MCQ 11 Mark
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 points $A(3, -1, 2), B(1, 2, -4), C(-1, 1, 2)$ and $D(1, -2, 8)$ are the vertices of a parallelogram.
Reason: Coordinates of mid$-$point of a line joining the points $A(x_1, y_1, z_1)$ and $B(x_1, y_2, z_2)$ is $\Big(\frac{\text{x}_{1}+\text{x}_{2}}{2},\frac{\text{y}_1+\text{y}_2}{2},\frac{\text{z}_{1}+\text{z}_{2}}{2}\Big).$
- ✓
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: A. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
Mid$-$point of $\text{AC}=\Big(\frac{3-1}{2},\frac{-1+1}{2},\frac{2+2}{2}\Big)=(1,0,2)$
Mid$-$point of $\text{BD}=\Big(\frac{1+1}{2},\frac{2-2}{2},\frac{-4+8}{2}\Big)=(1,0,2)$
$\because$ Mid$-$points of $\text{AC}$ and $\text{BD}$ coincides.
$\therefore \text{ABCD}$ is a parallelogram.
View full question & answer→MCQ 21 Mark
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 points $A(1, -1, 3), B(2, -4, 5)$ and $C(5, -13, 11)$ are collinear.
Reason: If $\text{AB + BC = AC,}$ then $\text{A, B, C}$ are collinear.
- ✓
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: A. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
$\mid\text{AB}\mid=\sqrt{(1)^{2}+(-3)^2+(2)^{2}}=\sqrt{1+9+4}=\sqrt{14}$
$\mid\text{BC}\mid=\sqrt{(3)^{2}+(-9)^2+(6)^{2}}=\sqrt{9+81+36}=3\sqrt{14}$
$\mid\text{AC}\mid=\sqrt{(4)^{2}+(-12)^2+(8)^{2}}=\sqrt{16+144+64}=4\sqrt{14}$
$\because\text{AB}+\text{BC}=4\sqrt{14}=\text{AC}$
$\therefore$ Points $A, B$ and $C$ are collinear.
View full question & answer→MCQ 31 Mark
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: Coordinates of centroid of a triangle formed by the vertices $A(3, 2, 0), B(5, 3, 2)$ and $C(0, 2, 4)$ is $\Big(\frac{8}{3},\frac{8}{3},\frac{8}{3}\Big).$
Reason: Coordinates of centroid of a triangle with vertices $A(x_1, y_1, z_1), B(x_2, y_2, z_2)$ and $C(x_3, y_3, z_3)$ is $\Big(\frac{\text{x}_{1}+\text{x}_{2}+\text{x}_{3}}{3},\frac{\text{y}_{1}+\text{y}_{2}+\text{y}_{3}}{3},\frac{\text{z}_{1}+\text{z}_{2}+\text{z}_{3}}{3}\Big).$
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- ✓
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: D. Assertion is wrong statement but Reason is correct statement.
Coordinates of centroid ofa triangle with vertices $A(3, 2, 0), B(5, 3, 2)$ and $C(0, 2, 4)$ is
$\Big(\frac{3+5+0}{3},\frac{2+3+2}{3},\frac{0+2+4}{3}\Big)=\Big(\frac{8}{3},\frac{7}{3},2\Big)$
$\therefore$ Assertion is wrong but Reason is correct.
View full question & answer→MCQ 41 Mark
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 foot of perpendicular drawn from the point $A(1, 2, 8)$ on the $xy -$ plane is $(1, 2, 0).$
Reason: Equation of $xy -$ plane is $y = 0.$
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- ✓
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: C. Assertion is correct statement but Reason is wrong statement.
We know that in $xy -$ plane, $z -$ coordinate is $0.$
So, coordinate of foot of perpendicular drawn from point $A(1, 2, 8)$ on $xy -$ plane is $(1, 2, 0)$.
Equation of $xy -$ plane is $z = 0$
$\therefore$ Reason is wrong.
View full question & answer→MCQ 51 Mark
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 distance between the points $ (1+\sqrt{11}, 0, 0) $ and $(1, -2, 3)$ is $2\sqrt{6}$ units.
Reason: Distance between any two points $A(x_1, y_1, z_1)$ and $B(x_2, y_2, z_2)$
$\mid\text{AB}\mid=\sqrt{(\text{x}_{2}+\text{x}_{1})^{2}+(\text{y}_{2}+\text{y}_{1})^{2}(\text{z}_{2}+\text{z}_{1})^{2}}.$
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- ✓
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: C. Assertion is correct statement but Reason is wrong statement.
Let $\text{A}=(1+\sqrt{11}, 0, 0) $ and $B = (1, -2, 3)$
$\therefore\ \mid\text{AB}\mid=\sqrt{(1-1-\sqrt{11})^{2}+(-2-0)^{2}(3-0)^{2}}$
$=\sqrt{11+4+9}=\sqrt{24}=2\sqrt{6}$ units
$\therefore$ Assertion is correct but Reason is wrong.
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