MCQS Questions 6.1 A wire is stretched by a weight \( w \). If the diameter of the wire is reduced to half of its previous value, the extension will become: (a) one half (b) double (c) one fourth (d) four times Correct Option: (d) four times Reason: Extension is inversely proportional to the square…
MCQs Question 5.1 Work done is maximum when the angle between the force \( F \) and the displacement \( d \) is: (a) \( 0^\circ \) (b) \( 30^\circ \) (c) \( 60^\circ \) (d) \( 90^\circ \) Correct Option: (a) \( 0^\circ \) Reason: Work is maximum when the force and displacement are…
MCQs 1.1 The instrument that is most suitable for measuring the thickness of a few sheets of cardboard is: (a) metre rule (b) measuring tape (c) Vernier Callipers (d) micrometer screw gauge Correct Answer: (d) micrometer screw gauge Reason: A micrometer screw gauge is specifically designed for precise measurements of small thicknesses, such as sheets…
The solution of the new math book for 9th class step by step is given below. Question 1: Solve and represent the solution on a real line (i) \( 12x + 30 = -6 \) \[12x + 30 = -6\] \[12x = -6 – 30\] \[12x = -36\] \[x = -3\] Solution: \( x =…
Mathematics provides us with powerful formulas to simplify expressions and solve equations efficiently. Among these, square and cube formulas are widely used to expand or factorize algebraic expressions. These formulas help reduce complex calculations and are essential for solving problems in algebra, geometry, and physics. In this article, we will explore the key square and…
Question 1: Factorize by identifying common factors (i) \( 6x + 12 \) \[= 6(x + 2)\] (ii) \( 15y^2 + 20y \) \[= 5y(3y + 4)\] (iii) \( -12x^2 – 3x \) \[= -3x(4x + 1)\] (iv) \( 4a^2b + 8ab^2 \) \[= 4ab(a + 2b)\] (v) \( xy – 3x^2 + 2x \)…
Factorization is a fundamental concept in mathematics, enabling us to break down complex expressions into simpler, more manageable components. It plays a vital role in solving equations, simplifying fractions, and understanding the structure of algebraic expressions. By mastering factorization, you can tackle mathematical problems with greater confidence and efficiency. In this article, we will define…
1. State the domain and range of each relation. For \(A = \{1, 2, 3, 4\}\), find \(A \times A\) first, then solve other parts. Find \(A \times A\) \[A \times A = \{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3),…
Sets are a fundamental concept in mathematics, and operations on sets allow us to combine, compare, and analyze their elements. These operations help solve problems in various fields, including computer science, probability, and logic. This article covers the union, intersection, difference, and complement of sets, explores disjoint and overlapping sets, and delves into operations on…
1. Find the characteristic of the following numbers (i) \(5287\) \[\text{Characteristic }= 3\] (ii) \(59.28\) \[\text{Characteristic }= 1\] (iii) \( 0.0567\) \[\text{Characteristic }=\overline{2}\] (iv) \(234.7\) \[\text{Characteristic }= 2\] (v) \(0.000049\) \[\text{Characteristic }=\overline{5}\] (vi) \(145000\) \[\text{Characteristic }= 5\] 2 Find the logarithm of the following numbers (i) \(43\) \[\text{Characteristic }= 1\] \[\text{Mantissa }= 6335\] \[\log(43) =…
