MCQ 11 Mark
The domain of the relation, $R=\{(x, y): x, y \in Z, z x y=4\}$ is
- A
$\{-2,-1,1,2,4\}$
- B
$\{-2,-1,1,2\}$
- C
$\{1,2,4\}$
- ✓
$\{-4,-2,-1,1,2,4\}$
AnswerCorrect option: D. $\{-4,-2,-1,1,2,4\}$
(d) $\{-4,-2,-1,1,2,4\}$
Explanation: Given, $\mathrm{R}=\{(\mathrm{x}, \mathrm{y}): \mathrm{x}, \mathrm{y} \in \mathrm{Z}, \mathrm{zxy}=4\}$
$=\{(-4,-1),(-2,-2)$,
$(-1,-4),(1,4),(2,2),(4,1)\}$
Therefore, domain of $\mathrm{R}=\{-4,-2,-1,1,2,4\}$
View full question & answer→MCQ 21 Mark
How many even numbers can be formed by using all the digits $2,3,4,5,6$ ?
Answer(a) 72
Explanation: To form an even number the last number can only be an even digit, therefore the number of impossibility for the last digit of number $=3$
Now the ten's place can be filled by any of the remaining 4 digits, and hence the no. of ways for ten's place $=4$
Then there remain three digits, so no. of ways of filling hundred's place $=3$
Similarly no. of ways of filling thousand's place $=2$ and of ten thousand $=1$
Therefore, the total possibilities are $=3 \times 4 \times 3 \times 2 \times 1=72$
View full question & answer→MCQ 31 Mark
Mahesh invested an amount of ₹ 10000 in a fixed deposit scheme for 2 years at a compound interest rate $8 \%$ per annum. How much amount will Mahesh get on the maturity of the deposit?
Answer(a) ₹ 11664
Explanation: Amount $==10000\left(1+\frac{8}{100}\right)^{2}=\frac{10000 \times 108 \times 108}{100 \times 100}=₹ 11664$.
View full question & answer→MCQ 41 Mark
A biased coin with probability $\mathrm{p}, 0<\mathrm{p}<1$, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $2 / 5$, then p equals
- A
$\frac{2}{3}$
- B
$\frac{2}{5}$
- ✓
$\frac{1}{3}$
- D
$\frac{3}{5}$
AnswerCorrect option: C. $\frac{1}{3}$
(c) $\frac{1}{3}$
Explanation: p is the probability of getting head.
$\mathrm{q}=1-\mathrm{p}$ is the probability of getting tail.
The number of tosses required is even.
$=q p+q^{3} p+q^{5} p+q^{7} p+q^{9} p \ldots .$.
$=\mathrm{qp}\left(\frac{1}{1-q^{2}}\right)$
$=\frac{(1-p) p}{1-(1-p)^{2}}$
$=\frac{(1-p) p}{1-\left(1-2 p+p^{2}\right)}$
$=\frac{1-p}{2-p}$
Given $\frac{1-p}{2-p}=\frac{2}{5}$
$\Rightarrow p=\frac{1}{3}$
View full question & answer→MCQ 51 Mark
Three identical dice are rolled. The probability that the same number will appear on each of them is
- A
$\frac{1}{6}$
- B
$\frac{1}{18}$
- ✓
$\frac{1}{36}$
- D
$\frac{3}{28}$
AnswerCorrect option: C. $\frac{1}{36}$
(c) $\frac{1}{36}$
Explanation: Since throwing a single die three times is equivalent to throw three dice at a time.
$\therefore$ Sample space $=\{(1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6), \ldots \ldots .$.}
Here, $n(5)=6^{3}$
$\therefore$ Required Probability $=\frac{6}{6^{3}}=\frac{1}{6^{2}}=\frac{1}{36}$
View full question & answer→MCQ 61 Mark
A shopkeeper bought a TV from a distributor at a discount of $25 \%$ of the listed price of ₹ 32000 . The shopkeeper sells the TV to a consumer at the listed price. If the sales are intra-state and the rate of GST is $18 \%$, the price including tax (under GST) of the TV paid by the consumer is:
Answer(d) ₹ 37760
Explanation: ₹ 37760
View full question & answer→MCQ 71 Mark
Relationship between annual nominal rate of interest and annual effective rate of interest, if frequency of compounding is greater than one:
AnswerCorrect option: C. Effective rate > Nominal rate
(c) Effective rate > Nominal rate
Explanation: If interest is compounded more than once a year the effective interest rate for a year exceeds the per annum nominal interest rate i.e., effective rate > nominal rate
View full question & answer→MCQ 81 Mark
Standard form of 0.0029 is
- ✓
$2.9 \times 10^{-3}$
- B
$29 \times 10^{2}$
- C
$29 \times 10^{-2}$
- D
$2.9 \times 10^{-4}$
AnswerCorrect option: A. $2.9 \times 10^{-3}$
(a) $2.9 \times 10^{-3}$
Explanation: Standard form of 0.0029
$=2.9 \times 10^{-3}$
View full question & answer→MCQ 91 Mark
If $m$ is the geometric mean of
$\left(\frac{y}{z}\right)^{\log (y z)},\left(\frac{z}{x}\right)^{\log (z x)}$ and $\left(\frac{x}{y}\right)^{\log (z))}$
then what is the value of $m$ ?
Answer(d) 1
Explanation: Here, $\mathrm{m}=\left[\left(\frac{y}{z}\right)^{\log (y z)} \times\left(\frac{z}{x}\right)^{\log (z x)} \times\left(\frac{x}{y}\right)^{\log (x y)}\right]^{1 / 3}$
$\therefore \mathrm{m}^{3}=\mathrm{x}^{\log (\mathrm{xy})-\log (\mathrm{zx})} \times \mathrm{y}^{\log (\mathrm{yz})-\log (\mathrm{xy})} \times \mathrm{x}^{\log (\mathrm{zx})-\log (\mathrm{yx})}$
$\Rightarrow m^{3}=x^{\log \left(\frac{y}{z}\right)} \times y^{\log \left(\frac{z}{x}\right)} \times z^{\log \left(\frac{x}{y}\right)}$
Taking log on both sides, we get
$3 \log \mathrm{~m}=\log \left(\frac{y}{z}\right) \log \mathrm{x}+\log \left(\frac{z}{x}\right) \log \mathrm{y}+\log \left(\frac{x}{y}\right) \log \mathrm{z}$
$\Rightarrow 3 \log m=\log y \log x-\log z \log x+\log z \log y-\log x \log y+\log x \log z-\log y \log z$
$\Rightarrow 3 \log \mathrm{~m}=0 \Rightarrow \log \mathrm{~m}=0 \Rightarrow \mathrm{~m}=\mathrm{e}^{0}=\mathrm{m}=1$
View full question & answer→MCQ 101 Mark
Pointing to a woman in a photograph, Ramesh said She is the daughter of the father of the sister of my brother. How is that woman related to Ramesh?
Answer(c) Sister
Explanation: Father of sister of my brother is my father C also.
So, daughter of my father is my sister.
View full question & answer→MCQ 111 Mark
If $(x, 3)$ and $(3,5)$ are the extremities of a diameter of a circle with centre at $(2, y)$, then the values of $x$ and $y$ are
- ✓
- B
$(3,1)$
- C
$x=4, y=1$
- D
$x=8, y=2$
Answer(a) None of these
Explanation: The endpoints of the diameter of a circle are $(x, 3)$ and $(3,5)$.
According to the question, we have:
centre is midpoint of the endpoints of diameters.
$\frac{x+3}{2}=2, \mathrm{y}=\frac{5+3}{2}$
$\Rightarrow \mathrm{x}=1, \mathrm{y}=4$
View full question & answer→MCQ 121 Mark
A bag contains 5 brown and 4 black socks. A man pulls out two socks. The probability that these are of the same colour is:
- A
$\frac{30}{108}$
- B
$\frac{18}{108}$
- C
$\frac{5}{108}$
- ✓
$\frac{48}{108}$
AnswerCorrect option: D. $\frac{48}{108}$
(d) $\frac{48}{108}$
Explanation: P(same coloured socks) $=$ P(both brown) + P(both white)
$=\frac{5}{9} \times \frac{4}{8}+\frac{4}{9} \times \frac{3}{8}$
$=\frac{20}{72}+\frac{12}{72}$
$=\frac{32}{72}$
$=\frac{4}{9}=\frac{48}{108}$
View full question & answer→MCQ 131 Mark
If $5^{x+2}=625$ then value of $x$ is
Answer(d) 2
Explanation: as $5^{x+2}=625 \Rightarrow 5^{x+2}=5^{4}$
$\Rightarrow \mathrm{x}+2=4 \Rightarrow \mathrm{x}=2$
View full question & answer→MCQ 141 Mark
If set $A=\{1,2\}$ and set $B=\{a, b\}$, then cartesian product of set and $A$ set $B$ is given by
Answer(c) $\mathrm{A} \times \mathrm{B}=\{(1, \mathrm{a}),(1, \mathrm{~b}),(2, \mathrm{a}),(2, \mathrm{~b})\}$
Explanation: The set of all ordered pairs (a, b) such that $a \in A$ and $b \in B$ is called cartesian product of sets A and B .
$\therefore A \times B=\{(1, a),(1, b),(2, a),(2, b)\}$
View full question & answer→MCQ 151 Mark
If $\log _{\sqrt{3}} 27=x$, then the value of $x$ is
Answer(d) 6
Explanation: $\log _{\sqrt{3}} 27=x \Rightarrow(\sqrt{3})^{x}=27$
$\Rightarrow 3^{\frac{x}{2}}=3^{3} \Rightarrow \frac{x}{2}=3 \Rightarrow x=6$
View full question & answer→MCQ 161 Mark
A retailer purchases a fan for $₹ 1500$ from a wholesaler and sells it to a consumer at $10 \%$ profit. If the sales are intra-state and the rate of GST is $12 \%$, the selling price of the fan by the retailer (excluding tax) is:
Answer(b) ₹ 1650
Explanation: If a retailer purchases a fan for ₹ 1500 from a wholesaler and sells it to a consumer at $10 \%$ profit and the rate of GST is $12 \%$ then, including tax (under GST) the selling price would be ₹ $\frac{1500 \times 110}{100}=1650$
View full question & answer→MCQ 171 Mark
The mean of 20 observations is 15 . On checking, it was found that two observations were wrongly copied as 3 and 6 . If wrong observations are replaced by correct values 8 and 4, then the correct mean is
Answer(c) 15.15
Explanation: Sum of all observations $=20 \times 15=300$
Sum of correct observations $=300-(3+6)+(8+4)=303$
Correct mean $=\frac{303}{20}=15.15$
View full question & answer→MCQ 181 Mark
A digit is selected at random from either of the two sets $\{1,2,3,4,5,6,7,8,9\}$ and $\{1,2,3,4,5,6,7,8,9\}$. What is the chance that the sum of the digits selected is 10 ?
- ✓
$\frac{1}{9}$
- B
$\frac{2}{9}$
- C
$\frac{10}{18}$
- D
$\frac{10}{81}$
AnswerCorrect option: A. $\frac{1}{9}$
(a) $\frac{1}{9}$
Explanation: Let $A=\{1,2,3,4,5,6,7,8,9\}$ then, $n(A \times A)=g^{2}$
Let $B$ be the event that sum of the digits is 10 . Then,
$B=\{(1,9),(9,1),(4,6),(6,4),(8,2),(2,8),(7,3),(3,7),(5,5)\}$
$\therefore$ Required probability $=\frac{n(B)}{n(A \times A)}=\frac{9}{9^{2}}=\frac{1}{9}$
View full question & answer→