NPAT Common 2020 QP3

The cross-section of a canal is a rectangle surmounted by a semicircle. The length of the rectangle is the diameter of the semicircle and is equal to 10.5 m. The breadth of the rectangle is 6 m. If the water is flowing at a speed of 18 km/h, then the volume (in kilolitres) of the water discharged in 16 seconds is $$(\text{taken}  \pi =\frac{22}{7})$$ :

In an arithmetic progression $$a_{1},a_{2},......,a_{n}$$, if $$a_{1}+a_{3}+a_{5}=108$$ and $$a_{2}+a_{4}+a_{6}=102$$, then the $$16^{th}$$ term of the progression is:

In an arithmetic progression with 23 tenns, the sum of its $$21^{st},22^{nd}$$ and $$23^{rd}$$ terms is 264, and the sum of the three middle terms is 144. What is the $$18^{th}$$ term of the prngression?

The sum ofan infinite geometric series is 20 and the sum of the squares of its terms is 100. What is the sum of the first three terms of the original series?

If $$15x^{2}-9x+1=0,$$, then the va lue of $$9x^{2}+(25x^{2})^{-1}$$ is:

If ax + by - a + b = 0 and bx - ay - a - b = 0, then the value of (3x - 2y + 4) is:

If one root of the equation $$x^{2}+(2k+1)x+(k^{2}+2)=0$$ is twice the other root, then the value of k is a root of the equation:

The equation $$\mid x^{2}+x-6\mid -3x+7$$ has:

When 3 is subtracted from each of the given 'n' nmnbers, then the sum of the numbers so obtained is 84. When 8 is added to each of the given 'n' numbers, then the sum of the resulting numbers is 216. The mean of the given 'n' numbers is:

The mean of five observations is 4.4 and their variance is 8.24. If three of the five observations are I, 4 and 9, then the product of other two observations is: