Educational

Simplify 3(a^4b^3)^10 × 5(a^2b^2)^3 Simplify: \(3(a^4b^3)^{10} \times 5(a^2b^2)^3\) Solution \[ = 3 \times 5 \cdot a^{40}b^{30} \cdot a^{6}b^{6} \] \[ = 15 \cdot a^{46}b^{36} \] Final Answer: \[ \boxed{15a^{46}b^{36}} \] Next Question / Full Exercise

Assertion Reason MCQ on Rational Numbers Question Statement-1 (Assertion): There are two rational numbers whose sum and product both are rationals. Statement-2 (Reason): There are numbers which cannot be written in the form \( \frac{p}{q} \), \( q \neq 0 \), where \( p, q \) are integers. Options: (a) Statement-1 is true, Statement-2 is

Assertion Reason MCQ on √2 and Number Properties Question Statement-1 (Assertion): \( \sqrt{2} \) is an irrational number. Statement-2 (Reason): The sum of a rational number and an irrational number is an irrational number. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2 is

Assertion Reason MCQ on √3 Irrational Question Statement-1 (Assertion): \( \sqrt{3} \) is an irrational number. Statement-2 (Reason): The square root of a positive integer which is not a perfect square is an irrational number. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2

Assertion Reason MCQ on Irrational Numbers Product Question Statement-1 (Assertion): The product of any two irrational numbers is an irrational number. Statement-2 (Reason): There are two irrational numbers whose product is not an irrational number. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2

Assertion Reason MCQ on Irrational Numbers Question Statement-1 (Assertion): The sum of any two irrational numbers is an irrational number. Statement-2 (Reason): There are two irrational numbers whose sum is a rational number. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2 is true;

Assertion Reason MCQ on √2 Irrational Question Statement-1 (Assertion): \( \sqrt{2} \) is an irrational number. Statement-2 (Reason): The decimal expansion of \( \sqrt{2} \) is non-terminating and non-recurring. Options: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2 is true; Statement-2 is not a

Make 1/3 Terminating Decimal MCQ Question The smallest rational number by which \( \frac{1}{3} \) should be multiplied so that its decimal expansion terminates after one place of decimal is: (a) \( \frac{1}{10} \) (b) \( \frac{3}{10} \) (c) 3 (d) 30 Solution We want: \[ \frac{1}{3} \times x = \text{terminating decimal with one decimal

Trailing Zeros in Product MCQ Question The number of consecutive zeroes in \(2^3 \times 3^4 \times 5^4 \times 7\) is: (a) 3 (b) 2 (c) 4 (d) 5 Solution Trailing zeros are formed by factors of \(10 = 2 \times 5\). Count the number of 2s and 5s: \[ 2^3 \Rightarrow 3 \text{ factors of

Irrational Number Between 2 and 2.5 MCQ Question An irrational number between \(2\) and \(2.5\) is: (a) \( \sqrt{11} \) (b) \( \sqrt{5} \) (c) \( \sqrt{22.5} \) (d) \( \sqrt{12.5} \) Solution Square the interval: \[ 2^2 = 4, \quad (2.5)^2 = 6.25 \] So we need a number whose square lies between 4