PnC Basics Find the number of all positive integers up to 500 with non-repeating digits. Show/Hide Solution Type of Number Digit Positions Choices at Each Step Reasoning Count 1-digit _ 1-9 → 9 choices Any digit 1-9 is valid 9 2-digit Tens digit 1-9 → 9 choices Tens digit can’t be 0 81 Units digit … Read more
The number of distinct integer solutions (x, y) of the equation |x + y| + |x – y| = 2, is If 10^68 is divided by 13, the remainder is1) 8 2) 9 3) 4 4) 5 Find the number of all positive integers up to 500 with non-repeating digits. Show/Hide Solution Type of Number … Read more
After two successive increments, Gopal’s salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was ?1) 252) 203) 27.54) 30 A regular octagon ABCDEFGH has sides of length 6 cm each. Then the … Read more
Surd Algebra Question Q1 \( a \) and \( b \) are natural numbers, then the value of \( a + b \) is: \[ (a + b\sqrt{3})^2 = 52 + 30\sqrt{3} \] Sequence Sum Solution Q2 Consider the sequence: \[ t_1 = 1, \quad t_2 = -1, \quad t_n = \left( \frac{n – 3}{n … Read more
Question 1 Roots and Expression Value The roots \( \alpha, \beta \) of the equation \( 3x^2 + \lambda x – 1 = 0 \) satisfy \[ \frac{1}{\alpha^2} + \frac{1}{\beta^2} = 15. \] The value of \( (\alpha^3 + \beta^3)^2 \) is: Question 2 Trapezium + Triangles ABCD is a trapezium in which AB is … Read more
Ques 1 When 3^333 is divided by 11, the remainder is Ques 2 A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is 1) 4095 2) 1023 … Read more
Inequality Question All the values of \( x \) satisfying the inequality \( \frac{1}{x + 5} \leq \frac{1}{2x – 3} \) are: 1) \( -5 < x < \frac{3}{2} \) or \( x > \frac{3}{2} \) 2) \( -5 < x < \frac{3}{2} \) or \( \frac{3}{2} < x \leq 8 \) 3) \( x ... Read more
Ages + RatiosWhen Rajesh’s age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima’s age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become 1) 2 : 12) 3 : 23) 4 : 34) 5 : 4 Mixtures … Read more
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
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