NPAT Common 2020 QP2

Water is flowing at the rate of 4 km/h through a pipe of radius 7 cm into a rectangular tank with length and breadth as 25 m and 22 m, respectively. The time (in hours) in which the level of water in the tank will rise by 28 cm is $$(\text{ take } \pi=\frac{22}{7})$$:

In an arithmetic progression, the $$4^{th}$$ term equals three times the first term and the $$7^{th}$$ term exceeds two times the third term by one. The sum of its first ten terms is:

The ratio of the sum of the first m terms to the sum of the first n terms of an arithmetic progression is $$m^{2}:n^{2}$$. What is the ratio of its $$17^{th}$$ term to the $$29^{th}$$ term?

The sum of the first three tenns of an infinite geometric progression, with common ratio less than one, is 56. If 1, 7 and 21 are subtracted from its first, second and third term, respectively, then these three tenns are in the arithmetic progression. The common ratio of the progression is:

If $$a^{2}+c^{2}+17=2(a-2b^{2}-8b)$$, then the value of $$(a+b+c)[(a-b)^{2}+(b-c)^{2}+(c-a)^{2}]$$ is:

The graphs of 2x - y = 1 aud 3x - 2y = - 1 intersect at a point P, which lies on the graph of the equation:

If the roots of the equation $$x^{2}-2(1+3k)x+7(3+2k)=0$$ are equal, where k<0, then which of the following is true?

Which of the following statements is true about the solutions of the equation $$\mid x^{2}-5x\mid=6$$ ?

When 8 is added to each of the given 'n' numbers, the sum of the resulting numbers is 207. When 5 is subtracted from each of the given 'n' numbers, the sum of the resulting numbers is 77. What is the mean of the given 'n' numbers?

The variance of the ten integers 11 , 12, 13, .... , 20 is: