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MATHS Assertion (A) & Reason (B) MCQ

Conic Sections · Rajasthan Board (RBSE) STD 11 Science (Rajasthan - English Medium). 5 questions.

Questions

Assertion (A) & Reason (B) MCQ

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5 questions · auto-graded multiple-choice test.

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:
If the distances of foci and vertex of hyperbola from the centre are $c$ and $a$ respectively, then
Assertion: A line through the focus and perpendicular to the directrix is called the $x -$ axis of the parabola.
Reason: The point of intersection of parabola with the axis is called the vertex of the parabola.
  • 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.
Answer
Correct option: D.
Assertion is wrong statement but Reason is correct statement.
A line through the focus and perpendicular to the directrix is called the axis of the parabola.
The point of intersection of parabola with the axis is called the vertex of the parabola.
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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 sum of focal distances of a point on the ellipse $9x^2 + 4y^2 - 18x - 24y + 9 = 0$ is $4.$
Reason: The equation $9x^2+ 4y^2 - 18x - 24y + 9 = 0$ can be expressed as $9(x -1)^2 + 4(y - 3)^2 = 36.$
  • 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.
Answer
Correct option: D.
Assertion is wrong statement but Reason is correct statement.
We have, $9x^2+ 4y^2 - 18x - 24y + 9 = 0$
$9(x - 1)^2 + 4(y - 3)^2 = 36$
$\Rightarrow\frac{(\text{x}-1)^{2}}{2^{2}}+\frac{(\text{y}-3)^{2}}{2^{3}}=1$
Here, $b > a$
$\therefore$ Sum of focal distances of a point is $2b = 6.$
 
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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: The length of major and minor axes of the ellipse $5x^2 + 9y^2 - 54y + 36 = 0$ are $6$ and $10,$ respectively.
Reason: The equation $5x^2 + 9y^2 - 54y + 36 = 0$ can be expressed as $5x^2 + 9(y - 3)^2 = 45.$
  • 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.
Answer
Correct option: D.
Assertion is wrong statement but Reason is correct statement.
We have,$ 5x^2 + 9y^2 - 54y + 36 = 0$
$\Rightarrow 5x^2 + 9(y - 3)^2 = 45$
$\Rightarrow\frac{\text{x}^{2}}{3^{2}}+\frac{(\text{y}-3)^{2}}{(\sqrt{5})^{2}}=1$
$\therefore$ Length of major axis $= 2 \times 3 = 6$ and length of minor axis
$=2\times\sqrt{5}$
$=2\sqrt{5}.$
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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:
If the distances of foci and vertex of hyperbola from the centre are c and a respectively, then
Assertion: Eccentricity is always less than $1.$
Reason: Foci are at a distance of ae from the centre.
  • 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.
Answer
Correct option: D.
Assertion is wrong statement but Reason is correct statement.
Since, $c > a,$ the eccentricity is never less than one.
In terms of the eccentricity the foci are at a distance of ae from the centre.
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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:
Parabola is symmetric with respect to the axis of the parabola.
Assertion: If the equation of standard parabola has a term $y^2,$ then the axis of symmetry is along the $x - $ axis.
Reason: If the equation of standard parabola has a term $x^2,$ then the axis of symmetry is along the $x -$ axis.
  • 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.
Answer
Correct option: C.
Assertion is correct statement but Reason is wrong statement.
If the equation has a $y^2$ term, then the axis of symmetry is along the $x -$ axis and if the equation has $x^2$ term, then the axis of symmetry is along the $y -$ axis.
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