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Question : In a $\triangle \mathrm{PQR}$ and $\triangle\mathrm{ABC}$, $\angle$P = $\angle$A and AC = PR. Which of the following conditions is true for $\triangle$PQR and $\triangle$ABC to be congruent?
Option 1: AB = PQ by SSS
Option 2: AB = PQ by SAS
Option 3: BC = QR by ASS
Option 4: $\angle$Q = $\angle$B by AAA
Correct Answer: AB = PQ by SAS
Solution : In a $\triangle \mathrm{PQR}$ and $\triangle \mathrm{ABC}$, $\angle$P = $\angle$A AC = PR For triangle PQR and ABC to be congruent if AB = PQ then they will be congruent by SAS rule. Hence, the correct answer is AB = PQ
Question : Select the correctly spelt word
Option 1: Amatuer
Option 2: Amatueer
Option 3: Amture
Option 4: Amateur
Correct Answer: Amateur
Solution : The correct choice is the fourth option.
Explanation:
The correct spelling is amateur, which means someone who engages in an activity to enjoy rather than doing it professionally, or someone inept in a particular activity.
Question : The volume of a right circular cone having a base diameter of 14 cm is 196$\pi$ cm3. Find the perpendicular height of this cone
Option 1: 10 cm
Option 2: 12 cm
Option 3: 14 cm
Option 4: 8 cm
Correct Answer: 12 cm
Solution : Given: The volume of a right circular cone = $196\pi\ \text{cm}^3$ Diameter of base = 14 cm Radius = 7 cm Volume of the cone = $\frac{1}{3}\pi r^2 h$ ⇒ $196\pi = \frac{1}{3}\pi r^2 h$ ⇒ $196 = \frac{1}{3}\times7\times7\times h$ ⇒ $h = 12\
Question : Directions: Study the following histogram of data related to literate people of different age groups and answer the questions given below.
The number of literate people in the age group of 20-35 years is:
Option 1: 2050
Option 2: 1250
Option 3: 2150
Option 4: 1700
Correct Answer: 2050
Solution : The number of literate people in the age group of 20-25 = 800 The number of literate people in the age group of 25-30 = 650 The number of literate people in the age group of 30-35 = 600 The required answer = 800 +
Question : If $(a+b+c)=17$, and $\left(a^2+b^2+c^2\right)=115$, find the value of $(a+b)^2+(b+c)^2+(c+a)^2$.
Option 1: 402
Option 2: 408
Option 3: 394
Option 4: 404
Correct Answer: 404
Solution : Given, $(a+b+c)=17$ Squaring both sides $\left(a^2+b^2+c^2\right)+2(ac+bc+ab)=289$ ⇒ $115+2(ab+bc+ac)=289$ ⇒ $2(ab+bc+ac)=174$ Now, $(a+b)^2+(b+c)^2+(c+a)^2$ = $2(a^2+b^2+c^2)+2(ab+bc+ac)$ = $2\times 115+174$ = $230 + 174$ = $404$ Hence, the correct answer is 404.
Question : Directions: In a certain code language, HUSTLE is written as SFHEOT, and BRIGHT is written as IIBTSG. How will TUNNEL be written in that language?
Option 1: NRTPEN
Option 2: NGTYPN
Option 3: NFTLVN
Option 4: RNLPED
Correct Answer: NFTLVN
Solution : Given: HUSTLE is written as SFHEOT, and BRIGHT is written as IIBTSG.
Interchange the position of the first and third, fourth and sixth letters, and write the opposite letter of the second and fifth letters of HUSTLE, to obtain the required code –
Thus, HUSTLE
Question : Which of the following is used in the treatment of cancer?
Option 1: Physiotherapy
Option 2: Chemotherapy
Option 3: Electrotherapy
Option 4: Psychotherapy
Correct Answer: Chemotherapy
Solution : The correct option is Chemotherapy.
Chemotherapy is a medicinal therapy that uses potent chemicals to kill the body's rapidly proliferating cells. Chemotherapy is most frequently used to treat cancer because cancer cells reproduce and develop considerably more quickly than the majority of body cells.
Question : A bike is sold for 87,500 by allowing a discount of 44% on its marked price. The marked price (in Rs.) of the bike is:
Option 1: 1,56,100
Option 2: 1,58,225
Option 3: 1,56,250
Option 4: 1,55,500
Correct Answer: 1,56,250
Solution : Given: A bike is sold for 87,500 by allowing a discount of 44% on its marked price. Let the marked price be $x$. So, $x×\frac{100-44}{100} = 87500$ ⇒ $x×\frac{56}{100}= 87500$ ⇒ $x=\frac{8750000}{56}$ ⇒ $x= 156250$ Hence, the correct answer is 1,56,250.
Question : What is the set of ecosystems called?
Option 1: Stratosphere
Option 2: Hydrosphere
Option 3: Biome
Option 4: Atmosphere
Correct Answer: Biome
Solution : The correct option is Biome.
The collective name for the collection of ecosystems present in a particular geographic area or region is called a biome. A biome is an extensive, distinct ecological community characterised by its flora and climate and the types of organisms
Question : Directions: In this question, a sentence is given with a blank to be filled in with an appropriate word. Four alternatives are suggested for each question. Choose the correct alternative out of the four alternatives.
I’ll take ____ now as I have another appointment somewhere else.
Option 1: Departure
Option 2: My leave
Option 3: Permission
Option 4: Leave from work
Correct Answer: My leave
Solution : The correct answer is the second option.
The word leave is appropriate in this context to indicate that the person is departing or saying goodbye. So, the correct answer is leave.
The meanings of the other options are as follows:
Departure: It denotes
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