NPAT 27th June 2021 Shift 1

A cylindrical container of 36 cm height and 48 cm diameter is filled with sand. Now, its sand is used to form a conical heap of radius 30 cm. The height (in cm) of the conical heap is:

The ratio of the sums of the first 12 terms and the first 18 terms of an arithmetic progression is 4:9. What is the ratio of the $$10^{th}$$ and the $$15^{th}$$ terms?

The sum of the first six terms of an arithmetic progression is 54 and the ratio of the 10^{th} term to its 30^{th} term is 11:31. What is the 50^{th} term of the progression?

$$\text{If }3x^{2}-5x+1=0,\text{ then the value of } x^{2}+\frac{1}{9x^{2}}\text{ will be:}$$

The sum of an infinite geometric progression is 18 and the sum of the squares of the terms of the progression is 81. The first term and the common ratio of the geometric progression are, respectively:

The cost of 2 oranges and 3 apples is ₹28. If the cost of an apple is doubled, then the cost of 3
oranges and 5 apples will be ₹75. The original cost of 7 oranges and 4 apples is:

If $$\alpha$$ and $$\beta$$ are the roots of the equation $$2x^2 + 5x + k = 0$$ and $$4(\alpha^2 + \beta^2 + \alpha \beta) = 23$$, then which of the following is true?

If -4 is a root of the equation $$x^2 + ax - 4 = 0$$ and the equation $$x^2 + ax + b = 0$$ has equal roots, then what will be the value of $$\sqrt{a^2 + b^2}$$?

There are n numbers. When 50 is subtracted from each of these numbers, the sum of the numbers so obtained is -10. When 46 is subtracted from each of the original n numbers, then the sum of the numbers so obtained is 70. What is the mean of the original n numbers?

The mean deviation (correct to one decimal place) of the numbers 3, 10, 6, 11, 14, 17, 9, 8, 12 about the mean is: