Assertion (A)
Consider the following frequency distribution:

Class interval 3-6 6-9 9-12 12-15 15-18 18-21

Frequency 2 5 21 23 10 12

The mode of the above data is 12.4.

Reason (R)
The value of the variable which occurs most often is the mode.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is a not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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Solution

(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is a not a correct explanation of Assertion (A).
Clearly, reason (R) is true.
The maximum frequency is 23 and the modal class is 12-15.
$Now, x_{k} = 12, f_{k} = 23, f_{k - 1} = 21, f_{k + 1} = 23 and h = 3 ∴ Mode = \{12 + 3 \times \frac{(23 - 21)}{(2 \times 23 - 21 - 10)}\} = (12 + 3 \times \frac{2}{15}) = (12 + 0.4) = 12 ∴ A s s e r t i o n (A) i s t r u e . However, r e a s o n (R) i s n o t a c o r r e c t e x p l a n a t i o n o f a s s e r t i o n (A) .$

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Assertion-and-Reason Type

Each question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) C o n s i d e r t h e f o l l o w i n g f r e q u e n c y & T h e v a l u e o f t h e v a r i a b l e w h i c h d i s t r i b u t i o n : & o c c u r s m o s t o f t e n i s t h e m o d e \begin{matrix} C l a s s i n t e r v a l & 3 - 6 & 6 - 9 & 9 - 12 & 12 - 15 & 15 - 18 & 18 - 21 F r e q u e n c y & 2 & 5 & 21 & 23 & 10 & 12 \end{matrix} T h e m o d e o f t h e a b o v e d a t a i s 12.4. \end{matrix}$

The correct answer is:(a)/(b)/(c)/(d).

This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) If ABCD is a rhombus whose one & Median of a triangle divides it angle is 60^{\circ} then the ratio of the & into two triangles of equal area. lenghts of its diagonals is \sqrt{3} : 1. \end{matrix}$

The correct answer is :(a) /(b)/(c)/(d).

Q. Assertion (A)
In an isosceles ∆ABC, if ∠C = 90°, then AB² = 3AC².
Reason (R)
In an isosceles ∆ABC, if AC = BC and AB² = 2AC², then ∠C = 90°.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A)
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion (A)
If the median and mode of a frequency distribution are 150 and 154 respectively, then its mean is 148.
Reason (R)
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(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is a not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

This question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

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