169}

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

\frac{5}{13}

","textHi":null,"imageUrl":null}],"correct":"d","sol":"$42","solHi":"$43","pos":2,"neg":0.5}],"test":{"slug":"ssc-chsl-tier-1--21-nov-2025-shift-2-quant","title":"SSC CHSL Tier-1 21 November 2025 Shift-2 — Quantitative Aptitude Sectional Test","examName":"CHSL Tier-1","paperLabel":"21 November 2025 · Shift 2","sectionSubject":"Quantitative Aptitude","durationMinutes":15,"format":"sectional_test"}}]