Statement-1 (A): a^3+3 8 a x+1 64 x^3-1 8 = (a+x 4 -1 2 ) (a^2+x^… - Vidyadip

MCQ

Statement-1 (A): $a^3+\frac{3}{8} a x+\frac{1}{64} x^3-\frac{1}{8}=\left(a+\frac{x}{4}-\frac{1}{2}\right)\left(a^2+\frac{x^2}{16}+\frac{1}{4}-\frac{a x}{4}+\frac{x}{8}+\frac{a}{2}\right)$
Statement-2 (R): $a^3+b^3+c^3+3 a b c=(a+b+c)\left(a^2+b^2+c^2+a b+b c+c a\right)$

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.
✓
Statement-1 is true, Statement-2 is false.
D
Statement- 1 is false, Statement- 2 is true.

✓

Answer

Correct option: C.

Statement-1 is true, Statement-2 is false.

c

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 Algebraic Identities [NEW]→Algebraic Identities [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): The decimal representation of $\frac{3}{8}$ is terminating.
Statement-2 (R): If the denominator of a rational number is of the form $2^m \times 5^n$, where m, n are non-negative integers, then its decimal representation is terminating.

Statement-1 (A): If P, Q, R, S are four points such that $\angle Q P R=40^{\circ}$ and $\angle Q S R=80^{\circ}$, then $S$ is the centre of the circle through Q, R and P.
Statement-2 (R): If A, B, C and D are four points such that $\angle B A C=60^{\circ}$ and $\angle B D C=60^{\circ}$, then A, B, C, D are concyclic points.

Statement-1 (A): The point $P(-7,0)$ lies on $x$-axis.
Statement-2 (R): The ordinate of every point on $y$-axis is positive.

Statement-1 (A): In Fig. if PQ|| RS, then $\angle A C B=90^{\circ}$.
Statement-2 (R): If two parallel lines are intersected by a transversal, then each pair of alternate angles are equal.

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: If p and q are prime, then HCF (p, q) = 1
Reason: $\frac{123}{6250}$ is a terminating Decimal.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Assertion is true but the reason is false.
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: Every rational number is an integer.
Reason: $\frac{3}{5}$ is not an integer.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Assertion is true but the reason is false.
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 Decimal fraction of $\frac{12}{125}$ is 0.096
Reason: The Decimal fraction of $\frac{1}{9}$ is 0.111.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Assertion is true but the reason is false.
Both assertion and reason are false.

Statement-1 (A): The point $P(0,12)$ lies on $y$-axis.
Statement-2 (R): The abscissa of every point on $y$-axis is zero

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 product of two consecutive positive integers is divisible by 2
Reason: The decimal expansion of $\frac{15}{169999}=0.0065789$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Assertion is true but the reason is false.
Both assertion and reason are false.

Statement-1 (A): The graphical representation of the frequency distribution

Marks:	0 - 20	20 - 40	40 - 60	60 - 100
Number of students:	10	15	20	25

is as given in Fig.
Statement-2 (R): In a histogram, the areas of the rectangles are proportional to the frequencies.