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→Algebraic Identities — all question types→Maths STD 9 question papers→CBSE Board STD 9 question papers→CBSE Board question paper generator→

Similar questions

Statement-1 (A): The angles subtended by a chord at any two points of a circle are equal.
Statement-2 (R): Angles in the same segment of a circle 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: Median of the given data $34, 31, 42, 43, 46, 25, 39, 45, 32,$ is $39.$
Reason: When the number of observations $(n)$ is even arrange the numbers in the ascending order then the median is the mean of the and $|n + 1|$

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: Two diameters of a circle will necessarily intersect.
Reason: Diameters will always intersect each other at the centre 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: If $x = 2k - 1$ and $y = k$ is a solution of the equation $3x - 5y - 7 = 0$, then the value of $k$ is $10$.
Reason: A linear equation in two variables has infinitely many solutions.

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 median of the data $13, 15, 16, 17, 19, 20$ is $\frac{30}{2}$
Reason: Median $=\frac{(16+17)}{2}=\frac{33}{2}$

Statement-1 (A): The graph of the linear equation $4 x+3 y=24$ mects $x$-axis at (-6,0).
Statement-2 (R): Points on $x$-axis are of the form (a, 0), where a is a variable.

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: Tangent is a line that touches the circle at any point.
Reason: Radius is always parallel to the tangent at the point where it touches the circle.

Statement-1 $(A)$ : The product of $\left(x^2+4 y^2+z^2+2 x y+x z-2 y z\right)$ and $(-z+x-2 y)$ is $x^3-8 y^3-z^3-6 x y z$
Statement-2 $(R): \quad a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$

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: This system is a linear system: $x + y = 2, 2x - 3y = 0$.
Reason: Some equations may not even be linear to begin with, but they can be brought to a linear form by multiplying both sides of the equation by a suitable expression.

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 sides of a triangle are in the atio of $25 : 14 : 12$ and its perimeter is $510\ cm.$ Then the area of the triangle is $4449.08\ cm^2.$
Reason: Perimeter of a triangle $= a + b + c,$ where $a, b, c$ are sides of a triangle.