CGL 21 Tier 2 Maths Previous Year Paper Quantitative Aptitude PDF


Question 1

Rohit's income is ₹32000. If his expenses is 30 percent of total income, then what will be the saving of Rohit?

रोहित की आय ₹32000 है। यदि उसका खर्च कुल आय का 30 प्रतिशत है, तो रोहित की बचत कितनी होगी? 


Options

A

₹22400

₹22400

B

₹18600

₹18600

C

₹19200

₹19200

D

₹24600

₹24600


Solution:

Correct Answer:

A

₹22400

₹22400


Rohit's Income = 32000

Expenditure = 30% of 32000 = 9600

Now savings of Rohit = 32000 - 9600 = ₹22400

रोहित की आय = 32000

रोहित का खर्च = 30% of 32000 = 9600

अब रोहित की बचत = 32000 - 9600 = ₹22400

Question 2

Vinay and Mahesh are 250 metres apart from each other. They are moving towards each other with the speed of 36 km/hr and 54 km/hr respectively. In how much time will they meet each other? 

विनय तथा महेश एक-दूसरे से 250 मीटर दूर हैं। वे क्रमशः 36 km/hr तथा 54 km/hr की चाल से एक-दूसरे की ओर चल रहे हैं।वे एक-दूसरे से कितने समय बाद मिलेंगे?


Options

A

15 seconds 

15 seconds 

B

10 seconds 

10 seconds 

C

20 seconds 

20 seconds 

D

12 seconds

12 seconds


Solution:

Correct Answer:

B

10 seconds 

10 सेकंड 


Distance between Vinay and Mahesh = 250 meters

Speed of Vinay = 36 km/hr = 36×518\frac{36 \times 5}{18} = 10 m/s

Speed of Mahesh = 54 km/hr = 54 ×518\frac{54 \times 5}{18} = 15 m/s

Relative speed of vinay and mahesh as they are running towards each other = 10 + 15 = 25 m/s

Now time taken until they meet each other = 25025\frac{250}{25} = 10 seconds

विनय तथा महेश के बीच की दूरी  = 250 meters

विनय की चाल  = 36 km/hr = 36×518\frac{36 \times 5}{18} = 10 m/s

महेश की चाल  = 54 km/hr = 54 ×518\frac{54 \times 5}{18} = 15 m/s

विनय तथा महेश की सापेक्ष चाल जब वो एक-दूसरे की ओर चल रहे हैं = 10 + 15 = 25 m/s

एक-दूसरे से मिलने में लगा समय  = 25025\frac{250}{25} = 10 सेकंड

Question 3

The curved surface area of a solid hemisphere is 22 cm2. What is the total surface area of the hemisphere? (use π\pi = 22/7) 

एक ठोस अर्धगोले का वक्र पृष्ठीय क्षेत्रफल 22 cm2 है। अर्धगोले का संपूर्ण पृष्ठीय क्षेत्रफल कितना है? ( π\pi = 22/7 लीजिए)


Options

A

30 cm2

30 cm2

B

44 cm2

44 cm2

C

33 cm2

33 cm2

D

66 cm2

66 cm2


Solution:

Correct Answer:

C

33 cm2

33 cm2


The curved surface area of a solid hemisphere = 2π\piR2 = 22 cm2

The total surface area of the hemisphere = 3π\piR2 = 3 ×\times 11 = 33 cm2

एक ठोस अर्धगोले का वक्र पृष्ठीय क्षेत्रफल = 2π\piR2 = 22 cm2

ठोस अर्धगोले का संपूर्ण पृष्ठीय क्षेत्रफल = 3π\piR2 = 3 ×\times 11 = 33 cm2

Question 4

Three years ago, Raman’s salary was ₹45000. His salary is increased by 10 percent, A percent and 20 percent in first, second and third year respectively. Raman’s present salary is ₹83160. What is the value of A? 

तीन वर्ष पहले रमन का वेतन ₹45000 था। उसके वेतन में पहले, दूसरे तथा तीसरे वर्ष में क्रमशः 10 प्रतिशत, A प्रतिशत तथा 20 प्रतिशत की वृद्धि की गई है। रमन की वर्तमान आय ₹8360 है। A का मान क्या है?


Options

A

54

54

B

50

50

C

30

30

D

40

40


Solution:

Correct Answer:

D

40

40


Raman’s salary three years ago  = 45000

Raman’s present salary = 83160

45000 ×\times 110100\frac{110}{100} ×\times 100+A100\frac{100 + A}{100} ×\times 120100\frac{120}{100} = 83160

100 + A = 83160 × 1045× 11× 12\frac{83160 \times 10 }{45 \times 11 \times 12}

100 + A = 140

A = 40 %

तीन वर्ष पहले रमन का वेतन  = 45000

रमन की वर्तमान आय = 83160

45000 ×\times 110100\frac{110}{100} ×\times 100+A100\frac{100 + A}{100} ×\times 120100\frac{120}{100} = 83160

100 + A = 83160 × 1045× 11× 12\frac{83160 \times 10 }{45 \times 11 \times 12}

100 + A = 140

A = 40 %

Question 5

ABCDEEF is a regular hexagon. Side of the hexagon is 36 cm. What is the area of the triangle ABC?

ABCDEEF एक सम षट्भुज है। षट्भुज की भुजा 36 से.मी. है। त्रिभुज ABC का क्षेत्रफल क्या है?


Options

A

2403\sqrt{3} cm2

2403\sqrt{3} cm2

B

3243\sqrt{3} cm2

3243\sqrt{3} cm2

C

3603\sqrt{3} cm2

3603\sqrt{3} cm2

D

1923\sqrt{3} cm2

1923\sqrt{3} cm2


Solution:

Correct Answer:

B

3243\sqrt{3} cm2

3243\sqrt{3} से.मी2


Side of the hexagon ABCDEF = a = 36 cm

Area of triangle ABC = 2 ×\times Area of triangle ABG = 2 ×\times 12\frac{1}{2} ×\times AG ×\times BG =  183\sqrt{3} ×\times 18  = 3243\sqrt{3} cm2

ABCDEF सम षट्भुज की भुजा = a = 36 cm

 त्रिभुज ABC का क्षेत्रफल = 2 ×\times त्रिभुज ABG का क्षेत्रफल = 2 ×\times 12\frac{1}{2} ×\times AG ×\times BG =  183\sqrt{3} ×\times 18  = 3243\sqrt{3} से.मी2

Question 6

What is the value of 991199\frac{11}{99} + 991399\frac{13}{99} + 991599\frac{15}{99} + ..... + 996799\frac{67}{99}?

991199\frac{11}{99} + 991399\frac{13}{99} + 991599\frac{15}{99} + ..... + 996799\frac{67}{99} का मान क्या है?


Options

A

9712033\frac{97120}{33}

9712033\frac{97120}{33}

B

9512033\frac{95120}{33}

9512033\frac{95120}{33}

C

9422033\frac{94220}{33}

9422033\frac{94220}{33}

D

9622033\frac{96220}{33}

9622033\frac{96220}{33}


Solution:

Correct Answer:

B

9512033\frac{95120}{33}

9512033\frac{95120}{33}


991199\frac{11}{99} + 991399\frac{13}{99} + 991599\frac{15}{99} + ..... + 996799\frac{67}{99}

an = a + (n - 1)d  and S= n2\frac{n}{2}(a+an)

67 = 11 + (n - 1)2

n = 1 + 28 = 29

(99 + 99 + 99 + ... 29 times) + (11+13+15+......+6799\frac{11 + 13 + 15 + ...... + 67}{99})

99 (1 + 1 + 1 + .... 29 times) + 292×(11+67)99\frac{\frac{29}{2} \times (11 + 67)}{99}

99 ×\times 29   + 292×7899\frac{\frac{29}{2} \times 78}{99}

2871 + 37733\frac{377}{33}

94743+37733\frac{94743 + 377}{33}

9512033\frac{95120}{33}

 

991199\frac{11}{99} + 991399\frac{13}{99} + 991599\frac{15}{99} + ..... + 996799\frac{67}{99}

an = a + (n - 1)d और  S= n2\frac{n}{2}(a+an)

67 = 11 + (n - 1)2

n = 1 + 28 = 29

(99 + 99 + 99 + ... 29 times) + (11+13+15+......+6799\frac{11 + 13 + 15 + ...... + 67}{99})

99 (1 + 1 + 1 + .... 29 times) + 292×(11+67)99\frac{\frac{29}{2} \times (11 + 67)}{99}

99 ×\times 29   + 292×7899\frac{\frac{29}{2} \times 78}{99}

2871 + 37733\frac{377}{33}

94743+37733\frac{94743 + 377}{33}

9512033\frac{95120}{33}

Question 7

What will be the simple interest on a sum of ₹12000 at the rate of 15 percent per annum for three years?

एक ₹12000 की राशि पर 15 प्रतिशत प्रति वर्ष की दर से तीन वर्षों के लिए साधारण ब्याज क्या होगा? 


Options

A

₹4500

₹4500

B

₹7200

₹7200

C

₹6000

₹6000

D

₹5400

₹5400


Solution:

Correct Answer:

D

₹5400

₹5400


Simple Interest = PRT100\frac{PRT}{100}

Principle = P = 12000

Rate of Interest per annum = R = 15%

Time = T = 3 years

Simple Interest  = 12000×15×3100\frac{12000\times15\times3}{100} = ₹5400

साधारण ब्याज  = PRT100\frac{PRT}{100}

मूलधन  = P = 12000

प्रतिवर्ष ब्याज की दर  = R = 15%

समय  = T = 3 साल 

साधारण ब्याज = 12000×15×3100\frac{12000\times15\times3}{100} = ₹5400

Question 8

Which of the following is equal to tanθ+secθ-1tanθ- secθ+ 1\frac{\tanθ + \secθ - 1}{\tanθ - \secθ + 1} ?

निम्नलिखित में से कौनसा विकल्प tanθ+secθ-1tanθ- secθ+ 1\frac{\tanθ + \secθ - 1}{\tanθ - \secθ + 1} के बराबर है?


Options

A

1+sinθcosθ\frac{1 + \sinθ}{\cosθ}

1+sinθcosθ\frac{1 + \sinθ}{\cosθ}

B

1+cosθsinθ\frac{1 + \cosθ}{\sinθ}

1+cosθsinθ\frac{1 + \cosθ}{\sinθ}

C

1+tanθcotθ\frac{1 + \tanθ}{\cotθ}

1+tanθcotθ\frac{1 + \tanθ}{\cotθ}

D

1+cotθtanθ\frac{1 + \cotθ}{\tanθ}

1+cotθtanθ\frac{1 + \cotθ}{\tanθ}


Solution:

Correct Answer:

A

1+sinθcosθ\frac{1 + \sinθ}{\cosθ}

1+sinθcosθ\frac{1 + \sinθ}{\cosθ}


tanθ+secθ-1tanθ- secθ+ 1\frac{\tanθ + \secθ - 1}{\tanθ - \secθ + 1}

sinθcosθ+1cosθ-1sinθcosθ- 1cosθ+ 1\frac{\frac{\sinθ}{\cosθ} + \frac{1}{\cosθ} - 1}{\frac{\sinθ}{\cosθ} - \frac{1}{\cosθ} + 1}

sinθ- cosθ+ 1sinθ+cosθ- 1\frac{\sinθ - \cosθ + 1}{\sinθ + \cosθ - 1}

sinθ- cosθ+ 1sinθ+cosθ- 1\frac{\sinθ - \cosθ + 1}{\sinθ + \cosθ - 1} ×\times sinθ+ cosθ+ 1sinθ+cosθ+ 1\frac{\sinθ + \cosθ + 1}{\sinθ + \cosθ + 1}

1+2sinθ+sin2θ-cos2θ sin2θ+ cos2θ+2sinθcosθ-1\frac{1 + 2\sinθ + {\sin}^2θ - {\cos}^2θ}{ {\sin}^2θ + {\cos}^2θ+ 2\sinθ \cosθ - 1}

2sinθ+2sin2θ2sinθcosθ\frac{2\sinθ + 2{\sin}^2θ}{2\sinθ \cosθ}

2sinθ(1+sinθ) 2sinθcosθ\frac{2\sinθ (1 + \sinθ) }{2\sinθ \cosθ}

1+sinθcosθ\frac{1 + \sinθ}{\cosθ}

tanθ+secθ-1tanθ- secθ+ 1\frac{\tanθ + \secθ - 1}{\tanθ - \secθ + 1}

sinθcosθ+1cosθ-1sinθcosθ- 1cosθ+ 1\frac{\frac{\sinθ}{\cosθ} + \frac{1}{\cosθ} - 1}{\frac{\sinθ}{\cosθ} - \frac{1}{\cosθ} + 1}

sinθ- cosθ+ 1sinθ+cosθ- 1\frac{\sinθ - \cosθ + 1}{\sinθ + \cosθ - 1}

sinθ- cosθ+ 1sinθ+cosθ- 1\frac{\sinθ - \cosθ + 1}{\sinθ + \cosθ - 1} ×\times sinθ+ cosθ+ 1sinθ+cosθ+ 1\frac{\sinθ + \cosθ + 1}{\sinθ + \cosθ + 1}

1+2sinθ+sinθ2-cosθ2 sinθ2+ cosθ2+2sinθcosθ-1\frac{1 + 2\sinθ + {\sinθ}^2 - {\cosθ}^2}{ {\sinθ}^2 + {\cosθ}^2 + 2\sinθ \cosθ - 1}

2sinθ+2sinθ2  2sinθcosθ\frac{2\sinθ + 2{\sinθ}^2 } { 2\sinθ \cosθ }

2sinθ(1+sinθ)  2sinθcosθ\frac{2\sinθ (1 + \sinθ) }{ 2\sinθ \cosθ }

1+sinθcosθ\frac{1 + \sinθ}{\cosθ}

Question 9

The graph of the equation x = c  (c ≠ 0) is a ______ .

समीकरण x = c (c ≠ 0) का ग्राफ _____ है।


Options

A

line at an angle of 45 degree to x axis 

line at an angle of 45 degree to x axis 

B

line parallel to x axis

line parallel to x axis

C

line parallel to y axis

line parallel to y axis

D

line at an angle of 45 degree to y  axis 

line at an angle of 45 degree to y  axis 


Solution:

Correct Answer:

C

line parallel to y axis

y अक्ष के समानांतर रेखा 


 graph of the equation x = c always will be parallel to y axis.

The equation of y-axis is x = 0

Equation of a Line Parallel to Y Axis

समीकरण x = c (c ≠ 0) का ग्राफ y अक्ष के समानांतर रेखा है।

y अक्ष का समीकरण x = 0 होता है । 

Equation of a Line Parallel to Y Axis

 

Question 10

Sum ₹20000 and ₹40000 are given on simple interest at the rate of 10 percent and 15 percent per annum respectively for three years. What will be the total simple interest?

₹20000 तथा ₹40000 की राशियों को तीन वर्षों के लिए क्रमश: 10 प्रतिशत तथा 15 प्रतिशत प्रतिवर्ष की साधारण ब्याज दर पर
दिया गया है। कुल साधारण ब्याज कितना होगा?


Options

A

₹36000

₹36000

B

₹24000

₹24000

C

₹32000

₹32000

D

₹28000

₹28000


Solution:

Correct Answer:

B

₹24000

₹24000


Simple Interest = PRT100\frac{PRT}{100}

Total Simple Interest = 20000×10 ×3100\frac{20000 \times 10 \times 3}{100} + 40000×15 ×3100\frac{40000 \times 15 \times 3}{100} = 6000 + 18000 = ₹24000

साधारण ब्याज  = PRT100\frac{PRT}{100}

कुल साधारण ब्याज = 20000×10 ×3100\frac{20000 \times 10 \times 3}{100} + 40000×15 ×3100\frac{40000 \times 15 \times 3}{100} = 6000 + 18000 = ₹24000

 

Question 11

ABC and PQR are two triangles. AB = PQ = 6 cm, BC = QR = 10 cm and AC = PR = 8 cm. If angle ABC = x degree, then what is the value of angle PRQ? 

ABC तथा PQR त्रिभुज हैं। AB = PQ = 6 से.मी., BC = QR = 10 से.मी. तथा AC = PR = 8  से.मी. है। यदि कोण ABC = x डिग्री है, तो कोण PRQ का मान क्या है? 


Options

A

(90 - x) degree

(90 - x) degree

B

(180 - x) degree

(180 - x) degree

C

x degree

x degree

D

(90 + x) degree

(90 + x) degree


Solution:

Correct Answer:

A

(90 - x) degree

(90 - x) डिग्री


In triangles ABC and PQR

AB = PQ = 6 cm, BC = QR = 10 cm and AC = PR = 8 cm

By Side-Side-Side theorem: All three pairs of corresponding sides are equal.

We can say that triangles ABC and PQR are congruent to each other.

So corresponding angles will also be equal.

So angle ACB = angle PRQ = (90 - x) degree

ABC तथा PQR त्रिभुज में 

AB = PQ = 6 से.मी., BC = QR = 10 से.मी. तथा AC = PR = 8  से.मी.

भुजा-भुजा-भुजा प्रमेय से  : एक त्रिभुज की तीन भुजाएँ दूसरे त्रिभुज की क्रमशः तीनों संगत भुजाओं के बराबर होती हैं।

इसलिए ABC तथा PQR त्रिभुज एक दूसरे के सर्वांग्सम हो जाएँगे 

अब हम कह सकते है की तीनों संगत कोण भी बराबर होंगे ।

इसलिए कोण ACB = कोण PRQ = (90 - x) डिग्री

Question 12

A person sells an article for a loss of 18 percent. If he increases the selling price by ₹144 and decreases the cost price by 30 percent, then there is a profit of 20 percent. What is the original selling price?

एक व्यक्ति किसी वस्तु को 18 प्रतिशत की हानि पर बेचता है। यदि वह विक्रय मूल्य को ₹144 बढ़ा दे तथा क्रय मूल्य को 30 प्रतिशत घटा दे, तो 20 प्रतिशत का लाभ होता है। मूल विक्रय मूल्य कितना है?


Options

A

₹5068

₹5068

B

₹6036

₹6036

C

₹6124

₹6124

D

₹5904

₹5904


Solution:

Correct Answer:

D

₹5904

₹5904


Let's cost price = 100x

Selling price after 18% loss = 82x

Selling price after ₹144 increment = 82x + 144

New Cost price after 30% decrement = 70x

New selling price after 20% profit = 84x

We know that 84x = 82x + 144

2x = 144 or x = 72

Original selling price = 82x = 82 ×\times 72 = ₹5904

माना की क्रय मूल्य  = 100x

18% हानि के बाद विक्रय मूल्य  = 82x

₹144 की बढ़ोतरी के बाद विक्रय मूल्य  = 82x + 144

30% घटाने के बाद क्रय मूल्य  = 70x

20% लाभ के बाद विक्रय मूल्य  = 84x

हम जानते है की 84x = 82x + 144

2x = 144 or x = 72

अब मूल विक्रय मूल्य = 82x = 82 ×\times 72 = ₹5904

Question 13

Volume of a cone whose radius of a base and height are r and h respectively, is 400 cm³. What will be the volume of a cone whose radius of base and height are 2r cm and h cm respectively?

एक शंकु. जिसके आधार की त्रिज्या तथा ऊँचाई क्रमशः r तथा h है, का आयतन 400 cm3 है। एक शंकु, जिसके आधार की त्रिज्या तथा ऊँचाई क्रमशः 2r cm तथा h cm है, का आयतन क्या होगा?


Options

A

800 cm3

800 cm3

B

1200 cm3

1200 cm3

C

1600 cm3

1600 cm3

D

100 cm3

100 cm3


Solution:

Correct Answer:

C

1600 cm3

1600 cm3


The volume of a Cone = V  = 13\frac{1}{3} π \pi R2H

v = 13\frac{1}{3} π \pi r2h = 400 cm3

v1 = 13\frac{1}{3} π \pi (2r)2h

v1 = 4v = 1600 cm3

शंकु का आयतन V  = 13\frac{1}{3} π \pi R2H

v = 13\frac{1}{3} π \pi r2h = 400 cm3

v1 = 13\frac{1}{3} π \pi (2r)2h

v1 = 4v = 1600 cm3

Question 14

The height of a cylinder is 45 cm. If the circumference of its base is 132 cm, then what is the curved surface of this cylinder? (use π = 22/7)

एक बेलन की ऊँचाई 45 cm है। यदि इसके आधार की परिधि 132 cm हो, तो इस बेलन का वक्र पृष्ठीय क्षेत्रफल कितना है? (π =2 2/7 लीजिए)


Options

A

5940 cm2

5940 cm2

B

6270 cm2

6270 cm2

C

5720 cm2

5720 cm2

D

6360 cm2

6360 cm2


Solution:

Correct Answer:

A

5940 cm2

5940 cm2


The height of a cylinder = h = 45 cm

circumference of cylinder's base = 2 π r = 132 cm 

curved surface of the cylinder = 2 π r h = 132 ×\times 45 = 5940 cm2

बेलन की ऊँचाई = h = 45 cm

बेलन के आधार की परिधि = 2 π r = 132 cm 

बेलन का वक्र पृष्ठीय क्षेत्रफल = 2 π r h = 132 ×\times 45 = 5940 cm2

Question 15

Raju spends 10 percent and 20 percent of his income on transport and food respectively. He spends 30 percent of the remaining income on clothing. He saves rest of his income. If his saving is ₹26460, then what will be total expenditure on food and clothing together?

राजू यातायात तथा भोजन पर क्रमशः अपनी आय का 10 प्रतिशत तथा 20 प्रतिशत खर्च करता है वह शेष आय का 30 प्रतिशत कपड़ों पर खर्च करता है। अपनी शेष आय को वह बचा लेता है। यदि उसकी बचत ₹26460 हो, तो भोजन तथा कपड़ों पर मिलाकर कुल खर्च कितना होगा?


Options

A

₹23440

₹23440

B

₹26420

₹26420

C

₹22140

₹22140

D

₹24480

₹24480


Solution:

Correct Answer:

C

₹22140

₹22140


Let's Raju's total income = 100x

expenditure on transport = 10% of 100x = 10x

expenditure on food = 20% of 100x = 20x

expenditure on clothing = 30% of 70x = 21x

Savings of Raju = 100x - 51x = 49x = 26460

x = 540

Now total expenditure on food and clothing = 20x + 21x = 41x = 41 ×\times 540 = ₹22140

 

माना की राजू  की कुल आय = 100x

यातायात पर खर्च  = 10% of 100x = 10x

भोजन  पर खर्च = 20% of 100x = 20x

कपड़ों  पर खर्च = 30% of 70x = 21x

राजू की कुल बचत  = 100x - 51x = 49x = 26460

x = 540

अब भोजन तथा कपड़ों पर कुल खर्च = 20x + 21x = 41x = 41 ×\times 540 = ₹22140

Question 16

Two line charts are given below. Line chart 1 shows the ratio of number of males to the number of females in two companies A and B for the 5 years. Line chart 2 shows the total number of males (both companies A and B) and total number of females (both companies A and B) for the 5 years.

What is the ratio of number of males of company B in Y1 to the total number of females of company A in Y3 and Y5?

नीचे दो लाइन चार्ट दिए गए हैं। लाइन चार्ट 1, 5 वर्षों के लिए दो कंपनियों A और B में पुरुषों की संख्या का महिलाओं की संख्या से अनुपात दर्शाता है। लाइन चार्ट 2, 5 वर्षों के लिए पुरुषों की कुल संख्या (कंपनियां A और B दोनों) और महिलाओं की कुल संख्या (कंपनियां A और B दोनों) को दर्शाता है।

Y1 में कंपनी B के पुरुषों की संख्या का Y3 और Y5 में कंपनी A की महिलाओं की कुल संख्या से अनुपात कितना है?


Options

A

119 : 218

119 : 218

B

117 : 218

117 : 218

C

129 : 215

129 : 215

D

117 : 215

117 : 215


Solution:

Correct Answer:

D

117 : 215

117 : 215


With the help of the line chart - 1 

In Y1 the ratio of the number of males to the number of females in company A = 1.1

MAFA\frac{M_A}{F_A} = 1110\frac{11}{10}11x10x\frac{11x}{10x}

In Y1 the ratio of the number of males to the number of females in company B = 0.9

MBFB\frac{M_B}{F_B} = 910\frac{9}{10}9y10y\frac{9y}{10y}

With the help of the line chart - 2

Total number of males in Y1 = Y1(MA + MB) = 11x + 9y = 21100

Total number of males in Y1 = Y1(FA + FB) = 10x + 10y = 20600

x + y = 2060 or 11x + 11y = 22660

2y = 22660 - 21100 = 1560 or y = 780

number of males of company B in Y1 = 9y  = 7020

Now we will follow the same process for the calculation of the total number of females of company A in Y3 and Y5

For total number of females of company A in Y3 :-

4a + 27b = 18025 and 5a + 20b = 16000

135a - 80a = 55a = 432000 - 360500 = 71500

5a = 6500

number of females of company A in Y3 = 5a = 6500

For total number of females of company A in Y5 :-

7p + 17q = 13550 and 5p + 20q = 11800

140p - 85p = 55p = 271000 - 200600 = 70400

5p = 6400

number of females of company A in Y5 = 5p = 6400

total number of females of company A in Y3 and Y5 = 6500 + 6400 = 12900

Now ratio 7020 : 12900 or 117 : 215

With the help of the line chart - 1 

In Y1 the ratio of the number of males to the number of females in company A = 1.1

MAFA\frac{M_A}{F_A} = 1110\frac{11}{10}11x10x\frac{11x}{10x}

In Y1 the ratio of the number of males to the number of females in company B = 0.9

MBFB\frac{M_B}{F_B} = 910\frac{9}{10}9y10y\frac{9y}{10y}

With the help of the line chart - 2

Total number of males in Y1 = Y1(MA + MB) = 11x + 9y = 21100

Total number of males in Y1 = Y1(FA + FB) = 10x + 10y = 20600

x + y = 2060 or 11x + 11y = 22660

2y = 22660 - 21100 = 1560 or y = 780

number of males of company B in Y1 = 9y  = 7020

Now we will follow the same process for the calculation of the total number of females of company A in Y3 and Y5

For total number of females of company A in Y3 :-

4a + 27b = 18025 and 5a + 20b = 16000

135a - 80a = 55a = 432000 - 360500 = 71500

5a = 6500

number of females of company A in Y3 = 5a = 6500

For total number of females of company A in Y5 :-

7p + 17q = 13550 and 5p + 20q = 11800

140p - 85p = 55p = 271000 - 200600 = 70400

5p = 6400

number of females of company A in Y5 = 5p = 6400

total number of females of company A in Y3 and Y5 = 6500 + 6400 = 12900

Now ratio 7020 : 12900 or 117 : 215

Question 17

x, y and z are the sides of a triangle. If z is the largest side and x+ y> z2, then the triangle is a :

x y तथा z एक त्रिभुज की भुजाएँ हैं। यदि z सबसे लंबी भुजा तथा x+ y> z2 हो, तो त्रिभुज एक _ है|


Options

A

Isosceles right angled triangle

Isosceles right angled triangle

B

Right-angled triangle

Right-angled triangle

C

Obtuse angled triangle 

Obtuse angled triangle 

D

Acute angled triangle

Acute angled triangle


Solution:

Correct Answer:

D

Acute angled triangle

न्यून कोण त्रिभुज 


We know that when 0° < θ < 90° then cosθ is +ve

We know from cosine rule that $$ cosα = \frac{x^2 + y^2 - z^2}{2xy}$$

It is given in the question that x+ y> z2 or x2 + y2 - z> 0 

In turn, it means that cosα > 0 so 0° < α < 90°

So if the biggest angle of the triangle is less than 90° then all other will also be less than 90°.

Now we can say that Triangle is an Acute angled triangle

हम जानते है की जब  0° < θ < 90° तब  cosθ +ve होता है 

हम  cosine rule से कह सकते है की $$ cosα = \frac{x^2 + y^2 - z^2}{2xy}$$

प्रशन के अनुसार  x+ y> z2 or x2 + y2 - z> 0 

जिसका मतलब cosα > 0 और   0° < α < 90°

अगर त्रिभुज का सबसे बड़ा कोण 90° से कम  है तो सभी कोण  90° से कम होंगे ।

अब हम कह सकते है की त्रिभुज न्यून कोण त्रिभुज  होगा ।

Question 18

What is the value of $$\frac{\cos50^{\circ}}{\sin40^{\circ}}+\frac{3cosec 80^{\circ}}{\sec10^{\circ}}- 2\cos50^{\circ} cosec40^{\circ}°$$  ?​​​​​​​

$$\frac{cos50°}{sin 40°} + \frac{ 3 cosec80°}{  sec10°} - 2cos50°.cosec40° $$ का मान क्या है?


Options

A

5

5

B

3

3

C

4

4

D

2

2


Solution:

Correct Answer:

D

2

2


$$\frac{cos50°}{sin 40°} + \frac{ 3 cosec80°}{  sec10°} - 2cos50°.cosec40°$$

cos50° = cos(90° - 50°) = sin40°

cosec80° = sec10°

cosec40° = sec50°

1 + 3 - 2 = 2

$$\frac{cos50°}{sin 40°} + \frac{ 3 cosec80°}{  sec10°} - 2cos50°.cosec40°$$

cos50° = cos(90° - 50°) = sin40°

cosec80° = sec10°

cosec40° = sec50°

1 + 3 - 2 = 2

Question 19

A alone can do a work in 11 days. B alone can do the same work in 22 days. C alone can do the same work in 33 days. They work in the following manner:

Day1: A and B work.
Day2: B and C work.
Day3: C and A work.
Day4: A and B work. And so on.
In how many days will the work be completed?

A अकेला एक काम को 11 दिनों में कर सकता है। B अकेला उसी कार्य को 22 दिनों में कर सकता है। C अकेला उसी कार्य को 33 दिनों में कर सकता है। वे निम्नलिखित तरीके से काम करते हैं:

दिन 1: A और B काम करते हैं।

दिन 2: B और C काम करते हैं।

दिन 3: C और A काम करते हैं।

दिन 4: A और B काम करते हैं। और वे इसी तरह आगे भी काम करते हैं।

कार्य कितने दिनों में पूरा होगा?


Options

A

6 days

6 days

B

3 days

3 days

C

9 days

9 days

D

12 days

12 days


Solution:

Correct Answer:

C

9 days

9 दिनों में


Lets total work = 66 

Now efficiencies of A, B and C = 6, 3 and 2

Work done on Day 1 = A + B = 6 + 3 = 9

Work done on Day 2 = B + C = 3 + 2 = 5

Work done on Day 3 = C + A = 2 + 6 = 8

Work done in 3 days = 9 + 5 + 8 = 22

Now work done in 9 days = 12 × 3 = 66

माना कुल कार्य  = 66 

अब  A, B और  C की क्षमता  = 6, 3 और  2

पहले दिन किया गया कार्य  = A + B = 6 + 3 = 9

दूसरे  दिन किया गया कार्य = B + C = 3 + 2 = 5

तीसरे दिन किया गया कार्य = C + A = 2 + 6 = 8

3 दिनो में  किया गया कार्य = 9 + 5 + 8 = 22

9 दिनो में   किया गया कार्य = 12 × 3 = 66

Question 20

$$ \text{What is the simplified value of} \frac{(x+y+z) (xy+yz+zx)- xyz} { (x+y) (y+z) (z+x) } ?$$

$$ \frac{(x+y+z) (xy+yz+zx)- xyz} { (x+y) (y+z) (z+x) }$$ का सरलीकृत मान कितना होगा?


Options

A

1

1

B

x

x

C

y

y

D

z

z


Solution:

Correct Answer:

A

1

1


$$ \frac{(x+y+z) (xy+yz+zx)- xyz} { (x+y) (y+z) (z+x) }$$

$$ \text{Let's put  x = y = z = 1}$$

$$ \frac{(1+1+1) (1+1+1)- 1} { (1+1) (1+1) (1+1) }$$

$$ \frac{9 - 1} { 8 } = 1$$ 

$$ \frac{(x+y+z) (xy+yz+zx)- xyz} { (x+y) (y+z) (z+x) }$$

$$ \text{x = y = z = 1}$$

$$ \frac{(1+1+1) (1+1+1)- 1} { (1+1) (1+1) (1+1) }$$

$$ \frac{9 - 1} { 8 } = 1$$ 

Question 21

Average age of 7 students of a class is 28 years. Average age of first three students is 30 years. Age of fourth student is 4 years less than the age of fifth student. Ages of last two students is same and is 5 more than the average age of first three students. What is the average age of fourth and fifth student?

एक कक्षा के 7 छात्रों की औसत आयु 28 वर्ष है। प्रथम तीन छात्रों की औसत आयु 30 वर्ष है। चौथे छात्र की आयु, पाँचवें छात्र की आयु से 4 वर्ष कम है। अंतिम दो छात्रों की आयु समान है तथा प्रथम तीन छात्रों की औसत आयु से 5 वर्ष अधिक है। चौथे तथा पाँचवें छात्र की औसत आयु कितनी है?


Options

A

20 years

20 years

B

16 years 

16 years 

C

18 years 

18 years 

D

36 years 

36 years 


Solution:

Correct Answer:

C

18 years 

18 वर्ष


The average age of 7 students = 28 years

Total age of 7 students = 28 × 7 = 196

The average age of the first three students = 30 years

Total age of first three students = 30 × 3 = 90

Total age of last two students = 35 × 2 = 70

Age of fourth student = a

Age of fifth student = a + 4

average age of fourth and fifth student = a + 2

a + a + 4 + 70 + 90 = 196

2a + 4 = 36

a + 2 = 18 years

 

कक्षा के 7 छात्रों की औसत आयु = 28 years

कक्षा के 7 छात्रों की कुल  आयु = 28 × 7 = 196

प्रथम तीन छात्रों की औसत आयु = 30 years

प्रथम तीन छात्रों की कुल आयु = 30 × 3 = 90

अंतिम दो छात्रों  की कुल आयु = 35 × 2 = 70

चौथे छात्र की आयु = a

पाँचवें छात्र की आयु  = a + 4

चौथे तथा पाँचवें छात्र की औसत आयु = a + 2

a + a + 4 + 70 + 90 = 196

2a + 4 = 36

a + 2 = 18 years

Question 22

Salary of Mohit is 60 percent more than Vijay. Salary of Vijay is how much percent less than Mohit?

मोहित का वेतन विजय के वेतन से 60 प्रतिशत अधिक है। विजय का वेतन मोहित के वेतन से कितना प्रतिशत कम है?


Options

A

45

45

B

42.5 

42.5 

C

47.5

47.5

D

37.5

37.5


Solution:

Correct Answer:

D

37.5

37.5 प्रतिशत


Salary of Vijay = 100

Salary of Mohit = 160

$$\text{Salary of Vijay is percent less than Mohit = }\frac{60 × 100}{160} = 37.5%$$

 

विजय का वेतन = 100

मोहित का वेतन = 160

विजय का वेतन मोहित के वेतन से प्रतिशत कम है = $$\frac{60 \times 100}{160} = 37.5%$$

​​​​​​​

Question 23

A sum of ₹1250 has to be distributed among A, B, C and D. Total share of B and D is equal to (14/11) of total share of A and C. Share of D is half of share of A. Share of C is 1.2 of Share of A. What are the shares of A, B, C and D respectively?

₹1250 को A, B, C तथा D में विभाजित किया जाना है। B तथा D का कुल हिस्सा, A तथा C के कुल हिस्से का (14/11) है। D का | हिस्सा, A के हिस्से का आधा है। C का हिस्सा, A के हिस्से का 1.2 गुना है। A, B, C तथा D के हिस्से क्रमशः कितने-कितने है?


Options

A

₹350, ₹525, ₹300, ₹125

₹350, ₹525, ₹300, ₹125

B

₹250, ₹575, ₹300, ₹175

₹250, ₹575, ₹300, ₹175

C

₹250, ₹575, ₹300, ₹125

₹250, ₹575, ₹300, ₹125

D

₹250, ₹525, ₹300, ₹125

₹250, ₹525, ₹300, ₹125


Solution:

Correct Answer:

C

₹250, ₹575, ₹300, ₹125

₹250, ₹575, ₹300, ₹125


A + B + C + D = 1250

11(B + D) = 14(A + C)

A = 2D, C = 1.2A = 2.4D

11(B + D) = 14(2D + 2.4D) = 14 × (4.4D)

10B + 10D = 56D

B = 4.6D

2D + 4.6D + 2.4D + D = 1250

10D = 1250

D = 125

A = 2D = 250

B = 4.6D = 575

​​​​​​​C = 2.4D = 300

A + B + C + D = 1250

11(B + D) = 14(A + C)

A = 2D, C = 1.2A = 2.4D

11(B + D) = 14(2D + 2.4D) = 14 × (4.4D)

10B + 10D = 56D

B = 4.6D

2D + 4.6D + 2.4D + D = 1250

10D = 1250

D = 125

A = 2D = 250

B = 4.6D = 575

​​​​​​​C = 2.4D = 300

Question 24

How many numbers are there from 400 to 700 in which the digit 6 occurs exactly twice?

400 से 700 तक ऐसी कितनी संख्याएं हैं, जिनमें अंक 6 ठीक दो बार आता है?


Options

A

19

19

B

18

18

C

20

20

D

21

21


Solution:

Correct Answer:

C

20

20


Let's assume the number is - 66_

In the position of _ there can be any number except 6 then there are 9 numbers like that 

660, 661, 662, 663, 664, 665, 667, 668, 669

And the number is - 6_6

In the position of _ there can be any number except 6 then there are 9 numbers like that 

606, 616, 626, 636, 646, 656, 676, 686, 696

And the number is - _66

then there are only two numbers are possible which are in the range of 400 to 700

466, 566

So total numbers that are from 400 to 700 in which the digit 6 occurs exactly twice 

9 + 9 + 2 = 20

माना की वो संख्या है  - 66_

_  की जगह 6 के अलावा 9 संख्याए है जो आ सकती है 

660, 661, 662, 663, 664, 665, 667, 668, 669

और अगर संख्या  - 6_6

_  की जगह 6 के अलावा 9 संख्याए है जो आ सकती है 

606, 616, 626, 636, 646, 656, 676, 686, 696

और अगर संख्या - _66

तब ऐसे दो ही संख्याए ही हो सकती है जो 400 से 700 में आती है 

466, 566

400 से 700 तक आने वाली संख्याएं हैं, जिनमें अंक 6 ठीक दो बार आता है - 

9 + 9 + 2 = 20

Question 25

$$ \text{Which of the following given value is greater than} \sqrt[3]{12}?$$

दिया गया कोन सा मान $$\sqrt[3]{12}$$ से अधिक है?


Options

A

$$\sqrt[12]{33214}$$

$$\sqrt[12]{33214}$$

B

$$\sqrt[5]{60}$$

$$\sqrt[5]{60}$$

C

$$\sqrt[6]{121}$$

$$\sqrt[6]{121}$$

D

$$\sqrt[9]{1500}$$

$$\sqrt[9]{1500}$$


Solution:

Correct Answer:

A

$$\sqrt[12]{33214}$$

$$\sqrt[12]{33214}$$


Question 26


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 27


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 28


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 29


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 30


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 31


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 32


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 33


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 34


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 35


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 36


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 37


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 38


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 39


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 40


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 41


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 42


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 43


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 44


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 45


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 46


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 47


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 48


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 49


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 50


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 51


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 52


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 53


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 54


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 55


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 56


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 57


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 58


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 59


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 60


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 61


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 62


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 63


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 64


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 65


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 66


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 67


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 68


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 69


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 70


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 71


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 72


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 73


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 74


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 75


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 76


Options

A

B

C

5×10​​​-8

5×10​​​-8

D

6×10-8

6×10-8


Solution:

Correct Answer:

D

6×10-8

6×10-8


​​​​

Question 77


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 78


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 79


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 80


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 81


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 82


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 83


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 84


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 85


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 86


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 87


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 88


Options

A

B

C

D


Solution:

Correct Answer:

D


Question 89


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 90


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 91


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 92


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 93


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 94


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 95


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 96


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 97


Options

A

B

C

D


Solution:

Correct Answer:

A


Question 98


Options

A

B

C

D


Solution:

Correct Answer:

B


Question 99


Options

A

B

C

D


Solution:

Correct Answer:

C


Question 100


Options

A

B

C

D


Solution:

Correct Answer:

C


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