Comprehension:
In a certain number system there are only two notations to represent numbers: ▵ and β .
0 is represented by ▵ and 1 by β. The subsequent numbers are represented in the following manner:
2 is represented as β▵.
3 is represented as ββ,
4 is represented as β▵▵,
5 is represented as β▵β and so on.
How will you represent 81 in the given number system?
A principal amount of ₹1,000 yields a simple interest of ₹180 over a period of 2 years. What is the annual rate of simple interest?
"If the given symbols mean:
'+' means 'divided by'
'-' means 'multiplied by'
'x' means 'minus'
'÷' means 'plus'
Then, find the value of the following expressions: 60 + 5 - 4 × 10 ÷ 2=?
10 friends went for dinner and planned to split Rs. 200 equally. 2 didn't pay. How much did each of the rest pay?
A, B, and C invested ₹24,000, ₹36,000, and ₹40,000 respectively. A's investment was for 12 months, B's for 8 months, and C's for 6 months. The total profit is ₹50,000. What is B's share of the profit?
The average age of a committee of 9 members increases by 3 years when two men aged 42 and 44 years are replaced by two women. What is the average age of these two women?
There are 6 consecutive integers and 5 consecutive integers. The average of the 6 integers is 2 less than the average of the 5 integers. The sum of the 5 integers is 4 more than the sum of the 6 integers. Find the average of the 6 integers.
A TV set is available for ₹19,650 in cash or for ₹3,100 as a cash down payment and three equal annual instalments. If the shopkeeper charges interest at the rate of 10% per annum compounded annually, calculate the amount of each instalment.
A mobile phone retailer sells a phone for EP and earns a profit of 20%. For a special festive offer, he marks the same phone at ₹1.5P. At the offer, he provides a discount of 10%. What will be the percentage profit that he will make during the festive offer?
A gadget is sold at a 15% discount on its marked price. This sale leads to a profit of 20% on its cost price.If the profit earned is ₹450, what would have been the selling price if the gadget was sold at a 25% discount on its marked price?
A, B, and C can complete a certain task in 20, 30, and 60 days, respectively. How many days will it take for A to finish the work if he receives help from B and C every third day?
Two distinct grades of rice, one priced at ₹80 per kilogram and the other at ₹120 per kilogram, are amalgamated in an undisclosed proportion. The resultant blend is retailed at ₹132 per kilogram, securing a profit margin of 20% on the overall cost price. Determine the precise ratio in which the two rice varieties were intermingled.
The ratio of the speeds of a car and a bus is 3: 4. if the bus covers a distance of 320 km in 4 hours, what is the speed of the car in km/h?
An individual invested certain amounts in three different schemes P, Q, and R at simple interest rates of 7% p.a., 9% p.a., and 11% p.a. respectively. If the total interest accrued in one year was ₹2520 and the amount invested in Scheme R was 250% of the amount invested in Scheme P and 300% of the amount invested in Scheme 0, what was the amount invested in Scheme P?
A tower stands 50 meters tall. From its peak, the angles of depression to the top and bottom of a nearby building are measured at 30° and 45°, respectively. Determine the approximate height of the building as well as the horizontal distance separating the tower from the building.
A sphere is melted and recast into 8 identical cones, each with radius 3 cm and height 4 cm. What was the radius of the original sphere?
A circular fountain with a radius of 7 m is encircled by a grass bed that is 3.5 m wide. Determine the ratio of the area of the grass bed to the area of the fountain.
A tent designed as a triangular prism features a triangular base with an area of 20 m? and a height of 6 m. What is the volume of this tent?
Three non-overlapping, non-touching circles are drawn in a plane. What is the maximum number of distinct common tangents that can be drawn to them in total?
In a circle, chord AB and chord CD intersect at E such that AE : EB = 2: 3 and CE: ED = 5: 2. If AB =X and CD = y, which of the following is true?
A chord in a circle with radius 10 cm subtends an angle of 90° at the center. What is the area of the minor segment?
Find the part of the sentence that contains an error:
It was the misalignment between projected and actual data (1)/ that cast doubt not only on the calculations (2)/ but also on the assumptions that (3)/ underlied the funding strategy. (4)
Select the sentence containing the homonym of the highlighted word:
The artisan engraved a cartouche around the royal name.
The process of redirecting unacceptable desires into socially acceptable and valued activities is called :