List of top Questions asked in NPAT

The scores of a batsman in 10 different test matches were 42, 38, 48, 70, 46, 63, 55, 34, 54, and 44. What is the mean deviation about the median of these scores?
A die is constructed so that when it is thrown, each of the three even numbers 2, 4 and 6 is twice as likely to come up as each of the odd outcomes 1, 3 and 5. What is the probability that 4 comes up when the die is thrown once?
X and Y are the two points that are 135 m apart on the ground on either side of a pole and in the same line. The angles of elevation of a bird sitting on the top of the pole from X and Y are 30° and 60° respectively. The distance of Y from the foot of the pole (in m) is:
Calculate the variance of: 2, 4, 5, 6, 8, 17.
If the equations \( x^2 + px + 12 = 0 \), \( x^2 + qx + 15 = 0 \), and \( x^2 + (p+q)x + 36 = 0 \) have a common positive root, then what is the value of \( (2p - q) \)?
When 5 is subtracted from each of given \( n \) numbers, the sum of numbers so obtained is 210. When 8 is subtracted from each of the given \( n \) numbers, then the sum of numbers so obtained is 156. What is the mean of the given \( n \) numbers?
The graphs of the equations \( 2x + 3y = a \) and \( x + 2y = b \) intersect at a point \( P(\alpha, \beta) \). What is the value of \( (3\alpha + 2\beta) \)?
If \( a + b + c = 2 \), \( a^2 + b^2 + c^2 = 36 \), then the value of \( a^3 + b^3 + c^3 - 3abc \) is:
The ratio of the sum of the first \( n \) terms to the sum of the first \( s \) terms of an arithmetic progression is \( r^2 : s^2 \). What is the ratio of its 8th term to the 23rd term of this same progression?
The sum of the first \( n \) terms of a geometric progression is 255, the \( k \)-th term is 128, and the common ratio is 2. The value of \( k \) satisfies the equation:
The sum of the roots of the equation \( |x - 7|^2 + 2|x| - 7| = 24 \) is:
A person borrowed a certain sum on compound interest and agreed to return it in two years in two equal annual instalments. If the rate of interest is 10% p.a. and each annual instalment is ₹4,840, then the interest paid by him was:
Last year, the ratio of the prices of two articles A and B was 3 : 5. This year, the price of A is increased by 25% and that of B is decreased by ₹210. If the ratio of the present prices of A and B is 15 : 14, then the price of A last year was:
If \( a_1, a_2, a_3, \dots \) is an arithmetic progression with the common difference of 1 and \( a_2 + a_4 + a_6 + \dots + a_{98} = 93 \), then \( \sum_{i=1}^{98} a_i \) is equal to \( k \). The sum of the digits of \( k \) is:
A dealer allows 32% discount on the marked price of an article and still gains 28%. If the cost price of the article is reduced by 10%, how much discount percent should the dealer allow now to get the same percentage of profit as before?
Water flows at the rate of 20 metre/minute through a cylindrical pipe whose radius is 1.5 cm. Using this pipe, how long (in hours) would it take to fill a conical vessel whose radius is 120 cm and depth is 72 cm?
A boat can go \( 1 \frac{3}{5} \) km upstream and \( 4 \frac{4}{5} \) km downstream in 48 minutes, while it can go 2 km upstream and 600 m downstream in 33 minutes. How much time (in hours) will it take to go 28.8 km downstream?
In a school, the number of boys is 40% more than the number of girls. If 60% of the number of boys and 54% of the number of girls are scholarship holders, then the percentage of students in the school who are NOT scholarship holders is:
Anu earns a profit of 18% by selling an article at a certain price. If she were to sell it for ₹10.50 more, she would have gained 25%. The original cost price of 12 such articles is (in ₹):
If \( a \), \( b \), and \( c \) are three fractions such that \( a<b<c \), and if the smallest fraction is divided by the middle fraction, the result is \( \frac{15}{16} \), which exceeds the largest fraction by \( \frac{3}{16} \). If \( a + b + c = \frac{49}{24} \), then what is the difference between \( c \) and \( b \)?
The sum of the first 15 terms of the series \[ \frac{1}{24} + \frac{1}{104} + \frac{1}{234} + \dots = \frac{a}{b}, \text{ where HCF}(a,b) = 1. \text{ What is the difference between } a \text{ and } b? \]
What is the value of the expression \[ \frac{(4.8)^4 + (3.5)^4 + 282.24}{(4.8)^2 + (3.5)^2 - 16.8} \]
The value of the expression \[ \frac{0.1\overline{8} \times 11.0 \times 0.8\overline{3}}{2.\overline{4} \times 0.\overline{6} \times 3 \times 0.1\overline{6}} \] is:
If \[ \frac{\sqrt{11} - \sqrt{120}}{\sqrt{11} + 6\sqrt{2}} = A\sqrt{6} + B\sqrt{5} + C\sqrt{3} + D\sqrt{10}, \text{ then the value of } (A + B + C + D) \text{ is:} \]
If the numerator of a fraction (in lowest form) is increased by \( \frac{1}{3} \) of itself and the denominator is decreased by \( \frac{1}{4} \) of itself, the fraction so obtained is \( \frac{21}{64} \). What is the difference between the denominator and the numerator of the original fraction?