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Question : A dishonest trader says to customers that he sells his goods at a cost price, but he uses a false weight and gains 12.5% as profit. How many grams does he use to weight 1 kg?
Option 1: 900 g
Option 2: 880.5 g
Option 3: 850 g
Option 4: 888.8 g
Correct Answer: 888.8 g
Solution : According to the formula, $12.5\% = [\frac{\text{Error}}{\text{1000 – Error}}] × 100$ ⇒ $\frac{1}{8} = [\frac{\text{Error}}{\text{1000 – Error}}]$ ⇒ $8\text{Error} = \text{(1000 – Error)}$ ⇒ $\text{8Error + Error} = 1000$ ⇒ $9\text{Error} = 1000$ ⇒ $\text{Error} = \frac{1000}{9}$ So, the trader gives $1000 - \frac{1000}{9}=\frac{8000}{9}=888.8$
Question : If $x = \sqrt[3]{5} + 2$, then the value of $x^3-6x^2+12x-13$ is:
Option 1: $–1$
Option 2: $1$
Option 3: $2$
Option 4: $0$
Correct Answer: $0$
Solution : $x = \sqrt[3]{3} + 2$ ⇒ $x - 2 = \sqrt[3]{5}$ By cubing on both the sides, $⇒x^3-6x^2+3x (-2)^2-2^3=5$ [since $(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$] $⇒x^3-6x^2+12x-8-5=0$ $⇒x^3-6x^2+12x-8-5=0$ $⇒x^3-6x^3+12x-13=0$ Hence, the correct answer is $0$.
Question : Select the most appropriate antonym of the given word.
Sorcery
Option 1: Devilry
Option 2: Reality
Option 3: Spell
Option 4: Dismiss
Correct Answer: Reality
Solution : The correct choice is the second option.
Sorcery refers to the use of magical powers, often associated with the casting of spells or the use of supernatural forces. Reality, on the other hand, refers to the state of things as they actually exist, without
Question : The Rathas of Mahabalipuram was built during the reign of which of the following rulers?
Option 1:
Palas
Option 2: Cholas
Option 3: Rashtrakutas
Option 4: Pallavas
Correct Answer: Pallavas
Solution : The correct answer is Pallavas.
Pallava king Narasimhavarman I built the temple on the Coromandel coast of the Bay of Bengal in Tamil Nadu. This temple is dedicated to the goddess Durga and is also famous for the name of the Five Rathas, or Pandava
Question : Directions: A student walked out of the classroom towards the library. She went first to the canteen on the left side, 24 ft away after a cup of tea, took a right turn, and went to the laboratory 13 ft away. She then went to the physics block, 15 ft to the left. She talked to a friend, in the garden 3 ft on the left and continued walking in the same direction to the library, 10 ft more. What was the actual distance between the library and the classroom?
Option 1: 42 ft
Option 2: 65 ft
Option 3: 39 ft
Option 4: 34 ft
Correct Answer: 39 ft
Solution : Firstly, we will draw the diagram as per the given instructions –
Assume that the student starts walking in the north direction from the classroom towards the canteen.
Distance between classroom and library = 24 + 15 = 39 ft
Hence, the third option
Question : Select the most appropriate option to fill in the blank. Her notoriety increased after she single____________shot down a Rhodesian army helicopter.
Option 1: dose
Option 2: plainly
Option 3: stranded
Option 4: handedly
Correct Answer: handedly
Solution : The correct option will be the fourth option.
The sentence is describing an action performed by the subject (she) that resulted in an increase in her notoriety. The word "single-handedly" means that she accomplished the action alone or unaided by others. In this
Question : Directions: Select the number from among the given options that can replace the question mark (?) in the following series. 16, 23, 31, 40, 50, ?
Option 1: 60
Option 2: 62
Option 3: 61
Option 4: 63
Correct Answer: 61
Solution : Given: 16, 23, 31, 40, 50, ?
Add consecutive numbers starting from 7 in each number to obtain the next number. 16 + 7 = 23; 23 + 8 = 31; 31 + 9 = 40; 40 + 10 = 50; 50 + 11 =
Question : A field is in the form of a circle. The cost of fencing around it at INR 12 per metre is INR 2,640. What is the area (in m2) of the field? (Take $\pi=\frac{22}{7}$)
Option 1: 1,925 m2
Option 2: 3,850 m2
Option 3: 2,772 m2
Option 4: 5,544 m2
Correct Answer: 3,850 m2
Solution : Given: A field is in the form of a circle. Use the formulas, The perimeter of the circle = $2\pi r$, The area of the circle = $\pi r^2$, where $r$ is the radius. The cost of fencing around it at INR 12
Question : Directions: Which of the following numbers will replace the question mark (?) in the given series? $18,6,2, ?, \frac{2}{9}$
Option 1: $\frac{1}{3}$
Option 2: $\frac{1}{9}$
Option 3: $\frac{2}{3}$
Option 4: 1
Correct Answer: $\frac{2}{3}$
Solution : Given: $18,6,2, ?, \frac{2}{9}$
Multiply the previous term by $\frac{1}{3}$ to obtain the next term. $18×\frac{1}{3}=6;6×\frac{1}{3}=2;2×\frac{1}{3}=\frac{2}{3};\frac{2}{3}×\frac{1}{3}=\frac{2}{9}$
So, $\frac{2}{3}$ is the missing term in the given series. Hence, the third option is correct.
Question : If the sum of the diagonals of a rhombus is $L$ and the perimeter is $4P$, find the area of the rhombus.
Option 1: $\frac{1}{4}\left(\mathrm{~L}^2-\mathrm{P}^2\right)$
Option 2: $\frac{1}{4}\left(\mathrm{~L}^2-4 \mathrm{P}^2\right)$
Option 3: $\frac{1}{2}\left(\mathrm{~L}^2-4 \mathrm{P}^2\right)$
Option 4: $\frac{1}{4}\left(\mathrm{~L}^2+3 \mathrm{P}^2\right)$
Correct Answer: $\frac{1}{4}\left(\mathrm{~L}^2-4 \mathrm{P}^2\right)$
Solution : Given: The sum of the diagonals of a rhombus is $L$. Perimeter = $4P$ ⇒ Sides = $\frac{4P}{4}$ = $P$ Now, the sum of the diagonals = $L$ Let one of the diagonal be $d_1$ and another diagonal be $d_2$. ⇒ $(\frac{d_1}{2})^2 + (\frac{d_2}{2})^2
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