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).

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

(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).

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Solution

The correct answer is:

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

Clearly, Reason (R) is true.

But we got the value of mode thus:

The maximum frequency is 23 and the modal class is 12-15.

Using, $M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) * h$

where

l = lower limit of the modal class,

h = size of the class interval (assuming all class sizes to be equal),

$f_{1}$ = frequency of the modal class,

$f_{0}$ = frequency of the class preceding the modal class,

$f_{2}$ = frequency of the class succeeding the modal class.

$M o d e = 12 + (\frac{23 - 21}{2 * 23 - 21 - 10}) * 3$

$\Rightarrow M o d e = 12 + (\frac{2}{15}) * 3$

$\Rightarrow M o d e = 12 + 0.4$

$\Rightarrow M o d e = 12.4$

$∴$ Assertion (A) and Reason (R) are true.

However, Reason (R) isn't the correct explanation of Assertion (A).

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Similar questions

Q. 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.

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).

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).

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) The area of a trapezium whose & The area of an equailateral traingle parallel sides measure 25 cm and & of side 8 cm is 16 \sqrt{3} c m^{2} . 15 cm respectively and the distance between them is 6 cm,is 120 c m^{2} . \end{matrix}$

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).

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) The diagonals of a | | g m d i v i d e i t & A diagonal of a | | g m d i v i d e s i t i n t o into four triangles of equal area. & two diagonals of equal area. \end{matrix}$

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

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 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).

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

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) T h e c u r v e d s u r f a c e a r e a o f a & V o l u m e o f a c o n e = π r^{2} h . c o n e o f b a s e r a d i u s 3 c m a n d h e i g h t 4 c m i s (15 π) c m^{2} . \end{matrix}$

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

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