MathJax Inequality Region Area In the XY-plane, the area, in sq. units, of the region defined by the inequalities \( y \geq x + 4 \) and \( -4 \leq x^2 + y^2 + 4(x – y) \leq 0 \) is: 1. \( 3\pi \) 2. \( 2\pi \) 3. \( 4\pi \) 4. \( … Read more
MathJax Question Let \( x, y, \) and \( z \) be real numbers satisfying: \( 4(x^2 + y^2 + z^2) = a \), \( 4(x – y – z) = 3 + a \). Then \( a \) equals: 1. \( 1 \) 2. \( 4 \) 3. \( 3 \) 4. \( 1 … Read more
MathJax Question For any natural number \( n \), let \( a_n \) be the largest integer not exceeding \( \sqrt{n} \). Then the value of \( a_1 + a_2 + \cdots + a_{50} \) is When 10^100 is divided by 7, find the remainder. a. 1 b. 6 c. 3 d. 4
Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches … Read more
Ratios + Simple Equations A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold … Read more
Interactive Quiz: Renu and Seema’s Work Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of … Read more
Interactive Quiz: Radius of Incircle ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. What is the length, in cm, of the radius of the incircle of \( \triangle ADE \)? Your Answer: cm Submit Detailed Solution: Step 1: Understand the … Read more
Interactive Quiz: Initial Grains Quantity A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, … Read more
Interactive Quiz: Milk and Water Ratio A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass is: 1 : … Read more
Interactive Quiz An amount of Rs 10,000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank … Read more