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Question : From a cask of milk containing 64 litres, 8 litres are drawn out and the cask is filled up with water. If the same process is repeated a second, then a third time, what will be the proportion of milk to water in the resulting mixture?
Option 1: 343 : 179
Option 2: 333 : 169
Option 3: 443 : 179
Option 4: 343 : 169
Correct Answer: 343 : 169
Solution : The amount replaced by water each time is 8 litres. The amount of milk = Original amount$\times(1- \frac{\text{Amount replaced by water}}{\text{Original Amount}})^n$, where $n$ = No. times process repeated So, the amount of milk $= 64\times (1-\frac{8}{64})^3$ $= 64\times (1-\frac{1}{8})^3$ $= 64\times (\frac{7}{8})^3$
Question : The pie chart given below shows the price of 6 different articles. The total price of all these 6 articles is 5040. The price of a particular article is shown in terms of degree concerning the total price of all these 6 articles. Which of the following statements is NOT correct? I. The total price of A1, A2, A4, and A6 is 2772. II. The difference between the total price of A3 and A5 together and the total price of A4 and A6 together is 488.
Option 1: Only I
Option 2: Both I and II
Option 3: Only II
Option 4: Neither I nor II
Correct Answer: Only II
Solution : The total price of A1, A2, A4, and A6 is 2772. $\frac{\text{Sum of degrees of A3 and A5}}{\text{Total degrees in the pie chart}}$ × Total price Total Price = 5040 ⇒ Price of A1 = $\frac{32}{360}$ × 5040 = 448 ⇒ Price of A2
Question : If $\left(x-\frac{1}{x}\right)=10$, what is the value of $\left(x^4+\frac{1}{x^4}\right)?$
Option 1: 10404
Option 2: 10402
Option 3: 10406
Option 4: 10400
Correct Answer: 10402
Solution : $(x-\frac{1}{x})=10$ Squaring both sides, $x^{2}+ \frac{1}{x^{2}} – 2 = 100$ ⇒ $x^{2}+\frac{1}{x^{2}}=102$ Squaring both sides again, $x^{4}+\frac{1}{x^{4}}+2=10404$ ⇒ $x^{4}+\frac{1}{x^{4}}=10402$ Hence, the correct answer is 10402.
Question : A hemispherical bowl is made of 1 cm thick steel. The inside radius of the bowl is 4 cm. The volume of the steel (in cm3) used in making the bowl is:
Option 1: $40\frac{2}{3}\pi$
Option 2: $27\frac{1}{3}\pi$
Option 3: $41\frac{1}{3}\pi$
Option 4: $35\frac{1}{3}\pi$
Correct Answer: $40\frac{2}{3}\pi$
Solution : Given: Inner radius $(r)$ = 4 cm Outer radius $(R)$ = 4 + 1 = 5 cm According to the question, The volume of steel used = $\frac{2}{3}×\pi (R^3-r^3)$ = $\frac{2}{3}×\pi (5^3-4^3)$ = $\frac{2}{3}×\pi (125-64)$ = $\frac{2}{3}×\pi ×61$ = $\frac{122}{3}×\pi$ = $40\frac{2}{3}\pi\ \text{cm}^3$ Hence, the
Question : Directions: Three different positions of the same dice are shown. Select the letter that will be on the face opposite to the one having A.
Option 1: B
Option 2: F
Option 3: N
Option 4: Z
Correct Answer: Z
Solution : Taking dice positions 2 and 3 with Z as the common face – Moving clockwise from the common face with Z –
So, the opposite faces of the dice are –
Therefore, the opposite face of the A is Z. Hence, the fourth option is
Question : Directions: Which answer figure will complete the pattern in the question figure?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the question figure – In row 1: The number of vertical lines is 1 and the number of horizontal lines is increased by 1. In row 2: The number of vertical lines is 2 and the number of horizontal lines is increased by 1.
Question : Directions: In the following question, a series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series. XYZ, ABC, UVW, DEF, RST, GHI, ?
Option 1: UVW
Option 2: JKL
Option 3: OPQ
Option 4: NOP
Correct Answer: OPQ
Solution : Given: XYZ, ABC, UVW, DEF, RST, GHI, ?
In the above-given series, subtract 3 from the place value of each letter of the terms of odd places and add 3 to the place value of each letter of the given term at even places. Odd
Question : "Unfinished: A Memoir" is the autobiography of ___.
Option 1: Priyanka Chopra Jonas
Option 2: Deepika Padukone
Option 3: Kareena Kapoor
Option 4: Alia Bhatt
Correct Answer: Priyanka Chopra Jonas
Solution : The correct answer is Priyanka Chopra Jonas.
"Unfinished: A Memoir" is the autobiography of Priyanka Chopra Jonas. Priyanka Chopra is a Bollywood actress who is married to an American singer, actor Nick Jonas. Unfinished: A Memoir offers insights into Priyanka Chopra Jonas's
Question : " India Wins Freedom" is the autobiography of
Option 1: Abul Kalam Azad
Option 2: Muhammad Ali
Option 3: Zakir Hussain
Option 4: Syed Ahmad Khan
Correct Answer: Abul Kalam Azad
Solution : Correct Answer is Abul Kalam Azad
Maulana Azad's India Wins Freedom is an account of the partition of India from the point of view of the author. It contains the author's personal experiences during the independence of India, as well as his ideas
Question : Directions: The bar graph provided below gives the data on the production of paper (in lakh tonnes) by three different companies X, Y and Z over the years. Study the bar chart and answer the following questions. The difference between the production of company Z in 1998 and company Y in 1996 is:
Option 1: 25,00,000 tonnes
Option 2: 10,00,000 tonnes
Option 3: 15,00,000 tonnes
Option 4: 20,00,000 tonnes
Correct Answer: 20,00,000 tonnes
Solution : Production of company Z in 1998 = 45 (in lakh tonnes) Production of company Y in 1996 = 25 (in lakh tonnes) Difference = 45 – 25 = 20 (in lakh tonnes) = 20,00,000 tonnes Hence, the correct answer is 20,00,000 tonnes.
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