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The correct answer is (a) 9 : 4 (b) 4 : 13

Given two numbers are in the ratio 6: 13

Let the required number be 6x and 13x

The LCM of 6x and 13x is 78x

= 78x = 312

x = (312/78)

x = 4

Thus the numbers are 6x = 6 (4) = 24

13x = 13 (4) = 52

i. 72, 60

Ratio = \(\frac{72}{60}\) = \(\frac{12\,\times\,6}{12\,\times\,5}\) = \(\frac{6}{5}\) = 6 : 5

ii. 38, 57

Ratio = \(\frac{38}{57}\) = \(\frac{19\,\times\,2}{19\,\times\,3}\) = \(\frac{2}{3}\) = 2 : 3

iii. 52, 78

Ratio = \(\frac{52}{78}\) = \(\frac{26\,\times\,2}{26\,\times\,3}\) = \(\frac{2}{3}\) = 2 : 3

Length of a straw = 12 cm = 120 mm 

its diameter = 6 mm 

According to question, required ratio, 

= 6 : 120 = (6/120)

= 1/20 = 1 : 20

The ratio of present ages of Rehana and her mother is 2 : 7

Let the common multiple be x. 

∴ Present age of Rehana = 2x years and Present age of Rehana’s mother = 7x years 

After 2 years, 

Rehana’s age = (2x + 2) years 

Age of Rehana’s mother = (7x + 2) years

 According to the given condition, 

After 2 years, the ratio of their ages will be 1 : 3 

∴ \(\frac{2x\,+ \,2}{7x\, + \,2}\) =  \(\frac{1}{3}\)

∴ 3(2x + 2) = 1(7x + 2) 

∴ 6x + 6 = 7x + 2 

∴ 6 – 2 = 7x – 6x 

∴ 4 = x 

∴ x = 4 

∴ Rehana’s present age = 2x = 2 x 4 = 8 years 

∴ Rehana’s present age is 8 years.

(C) 10

x² = 4 x 25 

∴ x² = 100 

∴ x = 10

Present age of Vatsala = 14 years 

Present age of Sara = 10 years

After x years,

Vatsala’s age = (14 + x) years 

Sara’s age = (10 + x) years

 According to the given condition, 

After x years the ratio of their ages will become 5 : 4 

∴ \(\frac{14\, +\,x}{10\,+\,x}\) = \(\frac{5}{4}\)

∴ 4(14 + x) = 5(10 + x) 

∴ 56 + 4x = 50 + 5x 

∴ 56 – 50 = 5x – 4x 

∴ 6 = x 

∴ x = 6 

∴ After 6 years, the ratio of their ages will become 5 : 4.

The ratio of two numbers is 31 : 23 

Let the common multiple be x. 

∴ First number = 31x and 

Second number = 23x 

According to the given condition, 

Sum of the numbers is 216 

∴ 31x + 23x = 216 

∴ 54x = 216 

∴ x = 4 

∴ First number = 31x = 31 x 4 = 124 

Second number = 23x = 23 x 4 = 92

∴ The two numbers are 124 and 92.

(D) 9

3x + 5x = 24 

∴ 8x = 24 

∴ x = 3 

∴ Number of bananas with Shubham = 3x = 9

The ratio of length and breadth of a rectangle is 3 : 1 

Let the common multiple be x. 

Length of the rectangle (l) = 3x cm and 

Breadth of the rectangle (b) = x cm 

Given, perimeter of the rectangle = 36 cm 

Since, Perimeter of the rectangle = 2(l + b)

∴ 36 = 2(3x + x) 

∴ 36 = 2(4x) 

∴ 36 = 8x

∴ x = 36/8 = 9/2 = 4.5

Length of the rectangle = 3x = 3 x 4.5 = 13.5 cm 

∴ The length of the rectangle is 13.5 cm and its breadth is 4.5 cm.

Present age of Vatsala = 14 years 

Present age of Sara = 10 years 

After x years, 

Vatsala’s age = (14 + x) years 

Sara’s age = (10 + x) years 

According to the given condition, 

After x years the ratio of their ages will become 5 : 4

∴ (14 + x)/(10 + x) = 5 : 4

∴ 4(14 + x) = 5(10 + x) 

∴ 56 + 4x = 50 + 5x 

∴ 56 – 50 = 5x – 4x 

∴ 6 = x 

∴ x = 6 

∴ After 6 years, the ratio of their ages will become 5 : 4.

The ratio of present ages of Albert and Salim is 5 : 9 

Let the common multiple be x.

∴ Present age of Albert = 5x years and

Present age of Salim = 9x years 

After 5 years,

Albert’s age = (5x + 5) years and 

Salim’s age = (9x + 5) years

 According to the given condition, 

Five years hence ratio of their ages will be 3 : 5 

 \(\frac{5x+5}{9x+5}\) = \(\frac{3}{5}\)

∴ 5(5x + 5) = 3(9x + 5) 

∴ 25x + 25 = 27x + 15 

∴ 25 – 15 = 27 x – 25 x 

∴ 10 = 2x 

∴ x = 5 

∴ Present age of Albert = 5x = 5 x 5 = 25 years

 Present age of Salim = 9x = 9 x 5 = 45 years 

∴ The present ages of Albert and Salim are 25 years

 and 45 years respectively.

(a) Both ‘A’ and ‘R’ are true and ‘R’ is the correct explanation to ‘A’

India is the founding member of the WTO.  

(a) A (ii) B (iii) C (iv) D (i)

Total mass of organic compound = 0.468 

Mass of barium sulphate formed = 0.668 g 

1 mol of BaSO₄ = 233 g of BaSO₄ contains 32 g of Sulphur 

Thus, 0.668 g of BaSO₄ solution contains 

= \(\frac{32\times0.668}{233}\) g of Sulphur 

= 0.0917 g of Sulphur 

Therefore, Percentage of Sulphur, 

= \(\frac{0.0197}{0.468}\) × 100 

= 19.59% 

Hence, the percentage of Sulphur in the given compound is 19.59%

(iv) Assertion is wrong statement but reason is correct statement. 

Sulphur vapour like O₂ contains two unpaired electrons in antibonding orbitals (π*)and thus S vapour is paramagnetic.

Ozone being endothermic compound readily decomposes on heating to give dioxygen and nascent oxygen. O₃→ O₂ + [O] 

Due to nascent oxygen, O₃ is a powerful oxidizing agent.

‘B’ in BF₃ has sp² hybridisation.

BF₃ is weaker Lewis acid than BCl₃ because of more effective bonding in case of F due to smaller size, than Cl.

The Right option is : (d) iodine

Al₂O₃ is amphoteric where Cl₂O₇ is acidic oxide.

Three enzymes of industrial importance are proteases, pectinases and lipases.

Biodiesel is a fuel made from vegetable oils, fats or greases. Biodiesel fuel can be used in diesel engines without altering the engine. Pure biodiesel is non-toxic, biodegradable and produces lower level of air pollutants than petroleum-based diesel fuel. The Government of India approved the National Policy on Biofuels in December 2009 and identified Jatropha curcas as the most suitable oilseed for biodiesel production. Pongamia species is also a suitable choice for production of biodiesel.

(a) In both cases pollen grains come from the same plant. So they are genetically similar. 

(b) In geitonogamy pollen grains are transferred from the anther to the stigma of another flower, of the same plant whereas in xenogamy pollen grains are transferred from the anther, to the stigma of a different flower.

(a) Escherichia

Correct Answer is: (d) Lipase

A -Gobargas 

B – Saccharomyces cerevisiae 

C – Anabaena 

D-Biological control

(c) Jatropha curcas

Lipases are used in detergents to remove oily stains from the clothes.

The use of naturally occurring or genetically engineered microorganisms to reduce or degrade pollutants is called bioremediation. Bioremediation is less expensive and more sustainable than other remediations available. It is grouped into in-situ bioremediation (treatment of contaminated soil or water in the site) and ex-situ bioremediation (treatment of contaminated soil or water that is removed from the site and treated).

Correct option is: (c) Ozone

Correct option is: (d) photosynthesis

14th January 1986.

In 1985 Ganga Action Plan started.

Answer is (b) fungi

(c) Trichoderma

(b) India and Japan Government

(i) Male and female flowers are present on different plants. 

(ii) The stamens and stigma of a bisexual flower mature at different times. 

(a) Anthers mature earlier than the stigma and release pollens. 

(b) The stigma matures earlier than the anther. 

(iii) Flowers are self-sterile or self-incompatible. 

(iv) Chasmogamous flowers are present with exposed stamens and stigma which facilitate cross-pollination.

Grape wine is of two types, red wine and white wine. For red wine, black grapes are used including skins and sometimes the stems also are used. In contrast white wine is produced only from the juice of either white or red grapes without their skin and stems.

Correct option is: (b) Photosynthesis

Correct option is: (d) Calcium

1. Forest Fires

2. Photosynthesis

3. Industrial nitrogen fixation

4. Squirrel

Correct option is: (b) Herbivores

Correct option is: (b) 78

The Ganga action plan was launched on 14th January 1986. The main objective of the programme is to improve the water quality of River Ganges by interception, diversion and treatment of domestic sewage and to identify grossly polluting units to prevent pollution.

Cyclosporin A is used as an immunosuppressive agent in organ transplant patient.

Beer – 3 to 5 % alcohol; Wine – 9 to 14% alcohol; Distilled spirits – 35 to 50% alcohol.