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MATHS Assertion (A) & Reason (B) MCQ

Heron’s Formula · Rajasthan Board (RBSE) STD 9 (Rajasthan - English Medium). 28 questions.

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Assertion (A) & Reason (B) MCQ

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28 questions · timed · auto-graded

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 height the triangle is $18\ cm$ and its area is $72\ cm^2$ and it’s base is $8\ cm.$
Reason: Area of triangle $=\frac{1}{2} \times$ base $\times$ sheight
  • ✓
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • B
    Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  • C
    Assertion is true but the reason is false.
  • D
    Both assertion and reason are false.
Answer
Correct option: A.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 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 area of a triangle 8966.56 whose sides are respectively 150cm, 120cm and 200cm.
Reason: Heron’s formula $=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$
  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.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.


    2.  
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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 area of a triangle is $6\ cm^2$ whose sides are $3\ cm, 4\ cm$ and $5\ cm$ respectively.
Reason: Area of triangle $= \sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}.$
  • ✓
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • B
    Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  • C
    Assertion is true but the reason is false.
  • D
    Both assertion and reason are false.
Answer
Correct option: A.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 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 side of an equilateral triangle is 6cm then the height of the triangle is 9cm.
Reason: The height of an equilateral triangle is $\frac{\sqrt3}{2}\text{a}.$
  1. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
  2. Both assertion and reason are true but reason is not the correct explanation of assertion.
  3. Assertion is true but reason is false.
  4. Assertion is false but reason is true.
Answer
  1. Assertion is false but reason is true.
Solution:
The height of the triangle,
$\text{h}=\frac{\sqrt3}{2}\text{a}.$
$9=\frac{\sqrt3}{2}\text{a}.$
$\text{a}=\frac{9\times2}{\sqrt3}=\frac{18}{\sqrt3}=\frac{\sqrt3}{\sqrt3}$
$=\frac{18\sqrt3}{3}=6\sqrt3\text{cm}$
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Question 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 sides of a triangle are in the ratio of 25 : 14 : 12 and its perimeter is 510m. Then the greatest side is 250cm.
Reason: Perimeter of a triangle = a + b + c, where a, b, c are sides of a triangle.
  1. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
  2. Both assertion and reason are true but reason is not the correct explanation of assertion.
  3. Assertion is true but reason is false.
  4. Assertion is false but reason is true.
Answer
  1. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
Solution:
510 = a + b + c
510 = 25x + 14x + 12x
510 = 51x
x = 10
Three sides of the triangle are,
25x = 25 × 10 = 250cm
14x = 14 × 10 = 140cm
and 12x = 12 × 10 = 120cm
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MCQ 61 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 side of an equilateral triangle is $6\ cm$ then the area of the triangle is $9\ cm^2.$
Reason: All the sides of an equilateral triangle are equal.
  • A
    $A$ is true, $R$ is true; $R$ is a correct explanation for $A$.
  • B
    $A$ is true, $R$ is true; $R$ is nol a correct explanation for $A.$
  • C
    $A$ is true; $R$ is false.
  • ✓
    $A$ is false; $R$ is true.
Answer
Correct option: D.
$A$ is false; $R$ is true.
$A$ is false; $R$ is true.
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Question 71 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 perimeter of triangle is 36cm and it’s side are in the ratio a : b : c = 3 : 4 : 5 then a = 9cm, b = 12cm, c = 15cm.
Reason: Perimeter of triangle = sum of all side of triangle.
  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.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 81 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 height of the triangle is 18cm and its area is 72cm then, ils base is 8cm.
Reason: Area of a triangle $=\frac{1}{2}\times\text{base}\times\text{height}.$
  1. A is true, R is true; R is a correct explanation for A.
  2. A is true, R is true; R is nol a correct explanation for A.
  3. A is true; R is false.
  4. A is false; R is true.
Answer
  1. A is true, R is true; R is a correct explanation for A.
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MCQ 91 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: If $2\text{ S}=\frac{(\text{a}+\text{b}+\text{c})}{2}$ where $a,b,c$ are the sides of triangle then area $ =\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}.$
Reason: The sides of triangle are $3\ cm, 4\ cm, 5\ cm$ it’s area is $6\ cm^2$
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • B
    Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  • ✓
    Assertion is true but the reason is false.
  • D
    Both assertion and reason are false.
Answer
Correct option: C.
Assertion is true but the reason is false.
Assertion is true but the reason is false.
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Question 101 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 side of an equilateral triangle is 6cm then the area of the triangle is 9cm2.
Reason: All the sides of an equilateral triangle are equal.
  1. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
  2. Both assertion and reason are true but reason is not the correct explanation of assertion.
  3. Assertion is true but reason is false.
  4. Assertion is false but reason is true.
Answer
  1. Assertion is false but reason is true.
Solution:
$\text{s}=\frac{6+6+6}{2}=\frac{18}{2}=9\text{cm}$
Area $=\sqrt{9(9-6)(9-6)(9-6)}$
$=\sqrt{9\times3\times3\times3}=9\sqrt3\text{cm}^2$
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Question 111 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 sides of a triangle are in the atio of 25 : 14 : 12 and its perimeter is 510cm. Then the area of the triangle is 4449.08cm2.
Reason: Perimeter of a triangle = a + b + c, where a, b, c are sides of a triangle.
  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. 
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 121 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 sides of a triangle are in the ratio of 25 : 14 : 12 and its perimeter is 510cm. Then the area of the triangle is 4449.08cm2.
Reason: Perimeter of a triangle = a + b + c, where a, b, c are sides of a triangle.
  1. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
  2. Both assertion and reason are true but reason is not the correct explanation of assertion.
  3. Assertion is true but reason is false.
  4. Assertion is false but reason is true.
Answer
  1. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
Solution:
510 = a + b + c
510 = 25x + 14x + 12x
510 = 51x
x = 10
Three sides of the triangle are,
25x = 25 × 10 = 250cm
14x = 14 × 10 = 140cm
and 12x = 12 × 10 = 120cm
$\text{s}=\frac{250+140+120}{2}=255\text{cm}$
Area $=\sqrt{255\times5\times115\times135}$
$=4449.08\text{cm}^2$
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Question 131 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: perimeter of triangle $=\frac{(\text{a}+\text{b}+\text{c})}{2}$
Reason: If the sides of the triangle are 30m, 24m and 22m then it’s perimeter is 76m.
  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.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 141 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: Semi - perimeter of an equilateral triangle having area $4\sqrt3\text{cm}^2$ is 16cm.
Reason: $\text{s}=\frac{\text{a}+\text{b}+\text{c}}{2}$ where s is semi - perimeter and a, b and c are sides of triangle.
  1. A is true, R is true; R is a correct explanation for A.
  2. A is true, R is true; R is nol a correct explanation for A.
  3. A is true; R is false.
  4. A is false; R is true.
Answer
  1. A is false; R is true.
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Question 151 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: Area of triangle $= \sqrt{\text{s}(\text{s}-{a})(\text{s}-\text{b})(\text{s}-\text{c})}.$
Reason: $ \text{s}=\frac{(\text{a}+\text{b}+\text{c})}{2}$
  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.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 161 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 side of equilateral triangle is 6 cm then the area of triangle is $9\sqrt3\text{cm}^2.$
Reason: All the side of equilateral triangle are equal.
  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.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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MCQ 171 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: Area of rhombus whose side is $20\ cm$ and one diagonal is $24\ cm$ is $38\ cm^2.$
Reason: All sides of rhombus are equal.
  • ✓
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • B
    Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  • C
    Assertion is true but the reason is false.
  • D
    Both assertion and reason are false.
Answer
Correct option: A.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 181 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 area of an equilateral triangle having each side 4cm is $4\sqrt{3\text{cm}^2}$
Reason: Area of an equilateral triangle $ = \Big(\sqrt{\frac{3}{4}}\Big)\times\text{a}^2$
  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.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 191 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 height of equilateral triangle is $\sqrt{\frac{3}{2\text{a}}}.$
Reason: The side of equilateral triangle is 6cm then the height of triangle is 9cm.
  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.
Answer
  1. Assertion is true but the reason is false.
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MCQ 201 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 height of the triangle is $18\ cm$ and its area is $72\ cm^2$. Its base is $8\ cm.$
Reason: Area of a triangle $=\frac{1}{2}\times$ base $\times$ height.
  • ✓
    Both assertion and reason are true and reason is the correct enatixplaon of assertion.
  • B
    Both assertion and reason are true but reason is not the correct explanation of assertion.
  • C
    Assertion is true but reason is false.
  • D
    Assertion is false but reason is true.
Answer
Correct option: A.
Both assertion and reason are true and reason is the correct enatixplaon of assertion.
Area of $\triangle=\frac{1}{2}\times$ base $\times$ height.
$72=\frac{1}{2}\times18 \times {b}$
$\text{b}=\frac{72\times2}{18}$
$=8\text{ cm}.$
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MCQ 211 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 right angled triangle if hypotenus is $5\sqrt2\text{ cm}$ then other two side equal to $5\ cm$ each.
Reason: In right angled triangle base$^{2 } + $ perpendicular$^{2 } = $ hypotenus$^2$.
  • ✓
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • B
    Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  • C
    Assertion is true but the reason is false.
  • D
    Both assertion and reason are false.
Answer
Correct option: A.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 221 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 side of an equilateral triangle is 20cm then the height is $ 20\sqrt\frac{3}{3\text{cm}}.$
Reason: The height of an equilateral triangle is $\sqrt\frac{3}{2\text{a}}.$
  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. 
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 231 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: Semi perimeter of a equilateral triangle is s = 3 $\frac{\text{a}}{2},$ where, a, are side of triangle.
Reason: If the area of an equilateral triangle is $81\sqrt3\text{cm}2,$ then the semi perimeter of triangle is 20cm.
  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. 
Answer
  1. Assertion is true but the reason is false.
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Question 241 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: If the area of an equilateral triangle is $81\sqrt3\text{cm}^2,$ then the semi perimeter of triangle is 20.
Reason: Semi perimeter of a triangle is $\text{s}=\frac{(\text{a}+\text{b}+\text{c})}{2},$ where a, b, c are sides of triangle.
  1. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
  2. Both assertion and reason are true but reason is not the correct explanation of assertion.
  3. Assertion is true but reason is false.
  4. Assertion is false but reason is true.
Answer
  1. Assertion is false but reason is true.
Solution:
Area of an equilateral triangle $=\frac{\sqrt3}{4}\text{a}^2,$ 
where a is side of triangle $81\sqrt3=\frac{\sqrt3}{4}\text{a}^2,$
$81\times4=\text{a}^2$
$324=\text{a}^2$
$\text{a}=18\text{cm}$
$\text{s}=\frac{18+18+18}{2}=27\text{cm}$
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Question 251 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 sides of a triangle are in the ratio of 25 : 14 : 12 and its perimeter is 510m. Then the greatest side is 250cm.
Reason: Perimeter of a triangle = a + b + c, where a, b, c are sides of a triangle.
  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. 
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 261 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 sides of a triangle are 3cm, 4cm and 5cm. Its area is 6cm2.
Reason: If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area $=\sqrt{(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}.$
  1. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
  2. Both assertion and reason are true but reason is not the correct explanation of assertion.
  3. Assertion is true but reason is false.
  4. Assertion is false but reason is true.
Answer
  1. Assertion is true but reason is false.
Solution:
$\text{s}=\frac{\text{a}+\text{b}+\text{c}}{2}$
$\text{s}=\frac{3+4+5}{2}=6\text{cm}$
Area $=\sqrt{(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}.$
$=\sqrt{(6)(6-3)(6-4)(6-5)}$
$=\sqrt{(6)(3)(2)(1)}=6\text{cm}^2$
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MCQ 271 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 perimeter of a right angled triangle is $60\ cm$ and its hypotenuse is $26\ cm$. The other sides of the triangle are $10\ cm$ and $24\ cm.$ Also, area of the triangle is $120\ cm^2.$
Reason: $($Base$)^2 +($Perpendicular$)^2 = ($Hypotenuse$)^2.$
  • ✓
    Both assertion and reason are true and reason is the correct enatixplaon of assertion.
  • B
    Both assertion and reason are true but reason is not the correct explanation of assertion.
  • C
    Assertion is true but reason is false.
  • D
    Assertion is false but reason is true.
Answer
Correct option: A.
Both assertion and reason are true and reason is the correct enatixplaon of assertion.

$a + b + c = 60$
$a + b + 26 = 60$
$a + b = 34 ...(1)$
Now$, 26^2 + a^2 + b^2 ...(2)$
Squaring $(1)$ both sides, we get
$(a + b)^2 = (34)^2$
$a^2 + b^2 + 2ab = 34 \times 34$
$(26)^2 + 2ab = 1156 [$From $(2)]$
$2ab = 1156 - 676$
$2ab = 480$
$ab = 240 ...(3)$
Now, $\text{a}+\frac{240}{\text{a}}=34 [$From $(1)$ and $(3)]$
$a^2 - 24a - 10a + 240 = 0$
$a(a - 24) - 10(a - 24) = 0$
$a = 10, 24$
Now, other sides are $10\ cm$ and $24\ cm.$
$\text{s}=\frac{26+10+24}{2}$
$=30\text{ cm}$
Area of triangle $=\sqrt{30(30-26)(30-10)(30-24)}$
$\sqrt{30\times4\times20\times6}$
$=120\text{ cm}^2.$
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Question 281 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 sides of a triangle are 3cm, 4cm and 5cm. Its area is $9\sqrt3\text{cm}^2.$
Reason: If 2s = (a + b + c ), where a , b, c are the sides of a triangle, then area $= \sqrt{(\text{s}–\text{a})(\text{s}–\text{b})(\text{s}–\text{c})}.$
  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. 
Answer
  1. Assertion is true but the reason is false.
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