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Question : A thief is stopped by a policeman from a distance of 150 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief is 7 km/h and that of the policeman is 9 km/h, how far would the thief have run before he was overtaken by the policeman?
Option 1: 420 metres
Option 2: 630 metres
Option 3: 315 metres
Option 4: 525 metres
Correct Answer: 525 metres
Solution : Given: The speed of the thief is 7 km/h and that of the policeman is 9 km/h. At a distance of 150 metres, the policeman spots the thief. We know that, Distance = Speed × Time. Relative speed is given as 9 km/h –
Question : Select the most appropriate synonym of the given word. Unbiased
Option 1: Organisational
Option 2: Objective
Option 3: Definitive
Option 4: Subjective
Correct Answer: Objective
Solution : The correct answer is the second option.
It means not influenced by personal feelings or opinions; based on facts or unbiased analysis.
This is the closest synonym to unbiased in the context, which means without prejudice or partiality; not favouring one side over another.
The
Question : Directions: If A × B means that A is the brother of B, A – B means that A is the sister of B, and A + B means that A is the father of B, then which of the following expressions shows that P is the father of R?
Option 1: P + Q × R
Option 2: P × Q + R
Option 3: P + Q + R
Option 4: P – Q × R
Correct Answer: P + Q × R
Solution : Let's check the options – First option: P + Q × R According to the given expression, the family tree will be as follows – Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.
Question : Directions: 8 boys A, B, C, D, E, F, G and H are sitting around a square table facing towards the centre (not necessarily in the same order). 4 boys are sitting at each corner, and 4 boys are sitting at the middle of each side of the table. A is an immediate neighbour of H and G. A is sitting in a corner. B is an immediate neighbour of D and C. E is an immediate neighbour of C and F. G is third to the right of D. Three out of the following four options follow a similar rule and form a group. Which of the following does NOT belong to that group?
Option 1: EB
Option 2: BH
Option 3: AF
Option 4: GC
Correct Answer: GC
Solution : Given: (I) 8 boys A, B, C, D, E, F, G, and H are sitting around a square table facing towards the centre (not necessarily in the same order). 4 boys are sitting at each corner, and 4 boys are sitting at the middle of
Question : Directions: Select the number from among the given options that can replace the question mark (?) in the following series. 159, 146, ?, 120, 107, 94, 81
Option 1: 136
Option 2: 131
Option 3: 133
Option 4: 140
Correct Answer: 133
Solution : Given: 159, 146, ?, 120, 107, 94, 81
Subtract 13 from each number to obtain the next number. 159 – 13 = 146; 146 – 13 = 133; 133 – 13 = 120; 120 – 13 = 107; 107 – 13 = 94; 94 –
Question : The positive square root of [0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4 + 3 × 0.6 × 0.4 (0.6 + 0.4)] is equal to:
Option 1: 2.1736
Option 2: 1
Option 3: 0.21736
Option 4: 0.072
Correct Answer: 1
Solution : 0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4 + 3 × 0.6 × 0.4 (0.6 + 0.4) = 0.63 + 0.43 + 3 × 0.6 × 0.4 (0.6 + 0.4) The equation is in the form of (a + b)
Question : Concerning Manipuri classical dance, which of the following statements is correct?
a) Lai Haraoba is the earliest form of Manipuri dance.
b) Ras, Sankirtana and Thang-Ta are the most popular forms of this dance.
c) Manipuri dance has its origin in the Jain traditional dance form.
Option 1: a, b, c
Option 2: Both a and c
Option 3: Both a and b
Option 4: Both b and c
Correct Answer: Both a and b
Solution : The correct answer is Both a and b.
Question : In a journey of three unequal laps, a car covers a distance of 200 km in 4 hr in the first lap, while another 162 km at the speed of 15 m/s in the second lap. It covered the remaining distance of the final lap in 4 hr such that the average speed of the car for the entire journey was 50 km/hr. What was the speed of the car on the third lap of the journey?
Option 1: 47 km/hr
Option 2: 52 km/hr
Option 3: 42 km/hr
Option 4: 45 km/hr
Correct Answer: 47 km/hr
Solution : The concept used here is that the average speed is the total distance travelled divided by the total time taken. Speed in the second lap = 15 m/s = $\frac{15×18}{5}$ km/hr = 54 km/hr Time taken in second lap = $\frac{162}{54}$ hrs = 3
Question : If $\left (4x+\frac{1}{x} \right)=5,x\neq 0,$ then the value of $\frac{5x}{4x^{2}+10x+1}$ is:
Option 1: $\frac{1}{2}$
Option 2: $\frac{1}{3}$
Option 3: $\frac{2}{3}$
Option 4: $3$
Correct Answer: $\frac{1}{3}$
Solution : Given: $(4x+\frac{1}{x})=5$ ⇒ $\frac{4x^{2}+1}{x}=5$ ⇒ $4x^{2}+1=5x$ ⇒ $4x^{2}=5x-1$ Now, putting the value of $4x^{2}$ in $\frac{5x}{4x^{2}+10x+1}$ $=\frac{5x}{5x–1+10x+1}=\frac{5x}{15x}=\frac{1}{3}$ Hence, the correct answer is $\frac{1}{3}$.
Question : If $\sin P=\frac{15}{22}$, then what is the value of $\tan P$?
Option 1: $\frac{16}{\sqrt{259}}$
Option 2: $\frac{22}{\sqrt{259}}$
Option 3: $\frac{14}{\sqrt{259}}$
Option 4: $\frac{15}{\sqrt{259}}$
Correct Answer: $\frac{15}{\sqrt{259}}$
Solution : $\sin P=\frac{15}{22}$ We know, $\cos A = \sqrt{(1 - \sin^2 A)}$ So, $\cos A = \sqrt{(1 - (\frac{15}{22})^2}$ ⇒ $\cos A = \sqrt{(1 - (\frac{225}{484})}$ ⇒ $\cos A = \sqrt{\frac{259}{484}}$ ⇒ $\cos A = \frac{\sqrt{259}}{22}$ So, $\tan A = \frac{\sin A}{\cos A}= \frac{\frac{15}{22}}{ \frac{\sqrt{259}}{22}}= \frac{15}{\sqrt{259}}$
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