**The average age of a man and his son is 28 years. The ratio of their ages is 3 :1 respectively. What is the man's age?**- 30 years
- 38 years
- 44 years
- 42 years
- None of these

Answer: Option D

Total sum of man's age & his son's age =28 × 2 = 56 Now, the Ratio of their ages is 3 : 1.Therefore, Man's age = (3/4) × 56 = 42

So, the correct answer is option D.

**A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC is perpendicular to BD and ∠CAD = θ, then find the ∠ABC.**- θ
- θ/2
- 2θ
- 3θ

Answer: Option C

∠B + ∠D = 180°

∠A + ∠C = 180°

∠BAC = ∠BCA ∠DAC = ∠DCA

∴∠DAB = ∠DCB = 90°

∠DAC = θ

∴∠ADE = 90° - θ = ∠CDE

∴ ∠ABC = 180° – 2(90° - θ) = 2θ**If tan θ + cot θ = 2, then the value of tan**^{2}θ + cot^{2}θ is- 2
- 1
- √2
- 0

Answer: Option**A**

tan θ + cot θ = 2 , On squaring both sides,

(tan θ + cot θ)^{2}= 4, ⇒ tan^{2}θ + cot^{2}θ + 2 tan θ cot θ = 4,

⇒ tan^{2}θ + cot^{2}θ = 4 – 2 = 2 , [tan θ . cot θ = 1]

**How many integers are there between 300 and 600 that are divisible by 9?**- 33
- 31
- 28
- 25
- None of these

Answer: Option A.

The sequence is 306,… 594

594=306+(n-1)9⇒288=(n-1)9⇒n=33**What will be the ratio of petrol and kerosene in the final solution formed by mixing petrol and kerosene that are present in three identical vessels in the ratio 4:1,5:2 and 6 :1 respectively?**- 166 : 22
- 83 : 22
- 83 : 44
- 78 : 55
- None of these

Answer: Option B

Three identical vessels in the ratio 4:1,5:2 and 6 :1 respectively.

Petrol : kerosene

(4 : 1 = 5)7

(5 : 2 = 7)5

(6 : 1 = 7)5

28 : 7 = 35

25 : 10 = 35

30 : 5 = 35

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**The respective ratio of radii of two right circular cylinders (A & B) is 2 : 5. The respective ratio of the heights of cylinders A and B is 3 : 1. What is the respective ratio of volumes of cylinders A and B?**- 12 : 25
- 9 : 25
- 9 : 20
- 3 : 5
- 12 : 35

Answer: Option A

R_{1}/R_{2/}=2/5 H_{1}/H_{2}=3/1 V_{1}/V_{2}= (R_{1}/R_{2})^{2}× ( H_{1}/H_{2})= 12/25**Raja gives 30% of his salary to his mother, 40% of the remaining salary he invests in an insurance scheme and PPF in the respective ratio of 4 : 3 and the remaining he keeps in his bank account. If the difference between the amount he gives to his mother and that he invests in insurance scheme is Rs. 8400, how much is Raja’s salary?**- Rs. 60,000
- Rs. 62,000
- Rs. 64,000
- Rs. 65,000
- Rs. 54,000

Answer: Option A

Let Raja salary= R

Salary given to mother = 0.3 R

Money left=0.7 R

Now, Money invested in Insurance scheme= 0.7*0.4*4/7 R= 0.16 R

Difference of money in bank and with mother= 0.14R

Now, 0.14 R=8400, Hence R= 60,0000**A, B, C and D are four consecutive odd numbers and their average is 42. What is the product of B and D?**- 1860
- 1890
- 1845
- 1677
- None of these

Answer: Option C

As there are As diff. Is same so average should lie between B and C so B is 41 & C is 43 so D must be 45 as we have to find the product of B and D so it would be 1845.**A basket contains 3 blue, 5 black and 3 red balls. If 2 balls are drawn at random, what is the probability that one is black and one is red?**- 2/11
- 8/11
- 9/11
- 3/11
- None of these

Answer: Option D

Selecting 1 black ball out of 5 =^{5}C_{1}ways.Selecting on red ball out of 3 =^{3}C_{1}ways

The required probability = (^{5}C_{1}×^{3}C_{1})/^{11}C_{2}= 3/11**A man buys a land and gives for it 20 times the annual rent Find the rate of interest he gets for his money.**- 10%
- 24%
- 45%
- 18%
- 5%

Answer: Option B

Let annual rent is 1 Rs. so buys the land at 20 Rs. So by investing Rs.20 he is getting Rs.1 as interest. so on Rs.100 he gets Rs.5 . so rate%=5%.Hence option E is the answer.