Apex

Q.01- A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is: A. 12π $\mathrm{cm}^{3}$ B. 15π $\mathrm{cm}^{3}$ C. 16π $\mathrm{cm}^{3}$ D. 20π $\mathrm{cm}^{3}$ [bg_collapse view=”button-green” color=”#4a4949″ icon=”eye” expand_text=”Show Answer” collapse_text=”Hide Answer” ] Answer- A Solution:- Solution(By Apex…

Q- Men, women and children are employed to do a work in the proportion of 3 : 2 : 1 and their wages as 5 : 3 : 2. When 90 men are employed, total daily wages of all amounts to Rs.10350. Find the daily wages of a man. A. Rs.45 B. Rs.57.50 C. Rs.115 D. Rs.75 Show Answer Answer- D Solution:- Solution(By Apex team) Let the numbers of men, women and children are 3y, 2y and y, respectively Given,…

Q- 2 men and 1 woman can do a piece of work in 14 days. while 4 women and 2 men can do the same work in 8 days. If a man gets Rs.90 per day, what should be the wages per day of a women? A). Rs.48 B). Rs.60 C). Rs.72 D). Rs.135 [bg_collapse view=”button-green” color=”#4a4949″ icon=”eye” expand_text=”Show Answer” collapse_text=”Hide Answer” ] Answer- B Solution:- Solution(By Apex team) Let man…

Q- 4 men and 6 women get Rs.1600 by doing a piece of work in 5 days. 3 men and 7 women get Rs.1740 by doing the same work in 6 days. In how many days, 7 men and 6 women can complete the same work getting Rs.3760? A. 6 days B. 8 days C. 10 days D. 12 days Show Answer Answer- B Solution:- Solution(By Apex team) In 5 days, (4 men + 6 women) get = Rs.1600 Therefore, In 1 day, (4 men + 6 women)…

To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is:

Q. To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is: A. 2.5 kgB. 5 kgC. 7.5 kg D. 10 kg Show Answer Answer-B Solution:- Let the quantity of water mixed be x kg. Let CP of 1 kg of pure milk = Rs. 1. Hence,

In what ratio must a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength?

Q. In what ratio must a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength? A. 1 : 2B. 1 : 3C. 2 : 1 D. 3 : 1 Show Answer Answer-B Solution:-

In a 729 litres mixture of milk and water, the ratio of milk to water is 7 : 2. to get a new mixture containing milk and water in the ratio 7 : 3, the amount of water to be added is:

Q. In a 729 litres mixture of milk and water, the ratio of milk to water is 7 : 2. to get a new mixture containing milk and water in the ratio 7 : 3, the amount of water to be added is: A. 81 litresB. 71 litresC. 56 litres D. 50 litres Show Answer Answer-A Solution:- Quantity of milk in 729 litre of mixture Quantity of water = 729 – 567 = 162 litres Let x litre of water be added to become…

An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3…?

Q. An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in new alloy will be: A. B. C. D. Show Answer Answer-A Solution:- Ratio of Zinc, Copper and Tin is given as, Now, let the first alloy be 12 kg (taken as 4 kg…

The ratio, in which tea costing Rs. 192 per kg is to be mixed with tea costing Rs. 150 per kg so that the mixed tea when sold for Rs. 194.40 per kg, gives a profit of 20%.

Q. The ratio, in which tea costing Rs. 192 per kg is to be mixed with tea costing Rs. 150 per kg so that the mixed tea when sold for Rs. 194.40 per kg, gives a profit of 20%. A. 2 : 5B. 3 : 5C. 5 : 3 D. 5 : 2 Show Answer Answer-A Solution:- CP of first tea = Rs. 192 per kg. CP of Second tea = Rs. 150 per kg. Mixture is to be sold in Rs. 194.40 per kg, which has included 20% profit. So, SP…

There is a tree between houses of A and B. If the tree leans on A’s House, the tree top rests on his window which is 12 m from ground.

Q. There is a tree between houses of A and B. If the tree leans on A’s House, the tree top rests on his window which is 12 m from ground. If the tree leans on B’s House, the tree top rests on his window which is 9 m from ground. If the height of the tree is 15 m, what is distance between A’s and B’s house? A. 21 mB. 25 mC. 16 m D. 12 m Show Answer Answer-A Solution:- In ΔSTR, by Pythagoras…

Shadow of a man is 1/√3 times the height of the man. What will be the sun’s angle of elevation?

Q. Shadow of a man is   times the height of the man. What will be the sun’s angle of elevation? A. 135°B. 45°C. 30° D. 60° Show Answer Answer-D Solution:- Shadow length Height of man

Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45° with the ground. How far are the houses from each other if one house is 25m and other is 10m in height?

Q. Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45° with the ground. How far are the houses from each other if one house is 25m and other is 10m in height? A. 18 mB. 12 mC. 7.5 mD. 15 m Show Answer Answer-D Solution:- In ∠ABR, ∠ARB = 90° and ∠BAR = 45° Sum of angles of a triangle = 180° So ∠ABR = 180 – 90 – 45 =…

A tree breaks and falls to the ground such that its upper part is still partially attached to its stem. At what height did it break, if the original height of the tree was 24 cm and it makes an angle of 30° with the ground?

Q. A tree breaks and falls to the ground such that its upper part is still partially attached to its stem. At what height did it break, if the original height of the tree was 24 cm and it makes an angle of 30° with the ground? A. 12 cmB. 8 cmC. 9.5 cm D. 7.5 cm Show Answer Answer-B Solution:- Let the tree break at height h cm from ground at point M. The broken part makes angle of 30° ∴…

Mohan looks at a tree top and the angle made is 45°. He moves 10 cm back and again looks at the tree top but this time angle made is 30°. How high is the tree top from ground?

Q. Mohan looks at a tree top and the angle made is 45°. He moves 10 cm back and again looks at the tree top but this time angle made is 30°. How high is the tree top from ground? A. B. C. D. Show Answer Answer-D Solution:- Let PQ be three and M and N be positions where Mphan stands. (As, PQ = MQ)

Tree top’s angle of elevation is 30° from a point on ground, 300m away the tree. When the tree grew up its angle of elevation became 60° from the same point. How much did the tree grow?

Q. Tree top’s angle of elevation is 30° from a point on ground, 300m away the tree. When the tree grew up its angle of elevation became 60° from the same point. How much did the tree grow? A. B. C. D. Show Answer Answer-B Solution:-

A flagstaff is placed on top of a building. The flagstaff and building subtend equal angles at a point on level ground which is 200 m away from the foot of the building. If the height of the flagstaff is 50 m and the height of the building is h, which of the following is true?

Q. A flagstaff is placed on top of a building. The flagstaff and building subtend equal angles at a point on level ground which is 200 m away from the foot of the building. If the height of the flagstaff is 50 m and the height of the building is h, which of the following is true? A. h3 – 50h2 + (200)2h + (200)250 = 0 B. h3 – 50h2 – (200)2h + (200)250 = 0 C. h3 + 50h2 + (200)2h – (200)250 =…

From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30° and 60° respectively. What is the height of the pole?

Q. From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30° and 60° respectively. What is the height of the pole? A. 52 mB. 50 mC. 66.67 mD. 33.33 m Show Answer Answer-A Solution:- Consider the diagram shown above. AC represents the hill and DE represents the pole Given that AC = 100 m ∠XAD = ∠ADB = 30° (∵ AX || BD ) ∠XAE = ∠AEC = 60° (∵ AX ||…