26:I[81166,["/_next/static/immutable/chunks/2corl6wyj4669.js","/_next/static/immutable/chunks/38n271cv4vmyv.js","/_next/static/immutable/chunks/2pf73jja2520w.js"],"default"] 27:T544,Irrational numbers An irrational number cannot be written as a ratio of two integers, and the set of irrational numbers is not closed under addition.

Take

a = \sqrt{2}

and

b = \sqrt{3}

: then

a + b = \sqrt{2} + \sqrt{3}

, which is irrational. Now take b=-a: the two irrational parts cancel and

a + b = \sqrt{2} + (- \sqrt{2}) = 0

, which is rational. So the sum is neither always irrational nor always rational, and it does become rational when a=-b. Hence the correct option is (c).28:T785,अपरिमेय संख्याएँ अपरिमेय संख्या को दो पूर्णांकों के अनुपात के रूप में नहीं लिखा जा सकता, तथा अपरिमेय संख्याओं का समुच्चय योग के अंतर्गत संवृत नहीं है।

मान लीजिए

a = \sqrt{2}

तथा

b = \sqrt{3}

: तब

a + b = \sqrt{2} + \sqrt{3}

है, जो अपरिमेय है। अब b=-a लीजिए: दोनों अपरिमेय भाग कट जाते हैं और

a + b = \sqrt{2} + (- \sqrt{2}) = 0

प्राप्त होता है, जो परिमेय है। अतः यह योग न तो सदैव अपरिमेय है और न ही सदैव परिमेय, किंतु a=-b होने पर यह परिमेय हो जाता है। इसलिए सही विकल्प (c) है।29:T947,Trigonometric ratios 8,15,17 is a Pythagorean triplet, since

8^{2} + 15^{2} = 64 + 225 = 289 = 17^{2}

. So the angle opposite the longest side is a right angle:

∠ Q = 90^{\circ}

and PR is the hypotenuse.

For

∠ R

the opposite side is PQ=8 cm, the adjacent side is QR=15 cm and the hypotenuse is PR=17 cm. So

\tan R = \frac{8}{15}

and

\sin R = \frac{8}{17}

. For

∠ P

the opposite side is QR=15 cm and the adjacent side is PQ=8 cm, hence

\cot P = \frac{8}{15}

\tan R + \sin R + 2 \cot P = \frac{8}{15} + \frac{8}{17} + \frac{16}{15} = \frac{24}{15} + \frac{8}{17}

=1.6+0.470=2.070 Hence the correct option is (a).2a:Ta67,त्रिकोणमितीय अनुपात 8,15,17 एक पाइथागोरस त्रिक है, क्योंकि

8^{2} + 15^{2} = 64 + 225 = 289 = 17^{2}

। अतः सबसे बड़ी भुजा के सम्मुख कोण समकोण है:

∠ Q = 90^{\circ}

तथा PR कर्ण है।

∠ R

के लिए सम्मुख भुजा PQ=8 cm, संलग्न भुजा QR=15 cm तथा कर्ण PR=17 cm है। अतः

\tan R = \frac{8}{15}

तथा

\sin R = \frac{8}{17}

।

∠ P

के लिए सम्मुख भुजा QR=15 cm तथा संलग्न भुजा PQ=8 cm है, अतः

\cot P = \frac{8}{15}

।

\tan R + \sin R + 2 \cot P = \frac{8}{15} + \frac{8}{17} + \frac{16}{15} = \frac{24}{15} + \frac{8}{17}

=1.6+0.470=2.070 इसलिए सही विकल्प (a) है।2b:T422,Time and work efficiency Sonu is 30% less efficient than Monu, so if Monu's efficiency is 100, Sonu's is 70. Efficiency ratio Sonu : Monu =70:100=7:10.

Working together they do 7+10=17 units a day, and they finish in 40 days, so the total work

= 17 \times 40 = 680

units. 70% of the work

= \frac{70}{100} \times 680 = 476

units. Sonu alone does 7 units a day, so he needs

\frac{476}{7} = 68

days. Hence the correct option is (d).2c:T603,समय और कार्य - कुशलता सोनू, मोनू से 30% कम कुशल है, अतः यदि मोनू की कुशलता 100 हो तो सोनू की कुशलता 70 होगी। कुशलता का अनुपात सोनू : मोनू =70:100=7:10।

साथ मिलकर वे प्रतिदिन 7+10=17 इकाई कार्य करते हैं और 40 दिनों में कार्य पूरा करते हैं, अतः कुल कार्य

= 17 \times 40 = 680

इकाई। कार्य का 70%

= \frac{70}{100} \times 680 = 476

इकाई। सोनू अकेला प्रतिदिन 7 इकाई करता है, अतः उसे

\frac{476}{7} = 68

दिन लगेंगे। इसलिए सही विकल्प (d) है।2d:T5ed,Chord and radius Join the two ends of the chord to the centre; the two radii and the chord form a triangle.

Here OA=OB=r and

∠ A O B = 90^{\circ}

, so

△ A O B

is a right-angled isosceles triangle with AB=12 cm as its hypotenuse. By Pythagoras' theorem:

r^{2} + r^{2} = 12^{2}

2 r^{2} = 144 \Rightarrow r^{2} = 72

r = \sqrt{72} = 6 \sqrt{2}

cm. Hence the correct option is (b).2e:T736,जीवा और त्रिज्या जीवा के दोनों सिरों को केंद्र से मिलाइए; दोनों त्रिज्याएँ तथा जीवा मिलकर एक त्रिभुज बनाती हैं।

यहाँ OA=OB=r तथा

∠ A O B = 90^{\circ}

है, अतः

△ A O B

एक समकोण समद्विबाहु त्रिभुज है जिसका कर्ण AB=12 cm है। पाइथागोरस प्रमेय से:

r^{2} + r^{2} = 12^{2}

2 r^{2} = 144 \Rightarrow r^{2} = 72

r = \sqrt{72} = 6 \sqrt{2}

cm। इसलिए सही विकल्प (b) है।2f:T551,Length of a chord The perpendicular drawn from the centre of a circle to a chord bisects that chord.

So in right-angled

△ O M A

, OA=17 cm is the radius and OM=8 cm is the given distance.

A M = \sqrt{O A^{2} - O M^{2}} = \sqrt{17^{2} - 8^{2}} = \sqrt{289 - 64} = \sqrt{225} = 15

cm. Length of the chord

A B = 2 \times A M = 2 \times 15 = 30

cm. Hence the correct option is (c).30:T631,जीवा की लंबाई वृत्त के केंद्र से जीवा पर खींचा गया लंब उस जीवा को समद्विभाजित करता है।

अतः समकोण

△ O M A

में OA=17 cm त्रिज्या है तथा OM=8 cm दी गई दूरी है।

A M = \sqrt{O A^{2} - O M^{2}} = \sqrt{17^{2} - 8^{2}} = \sqrt{289 - 64} = \sqrt{225} = 15

cm। जीवा की लंबाई

A B = 2 \times A M = 2 \times 15 = 30

cm। इसलिए सही विकल्प (c) है।31:T4d1,Tangent-chord angle By the alternate segment theorem, the angle between a tangent and a chord drawn from the point of contact equals the angle that the chord subtends in the alternate segment.

The chord AB subtends

∠ A O B = 100^{\circ}

at the centre, and the angle at the circumference is half the angle at the centre. So the angle in the alternate segment

= \frac{100^{\circ}}{2} = 50^{\circ}

. Therefore the angle between the chord AB and the tangent at A is

50^{\circ}

. Hence the correct option is (b).32:T704,स्पर्श रेखा-जीवा कोण एकांतर वृत्तखंड प्रमेय के अनुसार, स्पर्श बिंदु से खींची गई जीवा तथा स्पर्श रेखा के बीच का कोण उस कोण के बराबर होता है जो वह जीवा एकांतर वृत्तखंड में अंतरित करती है।

जीवा AB केंद्र पर

∠ A O B = 100^{\circ}

अंतरित करती है, तथा परिधि पर बना कोण केंद्र पर बने कोण का आधा होता है। अतः एकांतर वृत्तखंड में बना कोण

= \frac{100^{\circ}}{2} = 50^{\circ}

। इसलिए जीवा AB तथा A पर खींची गई स्पर्श रेखा के बीच का कोण

50^{\circ}

है। इसलिए सही विकल्प (b) है।33:Taea,Cylinder surface and volume For a cylinder of radius r and height h: curved surface area

= 2 π r h

and total surface area

= 2 π r (h + r)

\frac{2 π r h}{2 π r (h + r)} = \frac{3}{4} \Rightarrow \frac{h}{h + r} = \frac{3}{4}

4 h = 3 h + 3 r \Rightarrow h = 3 r

Volume

= π r^{2} h = π r^{2} (3 r) = 3 π r^{3} = 3234

r^{3} = \frac{3234 \times 7}{3 \times 22} = 343 \Rightarrow r = 7

cm, so

h = 3 \times 7 = 21

cm. Curved surface area

= 2 π r h = 2 \times \frac{22}{7} \times 7 \times 21 = 924

{c m}^{2}

. Hence the correct option is (a).34:Tbfe,बेलन का पृष्ठ और आयतन r त्रिज्या तथा h ऊँचाई वाले बेलन के लिए: वक्र पृष्ठीय क्षेत्रफल

= 2 π r h

तथा संपूर्ण पृष्ठीय क्षेत्रफल

= 2 π r (h + r)

।

\frac{2 π r h}{2 π r (h + r)} = \frac{3}{4} \Rightarrow \frac{h}{h + r} = \frac{3}{4}

4 h = 3 h + 3 r \Rightarrow h = 3 r

आयतन

= π r^{2} h = π r^{2} (3 r) = 3 π r^{3} = 3234

r^{3} = \frac{3234 \times 7}{3 \times 22} = 343 \Rightarrow r = 7

cm, अतः

h = 3 \times 7 = 21

cm। वक्र पृष्ठीय क्षेत्रफल

= 2 π r h = 2 \times \frac{22}{7} \times 7 \times 21 = 924

{c m}^{2}

। इसलिए सही विकल्प (a) है।35:T472,Triangle with incircle The inscribed circle only fixes the points of contact S, U and T; the sides themselves come from the two given relations and the perimeter.

Let PQ=x cm.

P Q = Q R + 7 \Rightarrow Q R = x - 7

P Q = P R + 4 \Rightarrow P R = x - 4

Perimeter: x+(x-7)+(x-4)=34

3 x - 11 = 34 \Rightarrow 3 x = 45 \Rightarrow x = 15

cm. Therefore PR=15-4=11 cm. Hence the correct option is (c).36:T583,अंतःवृत्त सहित त्रिभुज अंतःवृत्त केवल स्पर्श बिंदु S, U तथा T निर्धारित करता है; भुजाएँ स्वयं दिए गए दोनों संबंधों तथा परिमाप से प्राप्त होती हैं।

माना कि PQ=x cm।

P Q = Q R + 7 \Rightarrow Q R = x - 7

P Q = P R + 4 \Rightarrow P R = x - 4

परिमाप: x+(x-7)+(x-4)=34

3 x - 11 = 34 \Rightarrow 3 x = 45 \Rightarrow x = 15

cm। अतः PR=15-4=11 cm। इसलिए सही विकल्प (c) है।37:T817,Simple interest Simple interest

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

, and here the rate is 8% for both, so the interest depends only on the product

P \times T

Equating the two interests:

P_{A} \times 5 = P_{B} \times 7

. B invested ₹12,000 less than A, so

P_{B} = P_{A} - 12000

5 P_{A} = 7 (P_{A} - 12000)

5 P_{A} = 7 P_{A} - 84000

2 P_{A} = 84000 \Rightarrow P_{A} = 42000

So A's investment is ₹42,000, and the correct option is (c).38:T926,साधारण ब्याज साधारण ब्याज

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

, तथा यहाँ दोनों के लिए दर 8% है, अतः ब्याज केवल गुणनफल

P \times T

पर निर्भर करता है।

दोनों ब्याजों को बराबर रखने पर:

P_{A} \times 5 = P_{B} \times 7

। B ने A से ₹12,000 कम निवेश किया, अतः

P_{B} = P_{A} - 12000

।

5 P_{A} = 7 (P_{A} - 12000)

5 P_{A} = 7 P_{A} - 84000

2 P_{A} = 84000 \Rightarrow P_{A} = 42000

अतः A का निवेश ₹42,000 है, और सही विकल्प (c) है।39:T570,Ratio and proportion Let the two numbers be 3x and 7x.

Given:

\frac{3 x + 14}{7 x + 14} = \frac{13}{17}

Cross-multiplying: 17(3x+14)=13(7x+14) 51x+238=91x+182

91 x - 51 x = 238 - 182 \Rightarrow 40 x = 56

x = \frac{56}{40} = \frac{7}{5}

Sum of the original numbers

= 3 x + 7 x = 10 x = 10 \times \frac{7}{5} = 14

, so option (a) is correct.3a:T639,अनुपात और समानुपात माना कि दोनों संख्याएँ 3x तथा 7x हैं।

दिया गया है:

\frac{3 x + 14}{7 x + 14} = \frac{13}{17}

तिर्यक गुणा करने पर: 17(3x+14)=13(7x+14) 51x+238=91x+182

91 x - 51 x = 238 - 182 \Rightarrow 40 x = 56

x = \frac{56}{40} = \frac{7}{5}

मूल संख्याओं का योग

= 3 x + 7 x = 10 x = 10 \times \frac{7}{5} = 14

, इसलिए सही विकल्प (a) है।3b:T552,HCF and LCM of two numbers The HCF is 13, so let the numbers be 13a and 13b where a and b are co-prime. Then

L C M = 13 a b

. Given

\frac{L C M}{H C F} = \frac{7}{1}

, so

\frac{13 a b}{13} = 7 \Rightarrow a b = 7

. As 7 is prime and a,b are co-prime, a=1 and b=7. The numbers are

13 \times 1 = 13

and

13 \times 7 = 91

Their sum 13+91=104 matches the condition, so option (b) is correct.3c:T6c6,दो संख्याओं का म.स. और ल.स. म.स. 13 है, अतः माना कि संख्याएँ 13a तथा 13b हैं, जहाँ a और b सह-अभाज्य हैं। तब

L C M = 13 a b

होगा। दिया गया है

\frac{L C M}{H C F} = \frac{7}{1}

, अतः

\frac{13 a b}{13} = 7 \Rightarrow a b = 7

। चूँकि 7 अभाज्य है तथा a,b सह-अभाज्य हैं, अतः a=1 और b=7। अतः संख्याएँ

13 \times 1 = 13

तथा

13 \times 7 = 91

हैं।

इनका योग 13+91=104 दी गई शर्त के अनुरूप है, इसलिए सही विकल्प (b) है।3d:T5eb,Marked price and discount Let the marked price be

MP

. A 35% discount means the buyer pays 65% of the marked price.

\frac{65}{100} \times MP = 7000 \Rightarrow MP = \frac{7000 \times 100}{65} = \frac{140000}{13}

With a 40% discount the selling price is 60% of the marked price. New SP

= \frac{60}{100} \times \frac{140000}{13} = \frac{84000}{13}

Equivalently, New SP

= 7000 \times \frac{60}{65} = \frac{84000}{13} = 6461.54

So the new selling price is ₹6,461.54, option (b).3e:T750,अंकित मूल्य और छूट माना कि अंकित मूल्य

MP

है। 35% छूट का अर्थ है कि क्रेता अंकित मूल्य का 65% चुकाता है।

\frac{65}{100} \times MP = 7000 \Rightarrow MP = \frac{7000 \times 100}{65} = \frac{140000}{13}

40% छूट पर विक्रय मूल्य अंकित मूल्य का 60% होगा। नया विक्रय मूल्य

= \frac{60}{100} \times \frac{140000}{13} = \frac{84000}{13}

अथवा सीधे, नया विक्रय मूल्य

= 7000 \times \frac{60}{65} = \frac{84000}{13} = 6461.54

अतः नया विक्रय मूल्य ₹6,461.54 है, इसलिए सही विकल्प (b) है।3f:T503,Mixture: milk and water Container A holds 40 litres in the ratio 3:5, so the parts total 3+5=8. Milk

= \frac{3}{8} \times 40 = 15

L and water

= \frac{5}{8} \times 40 = 25

L. Container B holds 60 litres in the ratio 5:1, so the parts total 5+1=6. Milk

= \frac{5}{6} \times 60 = 50

L and water

= \frac{1}{6} \times 60 = 10

After mixing, milk =15+50=65 L and water =25+10=35 L. Required ratio =65:35=13:7, so option (c) is correct.40:T657,मिश्रण: दूध और पानी पात्र A में 40 लीटर मिश्रण 3:5 के अनुपात में है, अतः कुल भाग 3+5=8 हैं। दूध

= \frac{3}{8} \times 40 = 15

L तथा पानी

= \frac{5}{8} \times 40 = 25

L। पात्र B में 60 लीटर मिश्रण 5:1 के अनुपात में है, अतः कुल भाग 5+1=6 हैं। दूध

= \frac{5}{6} \times 60 = 50

L तथा पानी

= \frac{1}{6} \times 60 = 10

L।

मिलाने के बाद दूध =15+50=65 L तथा पानी =25+10=35 L। अभीष्ट अनुपात =65:35=13:7, इसलिए सही विकल्प (c) है।41:T70a,Comparison of surds Surds of different orders can be compared only after they are written with a common index. The orders are 3, 2 and 6; their LCM is 6.

\sqrt[3]{3} = 3^{\frac{1}{3}} = 3^{\frac{2}{6}} = \sqrt[6]{9}

\sqrt{5} = 5^{\frac{1}{2}} = 5^{\frac{3}{6}} = \sqrt[6]{125}

\sqrt[6]{7} = 7^{\frac{1}{6}} = \sqrt[6]{7}

All three now have index 6, so compare the radicands: 125>9>7. Hence the largest value is

\sqrt{5}

, and option (b) is correct.42:T89d,करणी की तुलना भिन्न-भिन्न घातांक वाली करणियों की तुलना तभी की जा सकती है जब उन्हें समान घातांक में लिखा जाए। यहाँ घातांक 3, 2 तथा 6 हैं; इनका ल.स. 6 है।

\sqrt[3]{3} = 3^{\frac{1}{3}} = 3^{\frac{2}{6}} = \sqrt[6]{9}

\sqrt{5} = 5^{\frac{1}{2}} = 5^{\frac{3}{6}} = \sqrt[6]{125}

\sqrt[6]{7} = 7^{\frac{1}{6}} = \sqrt[6]{7}

अब तीनों का घातांक 6 है, अतः करणी के भीतर की संख्याओं की तुलना कीजिए: 125>9>7। अतः सबसे बड़ा मान

\sqrt{5}

है, इसलिए सही विकल्प (b) है।43:T546,Similar triangles: medians

In two similar triangles every pair of corresponding lengths is in the same ratio — sides, perimeters, altitudes, medians and angle bisectors alike. Only the areas behave differently: they are in the square of that ratio. Given

\frac{perimeter of △ A B C}{perimeter of △ M N Q} = \frac{7}{8}

, the scale factor is

\frac{7}{8}

. Let AD be the median from A and MP the median from M; these are corresponding medians. So

\frac{A D}{M P} = \frac{7}{8}

. Hence the required ratio is 7:8, option (a). The ratio 49:64 would be that of the areas.44:T80e,समरूप त्रिभुज: माध्यिकाएँ

दो समरूप त्रिभुजों में संगत लंबाइयों का प्रत्येक युग्म समान अनुपात में होता है — भुजाएँ, परिमाप, शीर्षलंब, माध्यिकाएँ तथा कोण-समद्विभाजक सभी। केवल क्षेत्रफल भिन्न व्यवहार करते हैं: वे उस अनुपात के वर्ग में होते हैं। दिया गया है

\frac{perimeter of △ A B C}{perimeter of △ M N Q} = \frac{7}{8}

, अतः समरूपता अनुपात

\frac{7}{8}

है। माना कि AD शीर्ष A से खींची गई माध्यिका है तथा MP शीर्ष M से; ये संगत माध्यिकाएँ हैं। अतः

\frac{A D}{M P} = \frac{7}{8}

। इस प्रकार अभीष्ट अनुपात 7:8 है, इसलिए सही विकल्प (a) है। 49:64 तो क्षेत्रफलों का अनुपात होता।45:T5a4,Basic proportionality theorem

Since

D E ∥ B C

, the basic proportionality (Thales) theorem applies to

△ A B C

. Formula:

\frac{A D}{D B} = \frac{A E}{E C}

\frac{8}{9} = \frac{16}{E C}

8 \times E C = 9 \times 16 = 144

E C = \frac{144}{8} = 18

cm, so option (b) is correct.46:T66f,आधारभूत समानुपातिकता प्रमेय

चूँकि

D E ∥ B C

है, अतः

△ A B C

में आधारभूत समानुपातिकता (थेल्स) प्रमेय लागू होती है। सूत्र:

\frac{A D}{D B} = \frac{A E}{E C}

\frac{8}{9} = \frac{16}{E C}

8 \times E C = 9 \times 16 = 144

E C = \frac{144}{8} = 18

cm, इसलिए सही विकल्प (b) है।1c:["$","$L26",null,{"mode":"practice","dropped":0,"bilingual":true,"choiceSubjects":[],"questions":[{"id":11451,"n":51,"subject":"Quantitative Aptitude","stem":"If

a

is irrational and

b

is irrational, then

a + b

is:","stemHi":"यदि

a

अपरिमेय है और

b

अपरिमेय है, तो

a + b

है:","context":null,"contextHi":null,"options":[{"key":"a","text":"Always irrational","textHi":"सदैव अपरिमेय","imageUrl":null},{"key":"b","text":"Always rational","textHi":"सदैव परिमेय","imageUrl":null},{"key":"c","text":"Rational if

a = - b

","textHi":"परिमेय, यदि

a = - b

","imageUrl":null},{"key":"d","text":"Never rational","textHi":"कभी भी परिमेय नहीं","imageUrl":null}],"correct":"c","sol":"$27","solHi":"$28","pos":2,"neg":0.5},{"id":11452,"n":52,"subject":"Quantitative Aptitude","stem":"In

△ PQR, PQ = 8 cm, QR = 15 cm

and

P R = 17 cm

. Find the value of

\tan R +

\sin R + 2 \cot P

","stemHi":"

△ PQR, PQ = 8 cm, QR = 15 cm

तथा

P R = 17 cm

में।

\tan R +

\sin R + 2 \cot P

का मान ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"2.070","textHi":null,"imageUrl":null},{"key":"b","text":"1.070","textHi":null,"imageUrl":null},{"key":"c","text":"2.170","textHi":null,"imageUrl":null},{"key":"d","text":"2.275","textHi":null,"imageUrl":null}],"correct":"a","sol":"$29","solHi":"$2a","pos":2,"neg":0.5},{"id":11453,"n":53,"subject":"Quantitative Aptitude","stem":"Sonu and Monu together can do a piece of work in 40 days. If Sonu is 30% less efficient than Monu, in how many days can Sonu, working alone, complete 70% of the work ?","stemHi":"सोनू और मोनू मिलकर किसी कार्य को 40 दिनों में पूरा कर सकते हैं। यदि सोनू, मोनू की तुलना में 30% कम कुशल है, तो अकेले कार्य करते हुए सोनू उस कार्य का 70% कितने दिनों में पूरा करेगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"62 days","textHi":"62 दिन","imageUrl":null},{"key":"b","text":"65 days","textHi":"65 दिन","imageUrl":null},{"key":"c","text":"60 days","textHi":"60 दिन","imageUrl":null},{"key":"d","text":"68 days","textHi":"68 दिन","imageUrl":null}],"correct":"d","sol":"$2b","solHi":"$2c","pos":2,"neg":0.5},{"id":11454,"n":54,"subject":"Quantitative Aptitude","stem":"The angle subtended by a chord at the center is 90°. Its length is 12 cm. What is the radius?","stemHi":"किसी जीवा द्वारा केंद्र पर अंतरित कोण 90° है। उसकी लंबाई 12 cm है। त्रिज्या क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"

5 \sqrt{2} cm

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

6 \sqrt{2} cm

","textHi":null,"imageUrl":null},{"key":"c","text":"6 cm","textHi":null,"imageUrl":null},{"key":"d","text":"12 cm","textHi":null,"imageUrl":null}],"correct":"b","sol":"$2d","solHi":"$2e","pos":2,"neg":0.5},{"id":11455,"n":55,"subject":"Quantitative Aptitude","stem":"The length of a chord that is at a distance of 8 cm from the center of a circle of radius 17 cm is:","stemHi":"17 cm त्रिज्या वाले वृत्त के केंद्र से 8 cm की दूरी पर स्थित जीवा की लंबाई है:","context":null,"contextHi":null,"options":[{"key":"a","text":"37 cm","textHi":null,"imageUrl":null},{"key":"b","text":"34 cm","textHi":null,"imageUrl":null},{"key":"c","text":"30 cm","textHi":null,"imageUrl":null},{"key":"d","text":"32 cm","textHi":null,"imageUrl":null}],"correct":"c","sol":"$2f","solHi":"$30","pos":2,"neg":0.5},{"id":11456,"n":56,"subject":"Quantitative Aptitude","stem":"The angle subtended by a chord at the center is 100°. The angle between the chord and the tangent at one endpoint is:","stemHi":"किसी जीवा द्वारा केंद्र पर अंतरित कोण 100° है। जीवा तथा उसके एक सिरे पर खींची गई स्पर्श रेखा के बीच का कोण है:","context":null,"contextHi":null,"options":[{"key":"a","text":"30°","textHi":null,"imageUrl":null},{"key":"b","text":"50°","textHi":null,"imageUrl":null},{"key":"c","text":"60°","textHi":null,"imageUrl":null},{"key":"d","text":"65*","textHi":null,"imageUrl":null}],"correct":"b","sol":"$31","solHi":"$32","pos":2,"neg":0.5},{"id":11457,"n":57,"subject":"Quantitative Aptitude","stem":"The ratio of curved surface area and total surface area of a cylinder is 3 : 4. If the volume of the cylinder is 3234

{cm}^{3}

, find the curved surface area of the cylinder.","stemHi":"एक बेलन के वक्र पृष्ठीय क्षेत्रफल तथा संपूर्ण पृष्ठीय क्षेत्रफल का अनुपात 3 : 4 है। यदि बेलन का आयतन 3234

{cm}^{3}

है, तो बेलन का वक्र पृष्ठीय क्षेत्रफल ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"

924 {cm}^{2}

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

851 {cm}^{2}

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

1051 {cm}^{2}

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

1151 {cm}^{2}

","textHi":null,"imageUrl":null}],"correct":"a","sol":"$33","solHi":"$34","pos":2,"neg":0.5},{"id":11458,"n":58,"subject":"Quantitative Aptitude","stem":"A circle is inscribed in

△ P Q R

touching the sides

QR, PR

and PQ at the points

S, U

and T , respectively.

PQ = (QR

+ 7) cm, PQ = (PR + 4) cm

. If the perimeter of

△ PQR

is 34 cm , then PR is equal to:","stemHi":"

△ P Q R

में एक वृत्त इस प्रकार अंतर्निहित है कि वह भुजाओं

QR, PR

तथा PQ को क्रमशः बिंदुओं

S, U

तथा T पर स्पर्श करता है।

PQ = (QR

+ 7) cm, PQ = (PR + 4) cm

। यदि

△ PQR

का परिमाप 34 cm है, तो PR बराबर है:","context":null,"contextHi":null,"options":[{"key":"a","text":"18 cm","textHi":null,"imageUrl":null},{"key":"b","text":"14 cm","textHi":null,"imageUrl":null},{"key":"c","text":"11 cm","textHi":null,"imageUrl":null},{"key":"d","text":"12 cm","textHi":null,"imageUrl":null}],"correct":"c","sol":"$35","solHi":"$36","pos":2,"neg":0.5},{"id":11459,"n":59,"subject":"Quantitative Aptitude","stem":"At 8% p.a. simple interest, the simple interest earned by A on his investment for 5 years equals the simple interest earned by B on his investment for 7 years. If B invested ₹ 12,000 less than

A

, what was A's investment (principal)?","stemHi":"8% प्रति वर्ष साधारण ब्याज की दर पर, A द्वारा अपने निवेश पर 5 वर्षों में अर्जित साधारण ब्याज, B द्वारा अपने निवेश पर 7 वर्षों में अर्जित साधारण ब्याज के बराबर है। यदि B ने

A

से ₹ 12,000 कम निवेश किया, तो A का निवेश (मूलधन) कितना था?","context":null,"contextHi":null,"options":[{"key":"a","text":"Rs. 44000","textHi":"रु. 44000","imageUrl":null},{"key":"b","text":"Rs. 40000","textHi":"रु. 40000","imageUrl":null},{"key":"c","text":"Rs. 42000","textHi":"रु. 42000","imageUrl":null},{"key":"d","text":"Rs. 48000","textHi":"रु. 48000","imageUrl":null}],"correct":"c","sol":"$37","solHi":"$38","pos":2,"neg":0.5},{"id":11460,"n":60,"subject":"Quantitative Aptitude","stem":"In a partnership, A, B, and C invested Rs 40,000 , Rs 30,000 , and Rs 80,000 respectively. If the total profit is Rs 30,000 , how much will

B

receive?","stemHi":"एक साझेदारी में, A, B और C ने क्रमशः रु. 40,000 , रु. 30,000 और रु. 80,000 का निवेश किया। यदि कुल लाभ रु. 30,000 है, तो

B

को कितना प्राप्त होगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"Rs 6,200","textHi":"रु. 6,200","imageUrl":null},{"key":"b","text":"Rs 6,000","textHi":"रु. 6,000","imageUrl":null},{"key":"c","text":"Rs 6,500","textHi":"रु. 6,500","imageUrl":null},{"key":"d","text":"Rs 7,000","textHi":"रु. 7,000","imageUrl":null}],"correct":"b","sol":"Partnership profit sharing\nWhen all the partners invest for the same period, the profit is divided in the ratio of their investments.\n40000:30000:80000=4:3:8\n $\"figure\"/$ \nTotal number of parts =4+3+8=15.\nB's share

= \frac{3}{15} \times 30000 = 6000

\nSo B receives ₹6,000, and the correct option is (b).","solHi":"साझेदारी में लाभ-विभाजन\nजब सभी साझेदार समान अवधि के लिए निवेश करते हैं, तो लाभ उनके निवेश के अनुपात में बाँटा जाता है।\n40000:30000:80000=4:3:8\n $\"figure\"/$ \nकुल भागों की संख्या =4+3+8=15।\nB का हिस्सा

= \frac{3}{15} \times 30000 = 6000

\nअतः B को ₹6,000 प्राप्त होते हैं, और सही विकल्प (b) है।","pos":2,"neg":0.5},{"id":11461,"n":61,"subject":"Quantitative Aptitude","stem":"Two numbers are in the ratio of 3 : 7. If 14 is added to each number, the new ratio becomes 13 : 17. What is the sum of the original two numbers?","stemHi":"दो संख्याएँ 3 : 7 के अनुपात में हैं। यदि प्रत्येक संख्या में 14 जोड़ दिया जाए, तो नया अनुपात 13 : 17 हो जाता है। मूल दोनों संख्याओं का योग क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"14","textHi":null,"imageUrl":null},{"key":"b","text":"15","textHi":null,"imageUrl":null},{"key":"c","text":"16","textHi":null,"imageUrl":null},{"key":"d","text":"18","textHi":null,"imageUrl":null}],"correct":"a","sol":"$39","solHi":"$3a","pos":2,"neg":0.5},{"id":11462,"n":62,"subject":"Quantitative Aptitude","stem":"What is the least value that should be added to 5757 to make it divisible by 7,11 , and 15 ?","stemHi":"5757 में कम से कम कौन-सा मान जोड़ा जाना चाहिए ताकि वह 7, 11 और 15 से विभाज्य हो जाए?","context":null,"contextHi":null,"options":[{"key":"a","text":"13","textHi":null,"imageUrl":null},{"key":"b","text":"18","textHi":null,"imageUrl":null},{"key":"c","text":"71","textHi":null,"imageUrl":null},{"key":"d","text":"153","textHi":null,"imageUrl":null}],"correct":"b","sol":"LCM and divisibility\nA number divisible by 7, 11 and 15 together must be a multiple of their LCM.\n7, 11 and 15 have no common factor, so

L C M = 7 \times 11 \times 15 = 1155

.\nDivide 5757 by 1155:

1155 \times 4 = 4620

and

1155 \times 5 = 5775

.\nSo 5757 lies between these two, and the next multiple of 1155 is 5775.\nLeast number to be added =5775-5757=18, so option (b) is correct.","solHi":"ल.स. और विभाज्यता\nजो संख्या 7, 11 तथा 15 तीनों से विभाज्य हो, वह उनके ल.स. का गुणज होनी चाहिए।\n7, 11 तथा 15 में कोई उभयनिष्ठ गुणनखंड नहीं है, अतः

L C M = 7 \times 11 \times 15 = 1155

।\n5757 को 1155 से भाग दीजिए:

1155 \times 4 = 4620

तथा

1155 \times 5 = 5775

।\nअतः 5757 इन दोनों के बीच है और 1155 का अगला गुणज 5775 है।\nजोड़ी जाने वाली न्यूनतम संख्या =5775-5757=18, इसलिए सही विकल्प (b) है।","pos":2,"neg":0.5},{"id":11463,"n":63,"subject":"Quantitative Aptitude","stem":"The sum of two numbers is 104 and their HCF is 13. If the ratio of their LCM to their HCF is 7 : 1, what are the two numbers?","stemHi":"दो संख्याओं का योग 104 है तथा उनका म.स. 13 है। यदि उनके ल.स. और म.स. का अनुपात 7 : 1 है, तो वे दोनों संख्याएँ क्या हैं?","context":null,"contextHi":null,"options":[{"key":"a","text":"38 and 66","textHi":"38 और 66","imageUrl":null},{"key":"b","text":"13 and 91","textHi":"13 और 91","imageUrl":null},{"key":"c","text":"26 and 78","textHi":"26 और 78","imageUrl":null},{"key":"d","text":"39 and 65","textHi":"39 और 65","imageUrl":null}],"correct":"b","sol":"$3b","solHi":"$3c","pos":2,"neg":0.5},{"id":11464,"n":64,"subject":"Quantitative Aptitude","stem":"The average of 20 numbers is 55 . If each number is decreased by 8, what will be the new average?","stemHi":"20 संख्याओं का औसत 55 है। यदि प्रत्येक संख्या में से 8 घटा दिया जाए, तो नया औसत क्या होगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"48","textHi":null,"imageUrl":null},{"key":"b","text":"47","textHi":null,"imageUrl":null},{"key":"c","text":"46","textHi":null,"imageUrl":null},{"key":"d","text":"44","textHi":null,"imageUrl":null}],"correct":"b","sol":"Average: uniform change\nRule: if the same quantity is subtracted from every observation, the average falls by exactly that quantity.\nSum of the 20 numbers

= 20 \times 55 = 1100

.\nAfter subtracting 8 from each, the sum falls by

20 \times 8 = 160

, giving 1100-160=940.\nNew average

= \frac{940}{20} = 47

, which is simply 55-8.\nHence the new average is 47, option (b).","solHi":"औसत: समान परिवर्तन\nनियम: यदि प्रत्येक प्रेक्षण में से समान मात्रा घटाई जाए, तो औसत भी ठीक उतना ही घट जाता है।\n20 संख्याओं का योग

= 20 \times 55 = 1100

।\nप्रत्येक में से 8 घटाने पर योग

20 \times 8 = 160

कम हो जाता है, अर्थात् 1100-160=940।\nनया औसत

= \frac{940}{20} = 47

, जो वस्तुतः 55-8 ही है।\nअतः नया औसत 47 है, इसलिए सही विकल्प (b) है।","pos":2,"neg":0.5},{"id":11465,"n":65,"subject":"Quantitative Aptitude","stem":"The average salary of employees in a company is ₹30,000. If a new employee with a salary of ₹60,000 joins, the average increases by ₹300. Find the number of employees originally in the company.","stemHi":"एक कंपनी में कर्मचारियों का औसत वेतन ₹30,000 है। यदि ₹60,000 वेतन वाला एक नया कर्मचारी शामिल होता है, तो औसत ₹300 बढ़ जाता है। कंपनी में मूल रूप से कर्मचारियों की संख्या ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"99","textHi":null,"imageUrl":null},{"key":"b","text":"95","textHi":null,"imageUrl":null},{"key":"c","text":"90","textHi":null,"imageUrl":null},{"key":"d","text":"89","textHi":null,"imageUrl":null}],"correct":"a","sol":"Average: new member\nLet the original number of employees be n.\nTotal salary of these employees =30000n.\nAfter the new employee joins, there are n+1 employees and the average is 30000+300=30300.\n

\frac{30000 n + 60000}{n + 1} = 30300

\n30000n+60000=30300n+30300\n

60000 - 30300 = 30300 n - 30000 n \Rightarrow 29700 = 300 n

n = \frac{29700}{300} = 99

\nSo the company originally had 99 employees, option (a).","solHi":"औसत: नया सदस्य\nमाना कि कर्मचारियों की मूल संख्या n है।\nइन कर्मचारियों का कुल वेतन =30000n।\nनया कर्मचारी जुड़ने पर कर्मचारी n+1 हो जाते हैं तथा औसत 30000+300=30300 हो जाता है।\n

\frac{30000 n + 60000}{n + 1} = 30300

\n30000n+60000=30300n+30300\n

60000 - 30300 = 30300 n - 30000 n \Rightarrow 29700 = 300 n

n = \frac{29700}{300} = 99

\nअतः कंपनी में मूल रूप से 99 कर्मचारी थे, इसलिए सही विकल्प (a) है।","pos":2,"neg":0.5},{"id":11466,"n":66,"subject":"Quantitative Aptitude","stem":"If P is 60% more than Q, and R is 80 % less than the sum of

P

and

Q

, then

R

is what percent of

P

?","stemHi":"यदि P, Q से 60% अधिक है तथा R,

P

और

Q

के योग से 80 % कम है, तो

R

P

का कितने प्रतिशत है?","context":null,"contextHi":null,"options":[{"key":"a","text":"32.5 %","textHi":null,"imageUrl":null},{"key":"b","text":"42.5 %","textHi":null,"imageUrl":null},{"key":"c","text":"35.5 %","textHi":null,"imageUrl":null},{"key":"d","text":"22.5 %","textHi":null,"imageUrl":null}],"correct":"a","sol":"Percentage comparison\nTake a convenient value Q=100.\nP is 60% more than Q, so P=100+60=160.\nP+Q=160+100=260\nR is 80% less than P+Q, so R is 20% of 260.\n

R = \frac{20}{100} \times 260 = 52

\n $\"figure\"/$ \nRequired percentage

= \frac{R}{P} \times 100 = \frac{52}{160} \times 100 = 32.5 %

\nHence option (a) is correct.","solHi":"प्रतिशत तुलना\nसुविधा के लिए Q=100 लीजिए।\nP, Q से 60% अधिक है, अतः P=100+60=160।\nP+Q=160+100=260\nR, P+Q से 80% कम है, अतः R, 260 का 20% है।\n

R = \frac{20}{100} \times 260 = 52

\n $\"figure\"/$ \nअभीष्ट प्रतिशत

= \frac{R}{P} \times 100 = \frac{52}{160} \times 100 = 32.5 %

\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.5},{"id":11467,"n":67,"subject":"Quantitative Aptitude","stem":"A train covers 200 km at a speed of

40 km / h

. Due to track repair, it reduces speed by 50% for the next 100 km. What is the total time taken for the full journey?","stemHi":"एक रेलगाड़ी

40 km / h

की चाल से 200 km की दूरी तय करती है। पटरी की मरम्मत के कारण वह अगले 100 km के लिए अपनी चाल 50% कम कर देती है। पूरी यात्रा में लिया गया कुल समय कितना है?","context":null,"contextHi":null,"options":[{"key":"a","text":"12 hours","textHi":"12 घंटे","imageUrl":null},{"key":"b","text":"14 hours","textHi":"14 घंटे","imageUrl":null},{"key":"c","text":"15 hours","textHi":"15 घंटे","imageUrl":null},{"key":"d","text":"10 hours","textHi":"10 घंटे","imageUrl":null}],"correct":"d","sol":"Time, speed and distance\nFormula:

time = \frac{distance}{speed}

\nFirst stretch:

\frac{200}{40} = 5

hours.\nReduced speed

= 40 - 50 %

of 40=40-20=20 km/h.\nSecond stretch:

\frac{100}{20} = 5

hours.\n $\"figure\"/$ \nTotal time =5+5=10 hours, so option (d) is correct.","solHi":"समय, चाल और दूरी\nसूत्र:

time = \frac{distance}{speed}

\nपहला भाग:

\frac{200}{40} = 5

घंटे।\nघटी हुई चाल =40-40 का

50 % = 40 - 20 = 20

km/h।\nदूसरा भाग:

\frac{100}{20} = 5

घंटे।\n $\"figure\"/$ \nकुल समय =5+5=10 घंटे, इसलिए सही विकल्प (d) है।","pos":2,"neg":0.5},{"id":11468,"n":68,"subject":"Quantitative Aptitude","stem":"16 men can complete a work in 28 days. After 8 days, 8 men leave. In how many more days will the remaining men finish the work?","stemHi":"16 पुरुष किसी कार्य को 28 दिनों में पूरा कर सकते हैं। 8 दिनों के बाद 8 पुरुष कार्य छोड़ देते हैं। शेष पुरुष उस कार्य को और कितने दिनों में पूरा करेंगे?","context":null,"contextHi":null,"options":[{"key":"a","text":"42 days","textHi":"42 दिन","imageUrl":null},{"key":"b","text":"43 days","textHi":"43 दिन","imageUrl":null},{"key":"c","text":"44 days","textHi":"44 दिन","imageUrl":null},{"key":"d","text":"40 days","textHi":"40 दिन","imageUrl":null}],"correct":"d","sol":"Time and work\nTotal work

= men \times days = 16 \times 28 = 448

man-days.\nWork done in the first 8 days

= 16 \times 8 = 128

man-days.\nRemaining work =448-128=320 man-days.\nMen still on the job =16-8=8.\n $\"figure\"/$ \nFurther days needed

= \frac{320}{8} = 40

days, so option (d) is correct.","solHi":"समय और कार्य\nकुल कार्य

= men \times days = 16 \times 28 = 448

पुरुष-दिन।\nपहले 8 दिनों में किया गया कार्य

= 16 \times 8 = 128

पुरुष-दिन।\nशेष कार्य =448-128=320 पुरुष-दिन।\nकार्य पर बचे पुरुष =16-8=8।\n $\"figure\"/$ \nआगे आवश्यक दिन

= \frac{320}{8} = 40

दिन, इसलिए सही विकल्प (d) है।","pos":2,"neg":0.5},{"id":11469,"n":69,"subject":"Quantitative Aptitude","stem":"If A purchases items worth ₹3,050 at a discount rate of

36 %

, what will be his total savings?","stemHi":"यदि A,

36 %

की छूट दर पर ₹3,050 मूल्य की वस्तुएँ खरीदता है, तो उसकी कुल बचत कितनी होगी?","context":null,"contextHi":null,"options":[{"key":"a","text":"₹ 930","textHi":null,"imageUrl":null},{"key":"b","text":"₹ 800","textHi":null,"imageUrl":null},{"key":"c","text":"₹ 1450","textHi":null,"imageUrl":null},{"key":"d","text":"₹ 1098","textHi":null,"imageUrl":null}],"correct":"d","sol":"Discount and saving\nThe amount saved on a purchase is exactly the discount allowed on the listed value.\nFormula:

saving = listed value \times \frac{rate of discount}{100}

= 3050 \times \frac{36}{100}

= 30.5 \times 36 = 1098

\nSo his total saving is ₹1,098, option (d).","solHi":"छूट और बचत\nकिसी खरीद पर बचत ठीक उतनी ही होती है जितनी अंकित मूल्य पर दी गई छूट।\nसूत्र:

saving = listed value \times \frac{rate of discount}{100}

= 3050 \times \frac{36}{100}

= 30.5 \times 36 = 1098

\nअतः उसकी कुल बचत ₹1,098 है, इसलिए सही विकल्प (d) है।","pos":2,"neg":0.5},{"id":11470,"n":70,"subject":"Quantitative Aptitude","stem":"After deducting 35% from the marked price, the item's selling price is ₹7,000. If the discount is raised to 40%, what will the selling price be ?","stemHi":"अंकित मूल्य पर 35% की छूट देने के बाद किसी वस्तु का विक्रय मूल्य ₹7,000 है। यदि छूट बढ़ाकर 40% कर दी जाए, तो विक्रय मूल्य कितना होगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"₹ 5461.54","textHi":null,"imageUrl":null},{"key":"b","text":"₹ 6461.54","textHi":null,"imageUrl":null},{"key":"c","text":"₹ 7461.54","textHi":null,"imageUrl":null},{"key":"d","text":"₹ 6861.54","textHi":null,"imageUrl":null}],"correct":"b","sol":"$3d","solHi":"$3e","pos":2,"neg":0.5},{"id":11471,"n":71,"subject":"Quantitative Aptitude","stem":"Two containers, A and B, hold 40 litres and 60 litres of liquid mixture, respectively. Container A has milk and water in the ratio

3 : 5

, while container

B

has them in the ratio

5 : 1

. If the entire contents of both containers are poured into a larger vessel and thoroughly mixed, what will be the resulting ratio of milk to water in the combined mixture?","stemHi":"दो पात्र A और B में क्रमशः 40 लीटर तथा 60 लीटर तरल मिश्रण है। पात्र A में दूध और पानी

3 : 5

के अनुपात में हैं, जबकि पात्र

B

में वे

5 : 1

के अनुपात में हैं। यदि दोनों पात्रों की संपूर्ण सामग्री को एक बड़े बर्तन में डालकर अच्छी तरह मिला दिया जाए, तो प्राप्त मिश्रण में दूध और पानी का अनुपात क्या होगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"

12 : 13

","textHi":null,"imageUrl":null},{"key":"b","text":"8 : 3","textHi":null,"imageUrl":null},{"key":"c","text":"

13 : 7

","textHi":null,"imageUrl":null},{"key":"d","text":"2 : 7","textHi":null,"imageUrl":null}],"correct":"c","sol":"$3f","solHi":"$40","pos":2,"neg":0.5},{"id":11472,"n":72,"subject":"Quantitative Aptitude","stem":"Which is the largest among these:

\sqrt[3]{3}, \sqrt{5}, \sqrt[6]{7}

?","stemHi":"इनमें से सबसे बड़ा कौन-सा है:

\sqrt[3]{3}, \sqrt{5}, \sqrt[6]{7}

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

\sqrt[4]{3}

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

\sqrt{5}

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

\sqrt[4]{7}

","textHi":null,"imageUrl":null},{"key":"d","text":"All are equal","textHi":"सभी बराबर हैं","imageUrl":null}],"correct":"b","sol":"$41","solHi":"$42","pos":2,"neg":0.5},{"id":11473,"n":73,"subject":"Quantitative Aptitude","stem":"What is the equation of the line with slope -4 passing through the point

(4, - 2)

?","stemHi":"ढाल -4 वाली तथा बिंदु

(4, - 2)

से होकर जाने वाली रेखा का समीकरण क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"

y = - 4 x + 10

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

y = - 4 x + 14

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

y = - 3 x + 12

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

y = - 4 x + 15

","textHi":null,"imageUrl":null}],"correct":"b","sol":"Equation of a straight line\nFormula: point-slope form

y - y_{1} = m (x - x_{1})

\nHere m=-4 and

(x_{1}, y_{1}) = (4, - 2)

.\ny-(-2)=-4(x-4)\ny+2=-4x+16\ny=-4x+14\n $\"figure\"/$ \nOnly this line gives y=-2 when x=4, so option (b) is correct.","solHi":"सरल रेखा का समीकरण\nसूत्र: बिंदु-ढाल रूप

y - y_{1} = m (x - x_{1})

\nयहाँ m=-4 तथा

(x_{1}, y_{1}) = (4, - 2)

है।\ny-(-2)=-4(x-4)\ny+2=-4x+16\ny=-4x+14\n $\"figure\"/$ \nकेवल यही रेखा x=4 पर y=-2 देती है, इसलिए सही विकल्प (b) है।","pos":2,"neg":0.5},{"id":11474,"n":74,"subject":"Quantitative Aptitude","stem":"Triangle

A B C

is similar to Triangle MNQ The ratio of their perimeters is

7 : 8

. What is the ratio of the length of the median from vertex

A

to the length of the median from vertex M ?","stemHi":"त्रिभुज

A B C

, त्रिभुज MNQ के समरूप है। उनके परिमापों का अनुपात

7 : 8

है। शीर्ष

A

से खींची गई माध्यिका की लंबाई तथा शीर्ष M से खींची गई माध्यिका की लंबाई का अनुपात क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"7:8","textHi":null,"imageUrl":null},{"key":"b","text":"49 : 64","textHi":null,"imageUrl":null},{"key":"c","text":"17 : 64","textHi":null,"imageUrl":null},{"key":"d","text":"18 : 17","textHi":null,"imageUrl":null}],"correct":"a","sol":"$43","solHi":"$44","pos":2,"neg":0.5},{"id":11475,"n":75,"subject":"Quantitative Aptitude","stem":"In triangle

A B C

, line

D E ‖ B C

intersects sides AB at D and AC at E . If

AD = 8 cm, DB = 9 cm

, and

AE = 16 cm

, find the value of EC .","stemHi":"त्रिभुज

A B C

में रेखा

D E ‖ B C

भुजा AB को D पर तथा भुजा AC को E पर काटती है। यदि

AD = 8 cm, DB = 9 cm

तथा

AE = 16 cm

है, तो EC का मान ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"19 cm","textHi":null,"imageUrl":null},{"key":"b","text":"18 cm","textHi":null,"imageUrl":null},{"key":"c","text":"15 cm","textHi":null,"imageUrl":null},{"key":"d","text":"16 cm","textHi":null,"imageUrl":null}],"correct":"b","sol":"$45","solHi":"$46","pos":2,"neg":0.5}],"test":{"slug":"ssc-chsl-tier-1--18-nov-2025-shift-3-quant","title":"SSC CHSL Tier-1 18 November 2025 Shift-3 — Quantitative Aptitude Sectional Test","examName":"CHSL Tier-1","paperLabel":"18 November 2025 · Shift 3","sectionSubject":"Quantitative Aptitude","durationMinutes":15,"format":"sectional_test"}}]