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MATHS Assertion (A) & Reason (B) MCQ

Model Paper 1 · Rajasthan Board (RBSE) STD 11 Science (Rajasthan - English Medium). 2 questions.

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Assertion (A) & Reason (B) MCQ

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2 questions · self-marked practice — reveal the answer and mark yourself.

MCQ 11 Mark
Assertion (A): The mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17 is 3.
Reason (R): The mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 is 8.5.
  • A
    Both A and R are true and R is the correct explanation of A.
  • B
    Both A and R are true but R is not the correct explanation of A.
  • C
    A is true but R is false.
  • D
    A is false but R is true.
Answer
(c) A is true but R is false. 
Explanation: Assertion: Mean of the given series 
$\begin{array}{l}\overline{\bar{x}}=\frac{\text { Sum of terms }}{\text { Number of terms }}=\frac{\sum x_i}{n} \\ 
=\frac{4+7+8+9+10+12+13+17}{8}=10\end{array}$
xi$| x i -\bar{x}|$
4$|4-10|=6$
7$|7-10|=3$
8$|8-10|=2$
9$|9-10|=1$
10$|10-10|=0$
12$|12-10|=2$
13$|13-10|=3$
17$|17-10|=7$
$\sum x_i=80$$\sum\left|x_i-\bar{x}\right|=24$
$\therefore$ Mean deviation about mean
$=\frac{\Sigma\left|x_i-\bar{x}\right|}{n}=\frac{24}{8}=3$
Reason Mean of the given series 
$\begin{array}{l}\bar{x}=\frac{\text { Sum of terms }}{\text { Number of terms }}=\frac{\sum x_i}{n} \\ =\frac{38+70+48+40+42+55}{+63+46+54+44}=50\end{array}$
$\therefore$ Mean deviation about mean
$\begin{array}{l}=\frac{\Sigma\left|x_i-\bar{x}\right|}{n} \\ 
=\frac{84}{10}=8.4\end{array}$
Hence, Assertion is true and Reason is false.
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MCQ 21 Mark
Assertion (A): The expansion of $(1+ x )^{ n }=n_{c_0}+n_{c_1} x+n_{c_2} x^2 \ldots+n_{c_n} x^n$.
Reason (R): If $x=-1$, then the above expansion is zero.
  • A
    Both A and R are true and R is the correct explanation of A.
  • B
    Both A and R are true but R is not the correct explanation of A.
  • C
    A is true but R is false.
  • D
    A is false but R is true.
Answer
(b) Both A and R are true but R is not the correct explanation of A. 
Explanation: Assertion: 
$(1+x)^n=n_{c_0}+n_{c_1} x+n_{c_2} x^2 \ldots+n_{c_n} x^n$
Reason
\begin{array}{l}
(1+(-1))^{n}=n_{c_0} 1^n+n_{c_1}(1)^{n-1}(-1)^1+n_{c_2}(1)^{n-2}(-1)^2+\ldots+{ }^n c_n(1)^{n-n}(-1)^n \\
=n_{c_8}-n_{c_1}+n_{c_2}-n_{c_3}+\ldots(-1)^{n} n_{c_n}
\end{array}
Each term will cancel each other 
$\therefore(1+(-1))^{ n }=0$
Reason is also the but not the correct explanation of Assertion.  

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Assertion (A) & Reason (B) MCQ - MATHS STD 11 Science Questions - Vidyadip