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Given that a // b and c // d. 

∠1 = ∠3 (∵ vertically opposite angles) 

∠1 = ∠5 (∵ corresponding angles)

∠1 = ∠9 (∵ corresponding angles) 

Also ∠1 = ∠3 = ∠5 = ∠7 ; 

∠1 = ∠11 = ∠9 = ∠13 = ∠15 

Similarly ∠2 = ∠4 = ∠6 = ∠8 

Also ∠2 = ∠10 = ∠12 = ∠14 = ∠16

(B) 8, 4 

The ratio of the interior angle of first polygon to that of the second polygon is 3 : 2 and the number of sides in first are twice that in the second. The number of sides of the two polygons are 8, 4 

The distance between the near point and the far point is called the range of vision.

The grandmother was an old woman. She was short, fat and slightly bent. Her face was a criss-cross of wrinkles running from everywhere to everywhere. But she was beautiful.

दादी एक वृद्ध महिला थीं। वह एक छोटी, मोटी तथा थोड़ी सी कुबड़ी थीं। उनके चेहरे पर चारों ओर झुर्रियों की रेखाएं थीं। लेकिन वह सुंदर थीं।

The grandmother used to hobble. She had to put one hand on her waist to balance her stoop. She used to tell the beads of her rosary with the other hand.

दादी लंगड़ाकर चलती थीं। अपने कूबड़ को सहारा देने के लिए वह एक हाथ कमर पर रखती थीं। वह दूसरे हाथ से माला फेरा करती थीं।

1. on Thursday, 

2. on Monday, 

3. on Sunday, 

4. on Wednesday evening, 

5. on Tuesday at 5-30.

The author did not like the games that his grandmother used to play as a child. They seemed quite absurd and undignified on her part. He treated them like the fables of the Prophets she used to tell them.

लेखक को वे खेल पसंद नहीं थे जिन्हें दादी जब बच्ची थीं खेला करती थीं। वे उनके लिए बिल्कुल अविवेकपूर्ण तथा गरिमाहीन प्रतीत होते थे। वह उन्हें पैगम्बरों की कहानियों की भाँति लिया करते थे जो वह उन्हें सुनाया करती थीं।

This question is to be answered on the basis of students’ own understanding and experience. It is strongly recommended that students prepare the answer on their own.

The author had seen his old grandma for twenty long years. She had the same wrinkles and hunchback.

Grandmother brought a bundle of stale chapattis with her to the temple. The village dogs followed her. On return, she went on throwing the chapattis to the dogs who growled and fought with each other to have a piece of chapatti.

Grandmother had strong values and had zest for life. She lived the life the way she wanted it. She spun the wheel, told her beads, fed the dog in the village and sparrows in the city unmindful of changes around her. She played the drum with joy when she realized her impending death. She died a peaceful death after predicting it to all her family members. She is really a strong lady.

People said that grandma was once pretty and she even had a husband. This was hard to believe as the author had seen her old right from his boyhood days.

The author’s grandmother “accepted her seclusion with resignation”. She spent her days of loneliness by engaging herself in the wheel-spinning activity, reciting prayers and feeding the sparrows.

1. (b) tan⁻¹ ( 1/2 )

2. (c) tan⁻¹ ( 4/3 )

3. (d) tan⁻¹ ( 11/2 )

4. (b) tan^-1 (1/8)

5. (c) R , (− \(\cfrac\pi2\) , \(\cfrac\pi2\) )

B) beat an old dmm and sang songs

1. ( b ) sin⁻¹ ( \(\cfrac12\) )

2. ( c ) cos⁻¹ (\(\cfrac{\sqrt3}2\))

3. ( d ) tan⁻¹ (√3)

4. ( c ) \(\cfrac{\pi}2\) 

5. ( c ) [ −1, 1 ], [0 , π]

She suspended her prayer for a while. She called the women from neighbourhood, sang and played the drum along with them. The next morning she had fever. She told the family that she was about to die! She died in bed telling her beads and lisping her last prayer.

D) she told them her end was near.

Yes, she predicted her death. As she fell ill, she thought differently. She told the family members that her end was near. She lay peacefully in bed praying and telling her beads.

The old grandmother became more and more secluded from the family bonds as the years passed. Perhaps this is part of the ageing process. She did not show any emotional changes when the grandson went abroad despite the fact that she had sensed her end. When her end actually neared, she gathered the neighbouring women and sang for the last time with them, playing the drums.

The ‘sagging skins’ and ‘dilapidated drum’ symbolize the old body of hers, the song ‘home-coming of the warrior’ indicates the return of the soul or death of mortal life. It also shows that even as the body sags, the soul sings and sings louder still.

The subscript in bracket can be a variable, a constant or an expression to integer

(a) dimension

Antigen-antibody reaction is the basis of the technique called ELISA

ELISA (Enzyme linked immuno - sorbent Assay)

Correct Answer is : (b) India

(c) In Belur (Karnataka)

65 North Indian and 52 South Indian foodstalls

Correct option is  D) ₹ 1504

Correct option is (D) ₹ 1504

Discount = 6% of Rs 1600

\(=Rs(\frac6{100}\times1600)\)

= Rs 96

\(\therefore\) Selling price = Marked price - discount

= Rs (1600 - 96)

= Rs 1504

Converting both the given quantities in the same units, we have:

We know that,

= 1 kg = 1000g

Then,

= (2 × 1000) g + 250g: (3 × 1000) g

= 2250g: 3000g

HCF of 2250 and 3000 is 750

= (2250 ÷ 750) / (3000 ÷ 750)

= (3/4)

= 3 g: 4g

Correct option is  B) ₹ 50

Correct option is (B) ₹ 50

\(S.I.=Rs\frac{PRT}{100}\)

\(=Rs\frac{500\times5\times2}{100}\)

= Rs 50

Correct option is   C) \(\frac{PTR}{100}\)

Correct option is (C) \(\frac{PTR}{100}\)

Simple Interest \(=\frac{\text{Principal value }(P)\times\text{Rate }(R)\times\text{Time }(T)}{100}\)

\(=\frac{PRT}{100}\)

Converting both the given quantities in the same units, we have:

We know that,

= 1 km = 1000m

Then,

= (1 × 1000) m: 750m

= 1000m: 750m

HCF of 1000 and 750 is 250

= (1000 ÷ 250) / (750 ÷ 250)

= (4/3)

= 4m: 3m

A: B = 7: 5 and B: C = 9: 14

= (A/B) = (7/5) and (B/C) = (9/14)

= (A/B) × (B/C) = (7/5) × (9/14)

= (A/C) = (9/10)

Hence, A: C = 9:10

 D)  \(P(1+\frac{R}{100})^n\,-P\)

Correct option is (A) 88.8

111 : 125 \(=\frac{111}{125}=\frac{111}{125}\times100\%\)

\(=\frac{111}{5}\times4\%\) \(=\frac{111}{10}\times8\%\)

\(=\frac{888}{10}\%\) = 88.8%

Correct option is  A) 88.8

A: B = 5: 8 and B: C = 16: 25

= (A/B) = (5/8) and (B/C) = (16/25)

= (A/B) × (B/C) = (5/8) × (16/25)

= (A/C) = (2/5)

Hence, A: C = 2:5

A: B = 5: 6 and B: C = 4: 7

HCF of 5 and 6 is 1

= (5/6)

Then,

B: C= (4 × (6/4))/ (7 × (6/4))

B: C = (6 / (21/2))

B: C = 6: (21/2)

∴ A: B: C = 5: 6: (21/2)

A: B: C = 10: 12: 21

Correct option is  C) 5

Correct option is (C) 5

Number of time periods \(=\frac{2\frac{1}{2}\,years}{6\,months}\)

\(=\cfrac{\frac{5}{2}\,years}{\frac{1}{2}\,year}\)  \((\because\) 6 months = \(\frac12\) year)

\(=\frac52\times\frac21=5\)

Correct option is (A) 88.8%

111 : 125 \(=\frac{111}{125}\)

\(=\frac{111}{5^3}\) \(=\frac{111}{5^3}\times\frac{2^3}{2^3}\)

\(=\frac{111\times8}{10^3}\) \(=\frac{888}{1000}\)

\(=\frac{888}{1000}\times100\%\) = 88.8%

Correct option is  A) 88.8%

A: B = 3: 5 and B: C = 10: 13

HCF of 3 and 5 is 1

= (3/5)

Then,

B: C= (10 ÷ 2)/ (13 ÷ 2)

B: C = 5: (13/2)

∴ A: B: C = 3: 5: (13/2)

A: B: C = 6: 10: 13

Correct answer is

(D) (B) and (C)

Correct option is (D) 1:8

12.5% \(=\frac{12.5}{100}\) \(=\frac{125}{1000}\)

\(=\frac18\) = 1 : 8

Correct option is  D) 1:8

3x=3000

x=1000

Total money distributed =7x=7*1000=Rs.7000

D=9x =1800 

x=200.

 A and B when combines in 1 day they does 

= 2x+5x=7x 

7*200=1400 

For 2 days they complete 1400*2=2800 task.

Correct answer is

(C) product of extremes

Correct answer is

(A) simplest form

(a² + b ²)(b² + c² ) = (ab + bc)² 

b = ck; a = ck²

 L.H.S = (a² + b² ) (b² + c² ) 

= [(ck² ) + (ck²) ] [(ck)² + c² ] … [From (i) and (ii)] 

= [c² k² + c² k² ] [c² k² + c² ] 

= c² k² (k² + 1) c² (k² + 1)

 = c4k² (k² + 1)² 

R.H.S = (ab + bc)² 

= [(ck² ) (ck) + (ck)c]² …[From (i) and (ii)] 

= [c² k² + c² k]² 

= [c² k (k² + 1)]²= c⁴ (k + 1)² 

∴ L.H.S = R.H.S 

∴ (a² + b² ) (b² + c² ) = (ab + bc)²

Distance Speed =\( \frac{\text { Distance }}{\text { Time taken }}\) 

Speed of Ragdhari express = \(\frac{2880}{18}\)

Speed of Nilachala express = \(\frac{2880}{24}\)

Ratio of average speed = \(\frac{2880}{18}\) : \(\frac{2880}{24}\)

= 24:18 = 4:3

Correct answer is

(C) \(\frac{c + md}{c - md}\)