26:I[81166,["/_next/static/immutable/chunks/2corl6wyj4669.js","/_next/static/immutable/chunks/38n271cv4vmyv.js","/_next/static/immutable/chunks/2pf73jja2520w.js"],"default"] 27:T89c,Incentre angle property For the incentre O of a triangle ABC the standard result is

∠ A O C = 90^{\circ} + \frac{∠ B}{2}

Substituting the given value:

160^{\circ} = 90^{\circ} + \frac{∠ B}{2}

\frac{∠ B}{2} = 160^{\circ} - 90^{\circ} = 70^{\circ}

∠ B = 140^{\circ}

. Check:

∠ A + ∠ C = 180^{\circ} - 140^{\circ} = 40^{\circ}

, so

∠ A O C = 180^{\circ} - \frac{40^{\circ}}{2} = 160^{\circ}

.28:T932,अंतःकेंद्र कोण गुणधर्म त्रिभुज ABC के अंतःकेंद्र O के लिए मानक परिणाम है:

∠ A O C = 90^{\circ} + \frac{∠ B}{2}

।

दिया गया मान रखने पर:

160^{\circ} = 90^{\circ} + \frac{∠ B}{2}

।

\frac{∠ B}{2} = 160^{\circ} - 90^{\circ} = 70^{\circ}

।

∠ B = 140^{\circ}

। जाँच:

∠ A + ∠ C = 180^{\circ} - 140^{\circ} = 40^{\circ}

, अतः

∠ A O C = 180^{\circ} - \frac{40^{\circ}}{2} = 160^{\circ}

।29:T7c9,Mensuration: cylinder CSA Let the length and the breadth be 22x and 7x. Perimeter:

2 (22 x + 7 x) = 174 \Rightarrow 58 x = 174 \Rightarrow x = 3

. So length =66 cm, breadth =21 cm and area

= 66 \times 21 = 1386 {cm}^{2}

The top of a solid cylinder is a circle, so

π r^{2} = 1386

r^{2} = 1386 \times \frac{7}{22} = 441 \Rightarrow r = 21

cm. The radius is 84% of the height:

21 = \frac{84}{100} h \Rightarrow h = 25

cm. Curved surface area

= 2 π r h = 2 \times \frac{22}{7} \times 21 \times 25 = 3300 {cm}^{2}

.2a:T932,क्षेत्रमिति: बेलन का वक्र पृष्ठीय क्षेत्रफल माना कि लंबाई और चौड़ाई क्रमशः 22x तथा 7x हैं। परिमाप:

2 (22 x + 7 x) = 174 \Rightarrow 58 x = 174 \Rightarrow x = 3

। अतः लंबाई =66 cm, चौड़ाई =21 cm तथा क्षेत्रफल

= 66 \times 21 = 1386 {cm}^{2}

।

ठोस बेलन का ऊपरी पृष्ठ एक वृत्त है, अतः

π r^{2} = 1386

।

r^{2} = 1386 \times \frac{7}{22} = 441 \Rightarrow r = 21

cm। त्रिज्या, ऊँचाई का 84% है:

21 = \frac{84}{100} h \Rightarrow h = 25

cm। वक्र पृष्ठीय क्षेत्रफल

= 2 π r h = 2 \times \frac{22}{7} \times 21 \times 25 = 3300 {cm}^{2}

।2b:T98d,Rhombus diagonals and area Let the diagonals be 5k and 12k. In a rhombus the diagonals bisect each other at right angles.

So the half-diagonals

\frac{5 k}{2}

and 6k form a right triangle with the side:

{(\frac{5 k}{2})}^{2} + {(6 k)}^{2} = 13^{2}

\frac{25 k^{2}}{4} + 36 k^{2} = 169 \Rightarrow \frac{169 k^{2}}{4} = 169

k^{2} = 4 \Rightarrow k = 2

. Diagonals

= 5 \times 2 = 10

cm and

12 \times 2 = 24

cm. Area

= \frac{1}{2} \times d_{1} \times d_{2} = \frac{1}{2} \times 10 \times 24 = 120 {cm}^{2}

.2c:Taef,समचतुर्भुज के विकर्ण एवं क्षेत्रफल माना कि विकर्ण 5k तथा 12k हैं। समचतुर्भुज में विकर्ण एक-दूसरे को समकोण पर समद्विभाजित करते हैं।

अतः अर्ध-विकर्ण

\frac{5 k}{2}

तथा 6k भुजा के साथ एक समकोण त्रिभुज बनाते हैं:

{(\frac{5 k}{2})}^{2} + {(6 k)}^{2} = 13^{2}

।

\frac{25 k^{2}}{4} + 36 k^{2} = 169 \Rightarrow \frac{169 k^{2}}{4} = 169

।

k^{2} = 4 \Rightarrow k = 2

। विकर्ण

= 5 \times 2 = 10

cm तथा

12 \times 2 = 24

cm। क्षेत्रफल

= \frac{1}{2} \times d_{1} \times d_{2} = \frac{1}{2} \times 10 \times 24 = 120 {cm}^{2}

।2d:T409,Speed conversion Distance covered : distance still left =5:9, so the journey is 5+9=14 equal parts. 14 parts =140 km, hence 1 part =10 km and the distance covered

= 5 \times 10 = 50

km. Time taken =3 hours 20 minutes

= \frac{10}{3}

hours. Speed

= \frac{50}{10 / 3} = 15

km/hr. Converting to metres per second:

15 \times \frac{5}{18} = \frac{25}{6} \approx 4.16

m/s.2e:T4c9,Successive discounts After a discount of 25% the price becomes

\frac{75}{100}

of the marked price, and the second discount of 20% leaves

\frac{80}{100}

of that. So

MP \times \frac{75}{100} \times \frac{80}{100} = 1200

MP \times \frac{3}{5} = 1200

MP = 1200 \times \frac{5}{3} = 2000

, i.e. ₹2,000. Note that the two discounts are not simply 45%: the single equivalent discount here is 40%.2f:T5c3,क्रमिक छूट 25% छूट के बाद मूल्य अंकित मूल्य का

\frac{75}{100}

रह जाता है, तथा 20% की दूसरी छूट के बाद उसका

\frac{80}{100}

शेष रहता है। अतः

MP \times \frac{75}{100} \times \frac{80}{100} = 1200

।

MP \times \frac{3}{5} = 1200

।

MP = 1200 \times \frac{5}{3} = 2000

, अर्थात् ₹2,000। ध्यान दीजिए कि दोनों छूटें मिलकर 45% नहीं होतीं: यहाँ समतुल्य एकल छूट 40% है।30:T4a8,Discount and marked price A discount of

22 %

is allowed on the marked price, so the selling price is only

(100 - 22) % = 78 %

of the marked price. Formula:

S P = M P \times \frac{100 - d}{100}

1560 = M P \times \frac{78}{100}

M P = \frac{1560 \times 100}{78} = 2000

Hence the marked price of the product is ₹2,000, so option (b) is correct.31:T57a,छूट एवं अंकित मूल्य अंकित मूल्य पर

22 %

की छूट दी गई है, अतः विक्रय मूल्य अंकित मूल्य का केवल

(100 - 22) % = 78 %

रह जाता है। सूत्र:

S P = M P \times \frac{100 - d}{100}

1560 = M P \times \frac{78}{100}

M P = \frac{1560 \times 100}{78} = 2000

अतः उत्पाद का अंकित मूल्य ₹2,000 है, इसलिए सही विकल्प (b) है।32:T5bc,Perimeter and area of a rectangle Let the width be x cm; the length then is (x+3) cm.

Perimeter:

2 (l + b) = 66 \Rightarrow 2 ((x + 3) + x) = 66

2 (2 x + 3) = 66 \Rightarrow 2 x + 3 = 33 \Rightarrow x = 15

So width = 15 cm and length = 15+3 = 18 cm. Area

= l \times b = 18 \times 15 = 270 {cm}^{2}

Hence the area of the rectangle is

270 {cm}^{2}

, option (d).33:T6a3,आयत का परिमाप एवं क्षेत्रफल माना कि चौड़ाई x cm है; तब लंबाई (x+3) cm होगी।

परिमाप:

2 (l + b) = 66 \Rightarrow 2 ((x + 3) + x) = 66

2 (2 x + 3) = 66 \Rightarrow 2 x + 3 = 33 \Rightarrow x = 15

अतः चौड़ाई = 15 cm तथा लंबाई = 15+3 = 18 cm। क्षेत्रफल

= l \times b = 18 \times 15 = 270 {cm}^{2}

अतः आयत का क्षेत्रफल

270 {cm}^{2}

है, इसलिए सही विकल्प (d) है।34:T462,Mixture and ratio Milk : water = 3:5, so the mixture has 3+5 = 8 equal parts in 80 litres. One part

= \frac{80}{8} = 10

litres, so milk = 30 litres and water = 50 litres.

Only water is poured in, so the milk stays 30 litres. Let x litres of water be added.

\frac{30}{50 + x} = \frac{4}{7}

210 = 200 + 4 x \Rightarrow 4 x = 10 \Rightarrow x = 2.5

Hence 2.5 litres of water must be added, option (d).35:T5e0,मिश्रण एवं अनुपात दूध : पानी = 3:5 है, अतः 80 लीटर मिश्रण में कुल 3+5 = 8 बराबर भाग हैं। एक भाग

= \frac{80}{8} = 10

लीटर, अतः दूध = 30 लीटर तथा पानी = 50 लीटर।

केवल पानी मिलाया जा रहा है, अतः दूध 30 लीटर ही रहेगा। माना कि x लीटर पानी मिलाया गया।

\frac{30}{50 + x} = \frac{4}{7}

210 = 200 + 4 x \Rightarrow 4 x = 10 \Rightarrow x = 2.5

अतः 2.5 लीटर पानी मिलाया जाना चाहिए, इसलिए सही विकल्प (d) है।36:T615,Chord, radius and diameter The perpendicular drawn from the centre to a chord bisects the chord, so half the chord

= \frac{30}{2} = 15

cm.

In right triangle OMA:

O A^{2} = O M^{2} + M A^{2}

O A^{2} = 8^{2} + 15^{2} = 64 + 225 = 289

O A = \sqrt{289} = 17

cm, and this OA is the radius. Diameter

= 2 \times 17 = 34

cm, so option (c) is correct.37:T71c,जीवा, त्रिज्या एवं व्यास केंद्र से जीवा पर डाला गया लंब जीवा को समद्विभाजित करता है, अतः आधी जीवा

= \frac{30}{2} = 15

cm।

समकोण त्रिभुज OMA में:

O A^{2} = O M^{2} + M A^{2}

O A^{2} = 8^{2} + 15^{2} = 64 + 225 = 289

O A = \sqrt{289} = 17

cm, तथा यही OA वृत्त की त्रिज्या है। व्यास

= 2 \times 17 = 34

cm, इसलिए सही विकल्प (c) है।38:Tac0,Parallel chords of a circle Drop

O M ⊥ P Q

and

O N ⊥ R S

; each perpendicular bisects its chord, so PM = 12 cm and RN = 9 cm.

Let the radius be r. Then

O M^{2} = r^{2} - 12^{2}

and

O N^{2} = r^{2} - 9^{2}

O N^{2} - O M^{2} = (r^{2} - 81) - (r^{2} - 144) = 63

The chords lie on opposite sides of O, so ON + OM = 21; hence

O N - O M = \frac{63}{21} = 3

. Solving the pair: ON = 12 cm and OM = 9 cm.

r^{2} = O M^{2} + P M^{2} = 9^{2} + 12^{2} = 81 + 144 = 225

r = \sqrt{225} = 15

cm, so option (a) is correct.39:Tc07,वृत्त की समांतर जीवाएँ

O M ⊥ P Q

तथा

O N ⊥ R S

खींचिए; प्रत्येक लंब अपनी जीवा को समद्विभाजित करता है, अतः PM = 12 cm तथा RN = 9 cm।

माना कि त्रिज्या r है। तब

O M^{2} = r^{2} - 12^{2}

तथा

O N^{2} = r^{2} - 9^{2}

।

O N^{2} - O M^{2} = (r^{2} - 81) - (r^{2} - 144) = 63

जीवाएँ O के विपरीत ओर हैं, अतः ON + OM = 21; इससे

O N - O M = \frac{63}{21} = 3

। दोनों समीकरण हल करने पर: ON = 12 cm तथा OM = 9 cm।

r^{2} = O M^{2} + P M^{2} = 9^{2} + 12^{2} = 81 + 144 = 225

r = \sqrt{225} = 15

cm, इसलिए सही विकल्प (a) है।3a:T618,Chord distance and diameter The perpendicular from the centre bisects the chord, so

P M = \frac{64}{2} = 32

cm and OM = 24 cm.

In right triangle OMP:

O P^{2} = O M^{2} + P M^{2}

O P^{2} = 24^{2} + 32^{2} = 576 + 1024 = 1600

O P = \sqrt{1600} = 40

cm, which is the radius. Diameter

= 2 \times 40 = 80

cm, so option (d) is correct.3b:T709,जीवा की दूरी एवं व्यास केंद्र से डाला गया लंब जीवा को समद्विभाजित करता है, अतः

P M = \frac{64}{2} = 32

cm तथा OM = 24 cm।

समकोण त्रिभुज OMP में:

O P^{2} = O M^{2} + P M^{2}

O P^{2} = 24^{2} + 32^{2} = 576 + 1024 = 1600

O P = \sqrt{1600} = 40

cm, जो वृत्त की त्रिज्या है। व्यास

= 2 \times 40 = 80

cm, इसलिए सही विकल्प (d) है।3c:T70f,Angle between two tangents A tangent is perpendicular to the radius at its point of contact, so

∠ O P T = ∠ O Q T = 90^{\circ}

OPTQ is a quadrilateral, and the angles of a quadrilateral add up to

360^{\circ}

∠ P O Q + 90^{\circ} + 90^{\circ} + 50^{\circ} = 360^{\circ}

∠ P O Q = 360^{\circ} - 230^{\circ} = 130^{\circ}

Note the short cut:

∠ P O Q = 180^{\circ} - ∠ P T Q

. Hence option (b) is correct.3d:T802,दो स्पर्श रेखाओं के बीच का कोण स्पर्श रेखा स्पर्श बिंदु पर त्रिज्या के लंबवत् होती है, अतः

∠ O P T = ∠ O Q T = 90^{\circ}

।

OPTQ एक चतुर्भुज है तथा चतुर्भुज के कोणों का योग

360^{\circ}

होता है।

∠ P O Q + 90^{\circ} + 90^{\circ} + 50^{\circ} = 360^{\circ}

∠ P O Q = 360^{\circ} - 230^{\circ} = 130^{\circ}

लघु विधि:

∠ P O Q = 180^{\circ} - ∠ P T Q

। अतः सही विकल्प (b) है।3e:T572,Tangent length and shortest distance Let P be the point of contact. The tangent is perpendicular to the radius there, so

∠ O P T = 90^{\circ}

In right triangle OPT:

O T^{2} = O P^{2} + P T^{2}

O T^{2} = 8^{2} + 15^{2} = 64 + 225 = 289 \Rightarrow O T = 17

cm The point of the circle nearest to T is S, where the line OT meets the circle. Shortest distance = ST = OT - OS = 17 - 8 = 9 cm, so option (d) is correct.3f:T6a6,स्पर्श रेखा एवं न्यूनतम दूरी माना कि P स्पर्श बिंदु है। स्पर्श रेखा वहाँ त्रिज्या के लंबवत् होती है, अतः

∠ O P T = 90^{\circ}

।

समकोण त्रिभुज OPT में:

O T^{2} = O P^{2} + P T^{2}

O T^{2} = 8^{2} + 15^{2} = 64 + 225 = 289 \Rightarrow O T = 17

cm T के निकटतम वृत्त का बिंदु S है, जहाँ रेखा OT वृत्त को काटती है। न्यूनतम दूरी = ST = OT - OS = 17 - 8 = 9 cm, इसलिए सही विकल्प (d) है।40:T691,Centroid of a triangle The centroid is the average of the three vertices:

G (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})

x-coordinate:

\frac{4 + (- 5) + x}{3} = 0 \Rightarrow - 1 + x = 0 \Rightarrow x = 1

y-coordinate:

\frac{6 + 0 + y}{3} = 0 \Rightarrow 6 + y = 0 \Rightarrow y = - 6

Hence the third vertex is (1,-6), so option (b) is correct.41:T73e,त्रिभुज का केंद्रक केंद्रक तीनों शीर्षों का औसत होता है:

G (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})

।

x-निर्देशांक:

\frac{4 + (- 5) + x}{3} = 0 \Rightarrow - 1 + x = 0 \Rightarrow x = 1

y-निर्देशांक:

\frac{6 + 0 + y}{3} = 0 \Rightarrow 6 + y = 0 \Rightarrow y = - 6

अतः तीसरा शीर्ष (1,-6) है, इसलिए सही विकल्प (b) है।42:T541,Slope of a straight line Bring the equation to the slope-intercept form y = mx + c, in which m is the slope.

x + 6 y = 12 \Rightarrow 6 y = - x + 12

y = - \frac{1}{6} x + 2

Comparing with y = mx + c gives

m = - \frac{1}{6}

, so the slope has the value

\frac{1}{6}

, the sign only telling us that the line falls from left to right. The same result comes straight from ax+by=c, where slope

= - \frac{a}{b} = - \frac{1}{6}

. Hence option (b) is correct.43:T70d,सरल रेखा की प्रवणता समीकरण को प्रवणता-अंतःखंड रूप y = mx + c में लाइए, जिसमें m प्रवणता होती है।

x + 6 y = 12 \Rightarrow 6 y = - x + 12

y = - \frac{1}{6} x + 2

y = mx + c से तुलना करने पर

m = - \frac{1}{6}

प्राप्त होता है, अर्थात् प्रवणता का मान

\frac{1}{6}

है तथा ऋण चिह्न केवल यह दर्शाता है कि रेखा बाएँ से दाएँ नीचे की ओर जाती है। यही परिणाम ax+by=c से सीधे भी मिलता है, जहाँ प्रवणता

= - \frac{a}{b} = - \frac{1}{6}

होती है। अतः सही विकल्प (b) है।44:T686,Angle in a semicircle PQ is a diameter and R lies on the circle, so

∠ P R Q = 90^{\circ}

— the angle in a semicircle is a right angle.

△ P R Q

the three angles add up to

180^{\circ}

∠ R P Q + ∠ P R Q + ∠ R Q P = 180^{\circ}

50^{\circ} + 90^{\circ} + ∠ R Q P = 180^{\circ}

∠ R Q P = 40^{\circ}

, so option (a) is correct.45:T762,अर्धवृत्त में बना कोण PQ व्यास है तथा R वृत्त पर स्थित है, अतः

∠ P R Q = 90^{\circ}

— अर्धवृत्त में बना कोण समकोण होता है।

△ P R Q

में तीनों कोणों का योग

180^{\circ}

होता है:

∠ R P Q + ∠ P R Q + ∠ R Q P = 180^{\circ}

50^{\circ} + 90^{\circ} + ∠ R Q P = 180^{\circ}

∠ R Q P = 40^{\circ}

, इसलिए सही विकल्प (a) है।46:T726,Cyclic quadrilateral and central angle Opposite angles of a cyclic quadrilateral are supplementary, so

∠ P S R + ∠ P Q R = 180^{\circ}

∠ P Q R = 180^{\circ} - 115^{\circ} = 65^{\circ}

∠ P Q R

and

∠ P O R

stand on the same arc PR, and the angle at the centre is twice the angle at the circumference.

∠ P O R = 2 \times ∠ P Q R = 2 \times 65^{\circ} = 130^{\circ}

Hence

∠ P O R = 130^{\circ}

, so option (c) is correct.47:T83a,चक्रीय चतुर्भुज एवं केंद्रीय कोण चक्रीय चतुर्भुज के सम्मुख कोण संपूरक होते हैं, अतः

∠ P S R + ∠ P Q R = 180^{\circ}

।

∠ P Q R = 180^{\circ} - 115^{\circ} = 65^{\circ}

∠ P Q R

तथा

∠ P O R

एक ही चाप PR पर बने हैं, और केंद्र पर बना कोण परिधि पर बने कोण का दोगुना होता है।

∠ P O R = 2 \times ∠ P Q R = 2 \times 65^{\circ} = 130^{\circ}

अतः

∠ P O R = 130^{\circ}

है, इसलिए सही विकल्प (c) है।48:T56a,Profit and loss on cost price Both the loss and the profit are reckoned on the cost price, so find the cost price first. At a

30 %

loss the selling price is

(100 - 30) % = 70 %

of the cost price.

14000 = C P \times \frac{70}{100} \Rightarrow C P = \frac{14000 \times 100}{70} = 20000

For a

25 %

profit:

S P = C P \times \frac{100 + 25}{100} = 20000 \times \frac{125}{100}

SP = 25000 Hence the item should be sold for ₹25,000, so option (a) is correct.49:T6a5,क्रय मूल्य पर लाभ-हानि हानि तथा लाभ दोनों क्रय मूल्य पर आधारित होते हैं, अतः पहले क्रय मूल्य ज्ञात कीजिए।

30 %

हानि पर विक्रय मूल्य क्रय मूल्य का

(100 - 30) % = 70 %

होता है।

14000 = C P \times \frac{70}{100} \Rightarrow C P = \frac{14000 \times 100}{70} = 20000

25 %

लाभ के लिए:

S P = C P \times \frac{100 + 25}{100} = 20000 \times \frac{125}{100}

SP = 25000 अतः वस्तु को ₹25,000 में बेचा जाना चाहिए, इसलिए सही विकल्प (a) है।1c:["$","$L26",null,{"mode":"practice","dropped":0,"bilingual":true,"choiceSubjects":[],"questions":[{"id":11551,"n":51,"subject":"Quantitative Aptitude","stem":"

O

is the incentre of triangle

A B C

. If angle

AOC = 160^{\circ}

, find angle ABC .","stemHi":"

O

, त्रिभुज

A B C

का अंतःकेंद्र है। यदि कोण

AOC = 160^{\circ}

है, तो कोण ABC ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"70°","textHi":null,"imageUrl":null},{"key":"b","text":"140°","textHi":null,"imageUrl":null},{"key":"c","text":"130°","textHi":null,"imageUrl":null},{"key":"d","text":"150°","textHi":null,"imageUrl":null}],"correct":"b","sol":"$27","solHi":"$28","pos":2,"neg":0.5},{"id":11552,"n":52,"subject":"Quantitative Aptitude","stem":"The length and breadth of a rectangle are in the ratio 22 : 7, respectively, and the perimeter of the rectangle is 174 cm . If the area of the rectangle is equal to the area of the top surface of a solid cylinder, then find the curved surface area of the cylinder given that its radius is 84% of its height.","stemHi":"एक आयत की लंबाई और चौड़ाई क्रमशः 22 : 7 के अनुपात में हैं तथा आयत का परिमाप 174 cm है। यदि आयत का क्षेत्रफल एक ठोस बेलन के ऊपरी पृष्ठ के क्षेत्रफल के बराबर है, तो बेलन का वक्र पृष्ठीय क्षेत्रफल ज्ञात कीजिए, जबकि उसकी त्रिज्या उसकी ऊँचाई का 84% है।","context":null,"contextHi":null,"options":[{"key":"a","text":"

3330 {cm}^{2}

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

3560 {cm}^{2}

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

3120 {cm}^{2}

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

3300 {cm}^{2}

","textHi":null,"imageUrl":null}],"correct":"d","sol":"$29","solHi":"$2a","pos":2,"neg":0.5},{"id":11553,"n":53,"subject":"Quantitative Aptitude","stem":"A rhombus has diagonals in the ratio 5 : 12. If the side length is 13 cm, find the exact lengths of the diagonals and hence the area of the rhombus.","stemHi":"एक समचतुर्भुज के विकर्ण 5 : 12 के अनुपात में हैं। यदि उसकी भुजा की लंबाई 13 cm है, तो विकर्णों की सटीक लंबाइयाँ तथा उससे समचतुर्भुज का क्षेत्रफल ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"16 cm and

25 cm, 200 {cm}^{2}

","textHi":"16 cm और

25 cm, 200 {cm}^{2}

","imageUrl":null},{"key":"b","text":"10 cm and

24 cm, 120 {cm}^{2}

","textHi":"10 cm और

24 cm, 120 {cm}^{2}

","imageUrl":null},{"key":"c","text":"14 cm and

20 cm, 140 {cm}^{2}

","textHi":"14 cm और

20 cm, 140 {cm}^{2}

","imageUrl":null},{"key":"d","text":"10 cm and

20 cm, 160 {cm}^{2}

","textHi":"10 cm और

20 cm, 160 {cm}^{2}

","imageUrl":null}],"correct":"b","sol":"$2b","solHi":"$2c","pos":2,"neg":0.5},{"id":11554,"n":54,"subject":"Quantitative Aptitude","stem":"A and B invested Rs. 80,000 and Rs.

1, 20, 000

, respectively. At the end of 8 months, the total profit is Rs. 60,000 . What is B's share in the profit?","stemHi":"A और B ने क्रमशः Rs. 80,000 तथा Rs.

1, 20, 000

निवेश किए। 8 महीने के अंत में कुल लाभ Rs. 60,000 है। लाभ में B का हिस्सा क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"Rs. 26,000","textHi":null,"imageUrl":null},{"key":"b","text":"Rs. 28,000","textHi":null,"imageUrl":null},{"key":"c","text":"Rs. 30,000","textHi":null,"imageUrl":null},{"key":"d","text":"Rs. 36,000","textHi":null,"imageUrl":null}],"correct":"d","sol":"Partnership profit share\nBoth partners keep their money in for the same 8 months, so the time cancels and the profit is shared in the ratio of the amounts invested.\nA:B=80000:120000=2:3.\nTotal parts =2+3=5, and 5 parts = Rs. 60,000, so 1 part = Rs. 12,000.\nB’s share

= 3 \times 12000 =

Rs. 36,000.","solHi":"साझेदारी में लाभ का बँटवारा\nदोनों साझेदारों की पूँजी समान 8 महीने तक लगी रहती है, अतः समय कट जाता है और लाभ निवेश की गई राशियों के अनुपात में बँटता है।\nA:B=80000:120000=2:3।\nकुल भाग =2+3=5, तथा 5 भाग = Rs. 60,000, अतः 1 भाग = Rs. 12,000।\nB का हिस्सा

= 3 \times 12000 =

Rs. 36,000।","pos":2,"neg":0.5},{"id":11555,"n":55,"subject":"Quantitative Aptitude","stem":"The average score of 40 students is 42 . When a group of 16 new students joins, the average rises to 50 . Find the average score of the new students.","stemHi":"40 विद्यार्थियों का औसत प्राप्तांक 42 है। जब 16 नए विद्यार्थियों का एक समूह जुड़ता है, तो औसत बढ़कर 50 हो जाता है। नए विद्यार्थियों का औसत प्राप्तांक ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"70","textHi":null,"imageUrl":null},{"key":"b","text":"66","textHi":null,"imageUrl":null},{"key":"c","text":"68","textHi":null,"imageUrl":null},{"key":"d","text":"74","textHi":null,"imageUrl":null}],"correct":"a","sol":"Average of a new group\nTotal score of the first 40 students

= 40 \times 42 = 1680

.\nAfter the new students join there are 40+16=56 students whose average is 50, so their total

= 56 \times 50 = 2800

.\nTotal score of the 16 new students =2800-1680=1120.\nTheir average

= \frac{1120}{16} = 70

.","solHi":"नए समूह का औसत\nपहले 40 विद्यार्थियों का कुल प्राप्तांक

= 40 \times 42 = 1680

।\nनए विद्यार्थियों के जुड़ने पर कुल 40+16=56 विद्यार्थी हैं जिनका औसत 50 है, अतः उनका कुल प्राप्तांक

= 56 \times 50 = 2800

।\n16 नए विद्यार्थियों का कुल प्राप्तांक =2800-1680=1120।\nउनका औसत

= \frac{1120}{16} = 70

।","pos":2,"neg":0.5},{"id":11556,"n":56,"subject":"Quantitative Aptitude","stem":"The average monthly salary of employees in a company is ₹ 60,000 . When 6 new employees with average salary ₹45,000 join, the average salary of the whole company decreases by ₹6,000. Find the original number of employees.","stemHi":"एक कंपनी के कर्मचारियों का औसत मासिक वेतन ₹ 60,000 है। जब ₹45,000 औसत वेतन वाले 6 नए कर्मचारी जुड़ते हैं, तो पूरी कंपनी का औसत वेतन ₹6,000 घट जाता है। कर्मचारियों की मूल संख्या ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"10","textHi":null,"imageUrl":null},{"key":"b","text":"16","textHi":null,"imageUrl":null},{"key":"c","text":"15","textHi":null,"imageUrl":null},{"key":"d","text":"9","textHi":null,"imageUrl":null}],"correct":"d","sol":"Average salary\nLet the original number of employees be n.\nThe new average is 60000-6000=54000.\nEquating the total salary before and after:

\frac{60000 n + 6 \times 45000}{n + 6} = 54000

.\n60000n+270000=54000n+324000.\n

6000 n = 54000 \Rightarrow n = 9

.\nSo the company originally had 9 employees.","solHi":"औसत वेतन\nमाना कि कर्मचारियों की मूल संख्या n है।\nनया औसत =60000-6000=54000 है।\nपहले और बाद के कुल वेतन को बराबर करने पर:

\frac{60000 n + 6 \times 45000}{n + 6} = 54000

।\n60000n+270000=54000n+324000।\n

6000 n = 54000 \Rightarrow n = 9

।\nअतः कंपनी में मूलतः 9 कर्मचारी थे।","pos":2,"neg":0.5},{"id":11557,"n":57,"subject":"Quantitative Aptitude","stem":"A cyclist covers a total distance of 54 km . After cycling for 3 hours and 30 minutes, he finds that the distance he has covered is

\frac{5}{7}

of the remaining distance. What is his speed in

km / hr

?","stemHi":"एक साइकिल चालक कुल 54 km की दूरी तय करता है। 3 घंटे 30 मिनट साइकिल चलाने के बाद वह पाता है कि उसके द्वारा तय की गई दूरी, शेष दूरी की

\frac{5}{7}

है। उसकी चाल

km / hr

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

7.8 km / hr

","textHi":null,"imageUrl":null},{"key":"b","text":"6.42 km/hr","textHi":null,"imageUrl":null},{"key":"c","text":"

2.0 km / hr

","textHi":null,"imageUrl":null},{"key":"d","text":"7.5 km/hr","textHi":null,"imageUrl":null}],"correct":"b","sol":"Speed from part of a journey\nDistance covered : distance still left =5:7, so the whole journey is 5+7=12 equal parts.\n12 parts =54 km, hence 1 part

= \frac{54}{12} = 4.5

km.\nDistance covered

= 5 \times 4.5 = 22.5

km.\nTime taken =3 hours 30 minutes =3.5 hours.\nSpeed

= \frac{22.5}{3.5} = \frac{45}{7} \approx 6.43

km/hr, which is the value listed in option (b).","solHi":"यात्रा के भाग से चाल\nतय की गई दूरी : शेष दूरी =5:7, अतः सम्पूर्ण यात्रा 5+7=12 बराबर भागों में है।\n12 भाग =54 km, अतः 1 भाग

= \frac{54}{12} = 4.5

km।\nतय की गई दूरी

= 5 \times 4.5 = 22.5

km।\nलगा समय =3 घंटे 30 मिनट =3.5 घंटे।\nचाल

= \frac{22.5}{3.5} = \frac{45}{7} \approx 6.43

km/hr, जो विकल्प (b) में दिया गया मान है।","pos":2,"neg":0.5},{"id":11558,"n":58,"subject":"Quantitative Aptitude","stem":"A train is on a 140 km journey. After travelling for 3 hours and 20 minutes, the distance it has covered is

\frac{5}{9}

of the remaining distance. What is the speed of the train in

m / s

?","stemHi":"एक ट्रेन 140 km की यात्रा पर है। 3 घंटे 20 मिनट चलने के बाद उसके द्वारा तय की गई दूरी, शेष दूरी की

\frac{5}{9}

है। ट्रेन की चाल

m / s

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

5.21 m / s

","textHi":null,"imageUrl":null},{"key":"b","text":"4.50 m/s","textHi":null,"imageUrl":null},{"key":"c","text":"

4.16 m / s

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

6.25 m / s

","textHi":null,"imageUrl":null}],"correct":"c","sol":"$2d","solHi":"चाल का रूपांतरण\nतय की गई दूरी : शेष दूरी =5:9, अतः यात्रा 5+9=14 बराबर भागों में है।\n14 भाग =140 km, अतः 1 भाग =10 km तथा तय की गई दूरी

= 5 \times 10 = 50

km।\nलगा समय =3 घंटे 20 मिनट

= \frac{10}{3}

घंटे।\nचाल

= \frac{50}{10 / 3} = 15

km/hr।\nमीटर प्रति सेकंड में बदलने पर:

15 \times \frac{5}{18} = \frac{25}{6} \approx 4.16

m/s।","pos":2,"neg":0.5},{"id":11559,"n":59,"subject":"Quantitative Aptitude","stem":"A and B together can complete a task in 30 days. If A alone can complete the task in 50 days, how long will B take to complete the task alone?","stemHi":"A और B मिलकर एक कार्य को 30 दिनों में पूरा कर सकते हैं। यदि A अकेला उस कार्य को 50 दिनों में पूरा कर सकता है, तो B अकेला उस कार्य को पूरा करने में कितना समय लेगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"41 days","textHi":"41 दिन","imageUrl":null},{"key":"b","text":"75 days","textHi":"75 दिन","imageUrl":null},{"key":"c","text":"80 days","textHi":"80 दिन","imageUrl":null},{"key":"d","text":"100 days","textHi":"100 दिन","imageUrl":null}],"correct":"b","sol":"Time and work\nTake the whole work as the LCM of 30 and 50, i.e. 150 units.\n $\"figure\"/$ \nThen A and B together do

\frac{150}{30} = 5

units a day, and A alone does

\frac{150}{50} = 3

units a day.\nSo B alone does 5-3=2 units a day.\nTime taken by B

= \frac{150}{2} = 75

days.","solHi":"समय और कार्य\nसम्पूर्ण कार्य को 30 और 50 का ल.स. अर्थात् 150 इकाई मान लीजिए।\n $\"figure\"/$ \nतब A और B मिलकर प्रतिदिन

\frac{150}{30} = 5

इकाई तथा A अकेला प्रतिदिन

\frac{150}{50} = 3

इकाई कार्य करता है।\nअतः B अकेला प्रतिदिन 5-3=2 इकाई कार्य करता है।\nB द्वारा लिया गया समय

= \frac{150}{2} = 75

दिन।","pos":2,"neg":0.5},{"id":11560,"n":60,"subject":"Quantitative Aptitude","stem":"A shopkeeper offers successive discounts of 25% and 20% on a bag and sells it for ₹1200. What was the original marked price of the bag?","stemHi":"एक दुकानदार एक बैग पर 25% और 20% की क्रमिक छूट देता है तथा उसे ₹1200 में बेचता है। बैग का मूल अंकित मूल्य क्या था?","context":null,"contextHi":null,"options":[{"key":"a","text":"₹2,000","textHi":null,"imageUrl":null},{"key":"b","text":"₹1,500","textHi":null,"imageUrl":null},{"key":"c","text":"₹1,406","textHi":null,"imageUrl":null},{"key":"d","text":"₹1,800","textHi":null,"imageUrl":null}],"correct":"a","sol":"$2e","solHi":"$2f","pos":2,"neg":0.5},{"id":11561,"n":61,"subject":"Quantitative Aptitude","stem":"A product is sold for ₹1,560 after a

22 %

discount is given on its marked price. What was the marked price of the product?","stemHi":"एक उत्पाद को उसके अंकित मूल्य पर

22 %

की छूट देने के बाद ₹1,560 में बेचा जाता है। उत्पाद का अंकित मूल्य क्या था?","context":null,"contextHi":null,"options":[{"key":"a","text":"₹2,900","textHi":null,"imageUrl":null},{"key":"b","text":"₹2,000","textHi":null,"imageUrl":null},{"key":"c","text":"₹1,100","textHi":null,"imageUrl":null},{"key":"d","text":"₹3,200","textHi":null,"imageUrl":null}],"correct":"b","sol":"$30","solHi":"$31","pos":2,"neg":0.5},{"id":11562,"n":62,"subject":"Quantitative Aptitude","stem":"The width of a rectangle is such that its length exceeds it by 3 cm. Given that the perimeter measures 66 cm , determine the area of the rectangle.","stemHi":"एक आयत की चौड़ाई ऐसी है कि उसकी लंबाई चौड़ाई से 3 cm अधिक है। यदि आयत का परिमाप 66 cm है, तो आयत का क्षेत्रफल ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"

244 {cm}^{2}

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

260 {cm}^{2}

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

250 {cm}^{2}

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

270 {cm}^{2}

","textHi":null,"imageUrl":null}],"correct":"d","sol":"$32","solHi":"$33","pos":2,"neg":0.5},{"id":11563,"n":63,"subject":"Quantitative Aptitude","stem":"In an 80 liter mixture of milk and water, the ratio of milk to water is

3 : 5

. How much water must be added to make the ratio of milk to water 4 : 7 ?","stemHi":"दूध और पानी के 80 लीटर मिश्रण में दूध और पानी का अनुपात

3 : 5

है। दूध और पानी का अनुपात 4 : 7 करने के लिए इसमें कितना पानी और मिलाया जाना चाहिए?","context":null,"contextHi":null,"options":[{"key":"a","text":"1.5 liters","textHi":"1.5 लीटर","imageUrl":null},{"key":"b","text":"2 liters","textHi":"2 लीटर","imageUrl":null},{"key":"c","text":"3.5 liters","textHi":"3.5 लीटर","imageUrl":null},{"key":"d","text":"2.5 liters","textHi":"2.5 लीटर","imageUrl":null}],"correct":"d","sol":"$34","solHi":"$35","pos":2,"neg":0.5},{"id":11564,"n":64,"subject":"Quantitative Aptitude","stem":"If a chord of a circle is 30 cm and the distance of the chord from the center is 8 cm , what is the diameter of the circle?","stemHi":"यदि किसी वृत्त की एक जीवा 30 cm लंबी है तथा केंद्र से उस जीवा की दूरी 8 cm है, तो वृत्त का व्यास क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"15 cm","textHi":null,"imageUrl":null},{"key":"b","text":"25 cm","textHi":null,"imageUrl":null},{"key":"c","text":"34 cm","textHi":null,"imageUrl":null},{"key":"d","text":"17 cm","textHi":null,"imageUrl":null}],"correct":"c","sol":"$36","solHi":"$37","pos":2,"neg":0.5},{"id":11565,"n":65,"subject":"Quantitative Aptitude","stem":"Two chords PQ and SN of a circle intersect at a point

A

inside the circle. If

PA = 8 cm, AQ = 12 cm

, and

SA = 6 cm

, what is the length of chord SN ?","stemHi":"किसी वृत्त की दो जीवाएँ PQ तथा SN वृत्त के भीतर एक बिंदु

A

पर प्रतिच्छेद करती हैं। यदि

PA = 8 cm, AQ = 12 cm

, तथा

SA = 6 cm

है, तो जीवा SN की लंबाई क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"20 cm","textHi":null,"imageUrl":null},{"key":"b","text":"22 cm","textHi":null,"imageUrl":null},{"key":"c","text":"26 cm","textHi":null,"imageUrl":null},{"key":"d","text":"28 cm","textHi":null,"imageUrl":null}],"correct":"b","sol":"Intersecting chords theorem\nWhen two chords of a circle cut each other inside it, the products of the two parts of each chord are equal.\n $\"figure\"/$ \nFormula:

P A \times A Q = S A \times A N

8 \times 12 = 6 \times A N

A N = \frac{96}{6} = 16

cm\nSN = SA + AN = 6 + 16 = 22 cm, so option (b) is correct.","solHi":"प्रतिच्छेदी जीवा प्रमेय\nजब किसी वृत्त की दो जीवाएँ वृत्त के भीतर एक-दूसरे को काटती हैं, तो प्रत्येक जीवा के दोनों खंडों के गुणनफल बराबर होते हैं।\n $\"figure\"/$ \nसूत्र:

P A \times A Q = S A \times A N

8 \times 12 = 6 \times A N

A N = \frac{96}{6} = 16

cm\nSN = SA + AN = 6 + 16 = 22 cm, इसलिए सही विकल्प (b) है।","pos":2,"neg":0.5},{"id":11566,"n":66,"subject":"Quantitative Aptitude","stem":"In a circle with center O , two parallel chords PQ and RS are on opposite sides of the center. If the length of chord PQ is 24 cm and chord RS is 18 cm , and the distance between them is 21 cm , find the radius of the circle.","stemHi":"केंद्र O वाले एक वृत्त में दो समांतर जीवाएँ PQ तथा RS केंद्र के विपरीत ओर स्थित हैं। यदि जीवा PQ की लंबाई 24 cm तथा जीवा RS की लंबाई 18 cm है और उनके बीच की दूरी 21 cm है, तो वृत्त की त्रिज्या ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"15 cm","textHi":null,"imageUrl":null},{"key":"b","text":"9 cm","textHi":null,"imageUrl":null},{"key":"c","text":"18 cm","textHi":null,"imageUrl":null},{"key":"d","text":"24 cm","textHi":null,"imageUrl":null}],"correct":"a","sol":"$38","solHi":"$39","pos":2,"neg":0.5},{"id":11567,"n":67,"subject":"Quantitative Aptitude","stem":"In a circle, chord PQ has a length of 64 cm and the perpendicular distance from the center

O

to the chord is 24 cm . What is the diameter of the circle?","stemHi":"एक वृत्त में जीवा PQ की लंबाई 64 cm है तथा केंद्र

O

से जीवा पर डाली गई लंब दूरी 24 cm है। वृत्त का व्यास क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"40 cm","textHi":null,"imageUrl":null},{"key":"b","text":"60 cm","textHi":null,"imageUrl":null},{"key":"c","text":"64 cm","textHi":null,"imageUrl":null},{"key":"d","text":"80 cm","textHi":null,"imageUrl":null}],"correct":"d","sol":"$3a","solHi":"$3b","pos":2,"neg":0.5},{"id":11568,"n":68,"subject":"Quantitative Aptitude","stem":"Two tangent segments, TP and TQ, are drawn from an external point T to a circle with center 0 . If

∠ PTQ = 50^{\circ}

, what is the measure of the angle

∠ POQ

?","stemHi":"केंद्र 0 वाले एक वृत्त पर बाह्य बिंदु T से दो स्पर्श रेखाखंड TP तथा TQ खींचे गए हैं। यदि

∠ PTQ = 50^{\circ}

है, तो कोण

∠ POQ

का माप क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"50°","textHi":null,"imageUrl":null},{"key":"b","text":"130°","textHi":null,"imageUrl":null},{"key":"c","text":"150°","textHi":null,"imageUrl":null},{"key":"d","text":"100*","textHi":null,"imageUrl":null}],"correct":"b","sol":"$3c","solHi":"$3d","pos":2,"neg":0.5},{"id":11569,"n":69,"subject":"Quantitative Aptitude","stem":"From a point T outside a circle, two tangents TP and TQ are drawn. If the length of TP is 10 units, what is the length of TQ ?","stemHi":"किसी वृत्त के बाहर स्थित बिंदु T से दो स्पर्श रेखाएँ TP तथा TQ खींची गई हैं। यदि TP की लंबाई 10 इकाई है, तो TQ की लंबाई क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"20 units","textHi":"20 इकाई","imageUrl":null},{"key":"b","text":"15 units","textHi":"15 इकाई","imageUrl":null},{"key":"c","text":"5 units","textHi":"5 इकाई","imageUrl":null},{"key":"d","text":"10 units","textHi":"10 इकाई","imageUrl":null}],"correct":"d","sol":"Equal tangents from a point\nThe two tangents drawn to a circle from the same external point are always equal in length.\n $\"figure\"/$ \nProof in one line: OP = OQ (radii), OT is common and

∠ O P T = ∠ O Q T = 90^{\circ}

, so

△ O P T ≅ △ O Q T

(RHS).\nTherefore TQ = TP = 10 units, so option (d) is correct.","solHi":"बाह्य बिंदु से समान स्पर्श रेखाएँ\nकिसी वृत्त पर एक ही बाह्य बिंदु से खींची गई दोनों स्पर्श रेखाओं की लंबाई सदैव बराबर होती है।\n $\"figure\"/$ \nएक पंक्ति में उपपत्ति: OP = OQ (त्रिज्याएँ), OT उभयनिष्ठ तथा

∠ O P T = ∠ O Q T = 90^{\circ}

, अतः

△ O P T ≅ △ O Q T

(RHS)।\nअतः TQ = TP = 10 इकाई है, इसलिए सही विकल्प (d) है।","pos":2,"neg":0.5},{"id":11570,"n":70,"subject":"Quantitative Aptitude","stem":"A circle with center O has a radius of 8 cm . A point T is outside the circle, and a tangent from

T

to the circle is 15 cm long. What is the length of the shortest distance from

T

to the circle ?","stemHi":"केंद्र O वाले एक वृत्त की त्रिज्या 8 cm है। एक बिंदु T वृत्त के बाहर स्थित है तथा

T

से वृत्त पर खींची गई स्पर्श रेखा की लंबाई 15 cm है।

T

से वृत्त तक की न्यूनतम दूरी की लंबाई क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"15 cm","textHi":null,"imageUrl":null},{"key":"b","text":"8 cm","textHi":null,"imageUrl":null},{"key":"c","text":"17 cm","textHi":null,"imageUrl":null},{"key":"d","text":"9 cm","textHi":null,"imageUrl":null}],"correct":"d","sol":"$3e","solHi":"$3f","pos":2,"neg":0.5},{"id":11571,"n":71,"subject":"Quantitative Aptitude","stem":"If the centroid of a triangle is at the origin

(0, 0)

and two of its vertices are at

(4, 6)

and

(- 5, 0)

, what are the coordinates of the third vertex ?","stemHi":"यदि किसी त्रिभुज का केंद्रक मूल बिंदु

(0, 0)

पर है तथा उसके दो शीर्ष

(4, 6)

और

(- 5, 0)

पर हैं, तो तीसरे शीर्ष के निर्देशांक क्या हैं?","context":null,"contextHi":null,"options":[{"key":"a","text":"

(2, - 5)

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

(1, - 6)

","textHi":null,"imageUrl":null},{"key":"c","text":"(3,-6)","textHi":null,"imageUrl":null},{"key":"d","text":"

(6, - 1)

","textHi":null,"imageUrl":null}],"correct":"b","sol":"$40","solHi":"$41","pos":2,"neg":0.5},{"id":11572,"n":72,"subject":"Quantitative Aptitude","stem":"What is the slope of the line represented by the equation

x + 6 y = 12

?","stemHi":"समीकरण

x + 6 y = 12

द्वारा निरूपित रेखा की प्रवणता (ढाल) क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"

- \frac{1}{3}

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

\frac{1}{6}

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

\frac{1}{5}

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

\frac{2}{3}

","textHi":null,"imageUrl":null}],"correct":"b","sol":"$42","solHi":"$43","pos":2,"neg":0.5},{"id":11573,"n":73,"subject":"Quantitative Aptitude","stem":"A circle has a diameter PQ . A point

R

is on the circumference. If

∠ R P Q = 50^{\circ}

, what is the measure of

∠ RQP

?","stemHi":"एक वृत्त का व्यास PQ है। एक बिंदु

R

वृत्त की परिधि पर स्थित है। यदि

∠ R P Q = 50^{\circ}

है, तो

∠ RQP

का माप क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"40°","textHi":null,"imageUrl":null},{"key":"b","text":"60°","textHi":null,"imageUrl":null},{"key":"c","text":"140°","textHi":null,"imageUrl":null},{"key":"d","text":"50°","textHi":null,"imageUrl":null}],"correct":"a","sol":"$44","solHi":"$45","pos":2,"neg":0.5},{"id":11574,"n":74,"subject":"Quantitative Aptitude","stem":"In a circle with center 0 , a cyclic quadrilateral PQRS is inscribed. If the measure of the

∠ PSR = 115^{\circ}

, what is the measure of the

∠ POR

?","stemHi":"केंद्र 0 वाले एक वृत्त में एक चक्रीय चतुर्भुज PQRS अंतर्निहित है। यदि

∠ PSR = 115^{\circ}

है, तो

∠ POR

का माप क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"65°","textHi":null,"imageUrl":null},{"key":"b","text":"150°","textHi":null,"imageUrl":null},{"key":"c","text":"130°","textHi":null,"imageUrl":null},{"key":"d","text":"160°","textHi":null,"imageUrl":null}],"correct":"c","sol":"$46","solHi":"$47","pos":2,"neg":0.5},{"id":11575,"n":75,"subject":"Quantitative Aptitude","stem":"An item was sold for ₹ 14000 at a

30 %

loss. At what price should it be sold to gain a

25 %

profit ?","stemHi":"एक वस्तु

30 %

की हानि पर ₹ 14000 में बेची गई।

25 %

का लाभ प्राप्त करने के लिए उसे किस मूल्य पर बेचा जाना चाहिए?","context":null,"contextHi":null,"options":[{"key":"a","text":"₹ 25,000","textHi":null,"imageUrl":null},{"key":"b","text":"₹ 20,000","textHi":null,"imageUrl":null},{"key":"c","text":"₹ 26,000","textHi":null,"imageUrl":null},{"key":"d","text":"₹ 27,000","textHi":null,"imageUrl":null}],"correct":"a","sol":"$48","solHi":"$49","pos":2,"neg":0.5}],"test":{"slug":"ssc-chsl-tier-1--19-nov-2025-shift-3-quant","title":"SSC CHSL Tier-1 19 November 2025 Shift-3 — Quantitative Aptitude Sectional Test","examName":"CHSL Tier-1","paperLabel":"19 November 2025 · Shift 3","sectionSubject":"Quantitative Aptitude","durationMinutes":15,"format":"sectional_test"}}]