List of top Mathematics Questions on Number System

The coefficient of \( x^3 \) in the power series expansion of \( \frac{1+4x-3x^2}{(1+3x)^3} \) is
If $-\frac{2}{3}<x<\frac{2}{3}$, then the value of the $5^{th}$ term in the expansion of $\frac{1}{\sqrt{2-3x}}$ when $x = \frac{1}{2}$ is
If 3 sisters and 8 brothers are together playing a game, then the number of ways in which all the sisters and brothers are to be seated around a circle such that all the three sisters are not seated together is
If \( {}^{27}P_{r+7} = 7722 \cdot {}^{25}P_{r+4} \), then r =
If $-\frac{2{3}<x<\frac{2}{3}$, then the value of the $5^{th}$ term in the expansion of $\frac{1}{\sqrt{2-3x}}$ when $x = \frac{1}{2}$ is}
If 3 sisters and 8 brothers are together playing a game, then the number of ways in which all the sisters and brothers are to be seated around a circle such that all the three sisters are not seated together is
If \( {}^{27}P_{r+7} = 7722 \cdot {}^{25}P_{r+4} \), then r =
The coefficient of \( x^3 \) in the power series expansion of \( \frac{1+4x-3x^2}{(1+3x)^3 \) is}
If $P_n$ denotes the product of the binomial coefficients in the expansion of $(1 + x)^n$, then find \[ \frac{P_{n+1}}{P_n}. \]
The number of all possible positive integral solutions of the equation \(xyz = 30\) is:
If \(x\) is so large that terms containing \(x^{-3}\), \(x^{-4}\), \(x^{-5}\), \ldots can be neglected, then the approximate value of \[ \left(\frac{3x - 5}{4x^2 + 3}\right)^{-4/5} \] is:
If \(k\) is a positive integer and \(10^k\) is a divisor of the number \(9^{11} + 11^9\), then the greatest value of \(k\) is:
The number of divisors of \(7!\) is:

In the following figure, four overlapping shapes (rectangle, triangle, circle, and hexagon) are given. The sum of the numbers which belong to only two overlapping shapes is ________.


 

The table shows the data of 450 candidates who appeared in the examination of three subjects – Social Science, Mathematics, and Science. How many candidates have passed in at least one subject?


 

Which one of the following numbers is odd one out?
31541 42651 53791 64871 75981
If \( \times \) means \( + \), \( + \) means \( \div \), \( - \) means \( \times \), and \( \div \) means \( - \), then evaluate: 8 \( \times \) 7 \( - \) 8 \( + \) 40 \( \div \) 2.
Let \( C \) denote the set of all tuples \( (x, y) \) which satisfy \( x^2 = 2^y \), where \( x \) and \( y \) are natural numbers. What is the cardinality of \( C \)?
The number of common tangents of two intersecting circles is:
If \(130 = 15 \times 8 + 10\) and \(15 = 5 \times 3 + 0\), then \(\mathrm{HCF}(130,\,15)\) will be:
Which of the following is a rational number?
The product of two numbers is \(8670\) and their HCF is \(17\). What is their LCM?
The HCF of two consecutive even numbers is:
If \(q\) is a positive integer, which of the following is {not an odd positive integer?}
Which of the following has a terminating decimal expansion?