Quantitative Aptitude:August 19 Interactive Quiz

Explanation
The fact that the discriminant is zero indicates that the quadratic equation has two equal real roots. This means that the solutions to the equation will be rational and equal.

Explanation
If the first natural number is less than or equal to eight, then the highest value of the second natural number can be found by substituting the first natural number with its maximum value of eight in the given equation. Using this substitution, we can solve the equation: 2(8) + 3x < 24. Simplifying, we get 16 + 3x < 24. Subtracting 16 from both sides, we have 3x < 8. Dividing both sides by 3, we find that x < 8/3. Since x is a natural number, the highest possible value for x is 2. Therefore, the highest value of the second natural number is 7.

Explanation
The shopkeeper bought 800 kg of rice for Rs 3840. He had to sell it at a loss equal to the amount he received for 16 kg. This means that the loss per kg is Rs 240 (3840/16). To find the selling price per kg, we subtract the loss from the cost price per kg. Therefore, the selling price per kg is Rs (3840/800) - 240 = Rs 40.

Explanation
The number of triangles formed by using 7 points in a plane can be calculated using the combination formula. Since no three points are collinear, we can choose any 3 points out of the 7 to form a triangle. Therefore, the number of triangles is given by the combination formula C(7, 3) which is equal to 35.

Explanation
There are 6 books that need to be arranged on a shelf. The number of ways to arrange these books can be found using the concept of permutations. Since the books are on different subjects, the order in which they are arranged matters. Therefore, the number of ways to arrange the books is equal to 6 factorial, denoted as 6!. This is calculated as 6 x 5 x 4 x 3 x 2 x 1, which equals 720. Therefore, the correct answer is 720.

Explanation
If the diameter of a wire is increased by 10%, the volume of the wire remains the same. Since the volume of a wire is directly proportional to its length, we can conclude that the length of the wire will decrease by approximately 17%. This can be calculated using the formula for the volume of a cylinder, V = πr^2h, where r is the radius of the wire and h is the height (length) of the wire. By increasing the diameter, the radius will increase by 10%, which means the new radius will be 1.1 times the original radius. To keep the volume the same, the length of the wire must decrease by 1/1.1 or approximately 0.909. This corresponds to a decrease of approximately 9.1% in length. Therefore, the answer is 17%.

Explanation
When S is increased by 10%, it means S becomes 1.1 times its original value. If we substitute this new value of S into the equation R = S^2, we get R = (1.1S)^2 = 1.21S^2. This means that R has increased by 21% compared to its original value.

Explanation
Pipe A can fill the remaining one-third of the cistern in 12 minutes, which means it can fill one-third of the cistern in 12 minutes. Similarly, pipe B can fill one-third of the cistern in 8 minutes. Therefore, the combined rate of filling the cistern is the sum of their individual rates. The combined rate is (1/12 + 1/8) = 5/24. To fill the entire cistern, it will take the combined rate 24/5 minutes, which is equal to 4 minutes and 48 seconds. Therefore, the correct answer is 14 minutes and 40 seconds.

Explanation
The train is crossing a platform, so we can calculate the length of the train by subtracting the length of the platform from the total distance covered by the train in 10 seconds. The total distance covered by the train in 10 seconds can be calculated by multiplying the speed of the train (90 km/hr) by the time (10 seconds). Converting the speed from km/hr to m/s by dividing by 3.6, we get 25 m/s. Multiplying the speed by the time, we get 250 m. Subtracting the length of the platform (160 m) from the total distance covered by the train, we get the length of the train as 90 meters.

Explanation
The average of 4 consecutive even numbers is 9, which means that the sum of these numbers is 36 (9 multiplied by 4). To find the first number, we can subtract the sum of the remaining three numbers from 36. Since the second number is 8, the sum of the remaining three numbers is 8 + 10 + 12 = 30. Subtracting 30 from 36 gives us 6, which is the first number in the sequence.

Explanation
If a certain sum of money doubles in 10 years at simple interest, it means that the interest earned is equal to the original sum of money. Therefore, the rate of interest would be 10%.

Explanation
The maximum value of a quadratic function occurs at the vertex of the parabola. To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. In this case, a = 1, b = 5, and c = 16. Plugging these values into the formula, we get x = -5/2(1) = -5/2. To find the maximum value of the function, we can substitute this x-coordinate into the function, f(x) = (-5/2)^2 + 5(-5/2) + 16 = 39/4. Therefore, the maximum value of the function is 39/4.