Download App

Factorization Of Algebraic Expressions [NEW] — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions [NEW]1 Mark
MCQ
Statement-1 (A): If $a+b+c=5$ and $a b+b c+c a=10$, then $a^3+b^3+c^3-3 a b c=25$
Statement-2 (R): $a^3+b^3+c^3-3 a b c=(a+b+c)\left\{(a+b+c)^2-3(a b+b c+c a)\right\}$
  • 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 correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • ✓
    Statement-1 is false, Statement-2 is true.
✓

Answer

Correct option: D.
Statement-1 is false, Statement-2 is true.
d

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Assertion (A) & Reason (B) MCQ" from Factorization Of Algebraic Expressions [NEW]→Factorization Of Algebraic Expressions [NEW] — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

Statement-1 (A): $a^3+b^3+3 a b-1=(a+b-1)\left(a^2+b^2+a+b-a b+1\right)$
Statement-2 (R): $ a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2+a b+b c+c a\right)$
→
Statement-1 (A): $\sqrt{2}$ is an irrational number.
Statement-2 (R): The sum of a rational number and an irrational number is an irrational number.
→
Statement-1 (A): If A, B, C, D are four points such that $\angle B A C=30^{\circ}$ and $\angle B D C=60^{\circ}$, then D is the centre of the circle through A, B and C.
Statement-2 (R): The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
→
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\text{x}^4=\frac{\text{X}^5}{\text{x}^1}.$ Reason: $ \frac{\text{a}^{\text{b}}}{\text{a}^{\text{c}}}=\text{a}^{\text{b - c}}.$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
→
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The real number is either rational or irrational.
Reason: $ \sqrt7$ is a rational number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
→
Statement-1 (A): If x and y are rational and irrational numbers respectively, then x + y is an irrational number.
Statement-2 (R): If x and y are two irrational numbers, then x + y is an irrational number
→
Statement-1 (A): If the surface areas of two spheres are in the ratio $9: 25$, then their radii are in the ratio $3: 5$.
Statement-2 (R) : If surface areas of two spheres are in the ratio $S_1: S_2$, then their radii are in the ratio $\sqrt{S_1}: \sqrt{S_2}$.
→
Consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
  1. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but Reason is not a correct explanation of Assertion (A).
  3. Assertion (A) is true and Reason (R) is false.
  4. Assertion (A) is false and Reason (R) is true.
Assertion (A)Reason (R)
$\sqrt{3}$ is an irrational number.Square root a positive integer which is not a perfect square is an irrational number.
The correct answer is: (a), (b), (c), (d).
→
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $32^{\frac{2}{5}}=4$
Reason: $(32)^{\frac{2}{5}}=(2^5)^{\frac{2}{5}}=22=4$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
→
Statement-1 (A): The graph of the equation $x=-5$ is a line parallel to $y$-axis at a distance of 5 units to the left of $y$-axis.
Statement-2 (R): The line parallel to $y$-axis at a distance a units to the left of $y$-axis is given by the equation $x=-a$.
→