Quantitative Ap...

If it is given that A rook can attack all the cells that are either in the horizontal or vertical direction to the rook's position, find the number of ways you can place two identical rooks on the given 6*6 board such that they are not in attacking each other.

4 dice are thrown and the sum of the numbers noted is 10. Find the probability that all the numbers lie between 2 and 5 (both inclusive)?

AB = 8 cm and BC = 10 cm are sides of a rectangle ABCD. A perpendicular is drawn from A to the diagonal BD which meets the CB at X. What is the length of BX ?

A, B, C and D are natural numbers. A is 500% of the sum of C and D. A:B:C is 21:30:2. If B:D = x:y, where x and y are co-prime numbers, find the value of |x-y|.

Alloy P made up of 60% Cobalt, 24% Nickel and 16% Aluminium is fused with Alloy Q made up of Cobalt and Nickel. The final product is tagged as SS 100 and contains 54% Cobalt, 36% Nickel and 10% Aluminum. Which of the following best represents the constitution of Alloy Q?

What is the ratio of the maximum and the minimum distance of the point (8, 7) from the curve $$x^2 + y^2 - 4x +2y -20 = 0$$?

Aditya went to the market to purchase some fruits, he purchased 3 types of fruits which were mangoes, oranges and apples. He purchased mangoes and apples in the ratio of 5:8 and mangoes and oranges in the ratio 4:7. Find the minimum number of fruits that Aditya purchased.

Kaushik has Rs 90,000 with him and buys a refrigerator, sofa set, TV and dining table at Rs 23000, Rs 18000, Rs 21000, and Rs 13000 respectively, and he deposits the remaining money in the bank at the interest rate of 8% per annum for two years(Assume compound Interest). At the end of 2 years, he withdraws the money and sells all the items. He sells the refrigerator and sofa set at a profit of 12% and sells the TV and dining table at a loss of 8%. What is the approximate percentage change in the amount that Kaushik has at the end of two years? 

An infinite number of pipes numbered $$A_1,\ A_2\ ,\ A_3\ ,...$$, are connected to a tank such that each subsequent pipe (except $$A_1$$) is half as efficient as the previous one. These pipes, when functioning as inlet pipes, fill the tank together in 4 hours. In how many hours will the tank be filled if the even-numbered pipes ($$A_2,\ A_4\ ,\ A_6\ ,...$$) function as outlet pipes while the remaining continue filling the tank?

A shopkeeper buys 60 mangoes at a price of Rs 200 each . While travelling 20 of them get partly spoiled and he sells them at a price of Rs 140 each. He decides to earn an overall profit of 5 percent and looks at various alternative pricing strategies to sell the rest of the mangoes :

1) If he decides to mark up the price by 25 percent he must provide a discount of x percent so that he meets his target profit percentage .

2) If he decides to mark up the price by 50 percent he must provide a discount of y percent so that he meets his target profit percentage .

What is the value of [y-x] where [k] represents the greatest integer less than k.

If $$5X + 2 < 3Y$$ and $$Y = Z^{2} + 10$$, which of the following is necessarily true, given that X, Y and Z are real numbers?

Three taps A, B and C fill a tank in 20 hours, 15 hours, 30 hours respectively. There are 2 leakages with the same rate, one situated at one-fourth of the height of the tank and the other at half the height of the tank. If only one of the above leakages is present at the bottom of the full tank, then it alone can individually empty the tank in 60 hours, what is the total time taken to fill the tank(in hours)

In a small town called Hanumanthawaka, there are four busy milk vendors. Ramu, Laxmanan, Bharata Kumar and Shatrugn Sinha. Ramu sold milk to 70% of the households in the town. Laxmanan sold milk to 75%. Bharata Kumar sold to 80% and Shatrugn Sinha sold to 85% of the households. What is the minimum percentage of the households that bought from all four vendors?

It is known that all the households bought milk from atleast one of the four vendors.

The following figure shows an equilateral triangle with an incircle in it. Three smaller circles each touch the incircle and 2 sides of the triangle. Also, the incircle of the equilateral triangle is the circumcircle to a right-angled triangle, which is also the largest possible right-angled triangle(in terms of area) that can be drawn inside the circle. Find the area of the shaded region. It is given that the radius of the incircle of the outermost triangle is 1 unit.

A, B, C and D run a race from point P to Q(8km apart). They start at 8 a.m., 8:20 a.m., 8:40 a.m. and 9 a.m. respectively. The ratio of their speeds is 1:2:3:8. If B and C reach Q at same time, what is the time difference in the reaching time of A and D to Q?

Salil invested some amount in the stock market. His investment increased by some percentage after one year but in the second year, it decreased by the same percentage. At the end of the second year, his investment became Rs.5,04,000. Similarly, on increasing and decreasing in the same pattern, also with the same percentage, at the end of the fourth year, his investment became Rs.4,96,125. Following the same pattern, his investment (in nearest integer) at the end of the fifth year was

If ‘y’ satisfies the following equation:

$$\log_2 (9^{y-1} + 7)$$ = $$2 + \log_2 (3^{y-1} + 1)$$, then which of the following is true?

Two trains are running on the same track towards each other at $$70$$ km/hr and $$80$$ km/hr, respectively. A bird starts flying between the two trains at a $$100$$ km/hr speed and continues the back and forth until the two trains collide. How much distance is covered by the bird if the two trains are at a distance of $$150$$ km when the bird starts this exercise?

How many natural numbers 'n' (less than 50) exist such that $$n^{2} + 5n$$ has exactly 4 divisors?

In a triangle PQR, such that PQ = 28cm, QR = 26cm and PR = 30cm. If PS and QT are the angle bisectors and RU is altitude from R on side PQ which intersects PS and QT at X and Y respectively then find out the value of XY (In cm)?

If the equations $$x^2-lx+3 = 0$$ and $$x^2+kx-4 = 0$$ have one common root which is an integer, how many values of k+l exist if both k and l are integers.

Find the sum of the first 10 terms of the series: 0.8, 0.98, 0.998, 0.9998, 0.99998......