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Question : The speed of a boat in still water is 44 km/hr and the speed of a stream is 26 km/hr. Find the upstream speed of the boat.
Option 1: 12 km/hr
Option 2: 18 km/hr
Option 3: 13 km/hr
Option 4: 14 km/hr
Correct Answer: 18 km/hr
Solution : The speed of a boat in still water is 44 km/hr and the speed of a stream is 26 km/hr. Upstream speed of a boat = Boat's speed in still water – Speed of the stream = 44 – 26 = 18 km/hr Hence,
Question : If $\triangle ABC$ is right-angled at B, AB = 30 units and $\angle ACB=60°$, what is the value of AC?
Option 1: $20$ units
Option 2: $20\sqrt3$ units
Option 3: $40$ units
Option 4: $60$ units
Correct Answer: $20\sqrt3$ units
Solution : $\triangle ABC$ is right-angled at B. $\sin\theta$ = $\frac{\text{Perpendicular}}{\text{Hypotenuse}}$ ⇒ $\sin 60°$ = $\frac{AB}{AC}$ ⇒ $\frac{\sqrt{3}}{2} = \frac{30}{AC}$ ⇒ AC = $\frac{60}{\sqrt{3}}$ $\therefore$ AC = $20\sqrt{3}$ units Hence, the correct answer is $20\sqrt{3}$ units.
Question : Directions: Two Statements are given followed by two conclusions numbered I and II Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All notebooks are pencils. Some pens are notebooks. Conclusions: I. All pens are pencils. II Some pencils are pens.
Option 1: Only conclusion I follows
Option 2: Both conclusions I and II follow
Option 3: Only conclusion II follows
Option 4: Neither conclusion I nor II follow
Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All pens are pencils – According to the Venn diagram, the circle of pens overlaps the circle of pencils. So, some pens
Question : The following figure shows the percentage growth in units of fans and coolers sold in some years. What is the difference between the averages of the growth rates in coolers and fans?
Option 1: 34
Option 2: 30
Option 3: 32
Option 4: 42
Correct Answer: 34
Solution : Total growth rate in coolers = 60 + 72 + 54 + 45 = 231 Average growth rate in coolers = $\frac{231}{4}$ = 57.75 Total growth rate in fans = 27 + 18 + 30 + 20 = 95 Average growth rate in fans =
Question : What is the value of (a + b)3 – a3 + b3?
Option 1: –3ab(a – b) + 2b3
Option 2: 3ab(a + b) + 2b3
Option 3: 3ab(a – b) + b3
Option 4: –3ab(a + b) + b3
Correct Answer: 3ab(a + b) + 2b3
Solution : Given expression is (a + b)3 _ a3 + b3 We know that (a + b)3 = a3 + b3 +3ab(a + b) So, (a + b)3 – a3 + b3
Question : Select the most appropriate synonym of the given word. Interfere
Option 1: Activate
Option 2: Masquerade
Option 3: Hasten
Option 4: Restrict
Correct Answer: Restrict
Solution : The fourth option is the correct answer.
"Interfere" means to intervene in a situation in a way that disrupts or hinders its normal course of operation or progress. Similarly, "restrict" means to limit or control the actions, movements, or access of someone or something, thereby
Question : Lala Lajpat Rai was an active member of which organisation?
Option 1: Arya Samaj
Option 2: Brahmo Samaj
Option 3: Brahmo Sabha
Option 4: Prarthana Samaj
Correct Answer: Arya Samaj
Solution : The correct answer is Arya Samaj.
Prominent lawyer, social activist, educationist, and freedom warrior Lala Lajpat Rai gave his life to ensure his motherland's independence. Since his undergraduate years, he has been a member of Arya Samaj, and actively participated in organising the
Question : Directions: Select the figure that will come next in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the given figures – The figure inside each box is rotated at 45° in the anticlockwise direction. So, following the above pattern, the required figure will be as follows –
Therefore, the figure in the second option is the required figure. Hence, the second
Question : Directions: Six students P, Q, R, S, T, and U are sitting around a circular table facing the centre. R is an immediate neighbour of both T and U. P is sitting third to the right of U. Q is sitting to the immediate left of S. S is sitting second to the right of P. Who is the immediate neighbour of both R and S?
Option 1: T
Option 2: Q
Option 3: U
Option 4: P
Correct Answer: U
Solution : Given: (I) P is sitting third to the right of U. S is sitting second to the right of P.
(II) R is an immediate neighbour of both T and U. Q is sitting to the immediate left of S.
So, U is the immediate
Question : The ability to distinguish two closely placed objects is:
Option 1: Resolving power
Option 2: Video power
Option 3: Distinguish power
Option 4: Magnifying power
Correct Answer: Resolving power
Solution : The correct option is resolving power.
The ability of an optical system, such as a telescope or microscope, to recognise two objects far off as distinct and separate objects is referred to as resolving power. It assesses the system's capacity to deliver precise, in-depth
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