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Question : The number of trees in a town is 17640. If the number of trees increases annually at a rate of 5%, how many trees were there two years ago?
Option 1: 14000
Option 2: 15000
Option 3: 16000
Option 4: 19450
Correct Answer: 16000
Solution : Let the number of trees 2 years ago be $P$. The number of trees increases annually at a rate of 5%. The number of trees at present is 17640. So, $P(1+\frac{r}{100})^n = 17640$ ⇒ $P(1+\frac{5}{100})^2 = 17640$ ⇒ $P(\frac{21}{20})^2 = 17640$ ⇒ $P = 16000$
Question : If $x=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $y=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, then the value of $x^{3} + y^{3}$ is:
Option 1: 950
Option 2: 730
Option 3: 650
Option 4: 970
Correct Answer: 970
Solution : $x=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}=\frac{(\sqrt{3}-\sqrt{2})×(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})×(\sqrt{3}-\sqrt{2})}=(\sqrt{3}-\sqrt{2})^2$ = $5-2\sqrt6$ $y=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}=\frac{(\sqrt{3}+\sqrt{2})×(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})×(\sqrt{3}+\sqrt{2})}=(\sqrt{3}+\sqrt{2})^2$ = $5+2\sqrt6$ $⇒x+y=5-2\sqrt6+5+2\sqrt6 =10$ Also, $xy=(5-2\sqrt6)(5+2\sqrt6)=25-24=1$ $\therefore x^3+y^3=(x+y)^{3} -3xy(x+y)$ $=10^3-3\times 1 \times 10$ $=1000-30$ $= 970$ Hence, the correct answer is 970.
Question : Which of the metals has the maximum thermal conductivity?
Option 1: Iron
Option 2: Aluminium
Option 3: Silver
Option 4: Copper
Correct Answer: Silver
Solution : The correct option is silver.
Silver has the highest heat conductivity of any metal. Thermal conductivity is a measure of a material's capacity to conduct heat, and silver is an exceptional heat conductor. Because of this feature, silver is widely employed in a variety of
Question : Directions: Select the option that is related to the fourth term in the same way as the first term is related to the second term and the fifth term is related to the sixth term. FAR : HDT :: ? : ODD :: PQR : RTT
Option 1: MAC
Option 2: MAB
Option 3: NBB
Option 4: NAB
Correct Answer: MAB
Solution : Given: FAR : HDT :: ? : ODD :: PQR : RTT
Add 2 and 3 alternately to the place value of each letter of the given term to obtain the required term – H – 2 = F; D – 3 = A; T
Question : In which of the following years did the government opt for a planned holiday after the seventh five-year plan?
Option 1: From 1991 to 1993
Option 2: From 1990 to 1992
Option 3: From 1992 to 1993
Option 4: From 1989 to 1991
Correct Answer: From 1990 to 1992
Solution : The correct answer is From 1990 to 1992.
The term "Plan Holiday" refers to the interruption in the continuous series of Five-Year Plans in India. During the Eighth Five-Year Plan (1990-1995), there was a break in 1990, and the subsequent years
Question : If K1 and K2 are two distinct prime numbers, then what is the product of the highest common factor and the least common multiple of K1 and K2?
Option 1: $1$
Option 2: $\frac{K1}{K2}$
Option 3: $K1 + K2$
Option 4: $K1 × K2$
Correct Answer: $K1 × K2$
Solution : Factors of K1 = 1 × K1 Factors of K2 = 1 × K2 Highest Common Factor of K1 and K2 = 1 Least common multiple of K1 and K2 = K1 × K2 Product of HCF and LCM of K1 and K2
Question : Directions: From the given options, choose the correct one that will replace the question mark (?) in the following series. 83, 74, 66, 59, 53, ?, 44, 41
Option 1: 42
Option 2: 50
Option 3: 44
Option 4: 48
Correct Answer: 48
Solution : Given: 83, 74, 66, 59, 53, ?, 44, 41
Subtract the consecutive numbers in the reverse order from the previous term to obtain the next term. 83 – 9 = 74; 74 – 8 = 66; 66 – 7 = 59; 59 – 6 =
Question : Directions: In the following question, find the odd number pair from the given alternatives.
Option 1: 14 – 12
Option 2: 24 – 7
Option 3: 42 – 4
Option 4: 37 – 4
Correct Answer: 37 – 4
Solution : Let's check the options – First option: 14 – 12→14 × 12 = 168 Second option: 24 – 7→24 × 7 = 168 Third option: 42 – 4→42 × 4 = 168 Fourth option: 37 – 4→37 × 4 = 148 ≠
Question : The value of $2 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}+\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)$ is:
Option 1: $\frac{25}{24}$
Option 2: $\frac{29}{24}$
Option 3: $\frac{35}{24}$
Option 4: $\frac{5}{24}$
Correct Answer: $\frac{29}{24}$
Solution : Given: $2 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}+\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)$ = $\frac{7}{3} \div \frac{5}{2}$ of $\frac{8}{5}+\left(\frac{3}{8}+\frac{1}{7} \times \frac{7}{4}\right)$ = $\frac{7}{3} \div (\frac{5}{2}\times\frac{8}{5})+\frac{5}{8}$ = $\frac{7}{3}\times\frac{1}{4}+\frac{5}{8}$ = $\frac{7}{12}+\frac{5}{8}$ = $\frac{14+15}{24}$ = $\frac{29}{24}$ Hence, the correct answer is $\frac{29}{24}$.
Question : Sariska and Ranthambore are the reserves for which of the following?
Option 1: Lion
Option 2: Deer
Option 3: Tiger
Option 4: Bear
Correct Answer: Tiger
Solution : The correct option is Tiger.
The Alwar district in the Indian state of Rajasthan is home to the Sariska Tiger Reserve, a national park and tiger reserve. One of the biggest national parks in Rajasthan is called Ranthambore. Bengal tigers are famous in both
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