If $y=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\dots .,$ then $x$ is equal to
 

Important Questions on Fundamentals of Mathematics

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 1 - Fundamentals of Mathematics>Exercise 1>Q 1

$P, Q$ and $R$ are three natural numbers such that $P$ and $Q$ are primes and $Q$ divides $PR$. Then out of the following the correct statement is:

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 1 - Fundamentals of Mathematics>Exercise 1>Q 2

The number of prime factors of ${\left(3\times 5\right)}^{12}{\left(2\times 7\right)}^{10}{\left(10\right)}^{25}$ is:

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 1 - Fundamentals of Mathematics>Exercise 1>Q 3

If $x, y$ are odd positive integers, then $x^2+y^2$ must be divisible by:

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 1 - Fundamentals of Mathematics>Exercise 1>Q 4

A $4$-digit number is formed by repeating a $2$-digit number such as $2525, 3232$ etc. Any number of this form is exactly divisible by:

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 1 - Fundamentals of Mathematics>Exercise 1>Q 5

Let $D$ be a recurring decimal of the form $D=0.a_1{a}_2{a}_1{a}_2{a}_1{a}_2\dots \dots ,$ where digits $a_1$ and $a_2$ lie between $0$ and $9.$ Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by $D?$

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 1 - Fundamentals of Mathematics>Exercise 1>Q 6

Let $Q=\left(\frac{x}{y}\right)$ where $x$ and $y$ are positive real numbers. If both $x$ and $y$ are increased equally, then

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 1 - Fundamentals of Mathematics>Exercise 1>Q 7

Solve for $x$ such that $\left|x+2\right|<4$

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 1 - Fundamentals of Mathematics>Exercise 1>Q 8

Solution of $\left|x-1\right|\ge \left|x-3\right|$ is