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Question : AD is the median of $\triangle \mathrm{ABC}$. G is the centroid of $\triangle \mathrm{ABC}$. If AG = 14 cm, then what is the length of AD?
Option 1: 42 cm
Option 2: 28 cm
Option 3: 35 cm
Option 4: 21 cm
Correct Answer: 21 cm
Solution : AD is the median of triangle ABC. G is the centroid of triangle ABC. If AG = 14 cm So, $\frac{AG}{GD}=\frac{2}{1}$ ⇒ $\frac{14}{GD} = \frac{2}{1}$ ⇒ $GD =7$ cm $\therefore$ AD = AG + GD = 14 + 7 = 21 cm Hence, the
Question : Directions: Three of the following four triads are alike in a certain way as they are formed by performing the same mathematical operations among themselves and thus form a group. Which triad does NOT belong to that group?
Option 1: 11 : 21 : 121
Option 2: 7 : 15 : 49
Option 3: 2 : 3 : 4
Option 4: 9 : 17 : 81
Correct Answer: 7 : 15 : 49
Solution : Let's check each option – First option: 11 : 21 : 121→(11 × 2) – 1 = 22 – 1 = 21; 112 = 121 Second option: 7 : 15 : 49→(7 × 2) – 1 = 14 – 1
Question : Select the most appropriate option to substitute the bracketed segment in the given sentence. If there is no need to substitute it, select 'no substitution required'. (Because he has been in custody from last July,) Pickard will now be released in four months.
Option 1: Because he had been under custody from last July,
Option 2: Because he has been in custody since last July,
Option 3: Because he had been in custody from last July,
Option 4: No substitution required
Correct Answer: Because he has been in custody since last July,
Solution : The correct option is the second option.
Explanation: This option maintains the correct tense and continuity by using the present perfect tense ("has been") to indicate an action that started in the past and continues up to
Question : Directions: Three of the following four-letter clusters are alike in a certain way and one is different. Pick the cluster that is different from the rest.
Option 1: IJK
Option 2: GIK
Option 3: LNP
Option 4: TVX
Correct Answer: IJK
Solution : Let's check the options – First option: IJK→I + 1 = J; J + 1 = K Second option: GIK→G + 2 = I; I + 2 = K Third option: LNP→L + 2 = N; N + 2 = P Fourth option: TVX→T +
Question : Identify the INCORRECTLY spelt word in the given sentence. The pyramids that you see in Egypt were built by the Pharoh dynasties who ruled the ancient kingdom of Egypt for thousands of years.
Option 1: Ensure
Option 2: Pharoh
Option 3: Strategy
Option 4: Fulfilment
Correct Answer: Pharoh
Solution : The second option is correct.
The incorrectly spelled word in the given sentence is pharoh. To correct it, add "a" after "r".
The correct spelling is Pharaoh. The word pharaoh refers to the rulers of ancient Egypt.
Therefore, the correct answer, which is
Question : If $\cos(A+B)=0$ and $\sin(A-B)=0$, then what is the value of $\angle A$ and $\angle B$ ? ( $0^\circ < A, B \leq 90 ^\circ$)
Option 1: $20^\circ, 70^\circ$
Option 2: $45^\circ, 45^\circ$
Option 3: $60^\circ, 30^\circ$
Option 4: $15^\circ, 75^\circ$
Correct Answer: $45^\circ, 45^\circ$
Solution : Given: $\cos(A+B)=0$ and $\sin(A-B)=0$ The equation $\cos(A+B)=\cos 90^\circ$ $A+B=90^\circ$............(equation 1) The equation $\sin(A-B)=\sin 0^\circ$ $A-B=0^\circ$............(equation 2) Solving these two equations, we get: $\angle A = \angle B = 45^\circ$ Hence, the correct answer is $45^\circ, 45^\circ$.
Question : Directions: A cube is made by folding the given sheet. In the cube so formed, which number letter will be on the face opposite to the face showing 7?
Option 1: A
Option 2: 4
Option 3: 6
Option 4: 8
Correct Answer: 4
Solution : The opposite pairs of faces are as follows –
So, in the 3D view of dice, the face opposite the face showing 7 is 4. Hence, the second option is correct.
Question : Identify the segment in the sentence which contains a grammatical error. If there is no error, select ‘No error’. You should tell these children to complete their projects himself.
Option 1: You should tell
Option 2: No error
Option 3: these children to complete
Option 4: their project himself
Correct Answer: their project himself
Solution : The correct choice is the fourth option.
Question : Which plants are included in Thallophyta?
Option 1: Ulva, Chara and Cladophora
Option 2: Lichens, vascular plants and Pteridophyta
Option 3: Rose, lotus, and Lichens
Option 4: Nostoc, Rose, and Melon
Correct Answer: Ulva, Chara and Cladophora
Solution : The correct options are Ulva, Chara and Cladophora.
Thallophytes are non-vascular plants, which means these plants do not possess xylem and phloem.
Question : Which of the following statements is correct regarding the marginal utility of a commodity?
I. It is the change in total utility due to the consumption of one additional unit of a commodity. II. It diminishes with an increase in consumption of the commodity.
Option 1: Both I and II
Option 2: Only II
Option 3: Only I
Option 4: Neither I nor II
Correct Answer: Both I and II
Solution : The correct option is Both I and II.
The following is an accurate statement about a commodity's marginal utility:
I. It is the difference in overall utility brought about by using one more unit of a resource.
The additional satisfaction or
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