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Question : What is the value of $\cos ^2 15°?$
Option 1: $(2+\sqrt{3})$
Option 2: $\frac{(2+\sqrt{3})}{4}$
Option 3: $\frac{(2+\sqrt{3})}{2}$
Option 4: $\frac{(1+\sqrt{3})}{2}$
Correct Answer: $\frac{(2+\sqrt{3})}{4}$
Solution : According to the formula, $\cos 2A = 2\cos^2 A - 1$ Let A = 15° ⇒ $\cos 30° = 2\cos^2 15° - 1$ ⇒ $\cos^2 15° = \frac{\cos 30°+1}{2}$ ⇒ $\cos^2 15° = \frac{\frac{\sqrt3}{2}+1}{2}$ $\therefore\cos^2 15°=\frac{\sqrt3 + 2}{4}$ Hence, the correct answer is $\frac{2+\sqrt3}{4}$.
Question : Select the most appropriate meaning of the underlined idiom. Some colleagues at a workplace are really hard nuts to crack.
Option 1: Hardcore traditions in a family
Option 2: An inflexible person who is hard to convince
Option 3: Someone showing extra concern over little things
Option 4: An easy-goer who can be easily convinced
Correct Answer: An inflexible person who is hard to convince
Solution : The correct choice is the second option.
The idiom hard nuts to crack refers to individuals who are difficult to understand, persuade, or influence. They are resistant to change or persuasion, making it challenging to get them to
Question : Lucknow Pact was signed between______.
Option 1: the Muslim League and Mahatma Gandhi
Option 2: the Indian National Congress and Arya Samaj
Option 3: the Indian National Congress and the Muslim League
Option 4: the Indian National Congress and Sayyid Ahmed Khan
Correct Answer: the Indian National Congress and the Muslim League
Solution : The correct answer is the Indian National Congress and the Muslim League.
The Lucknow Pact was signed between the Indian National Congress and the All-India Muslim League on December 19, 1916. It was an agreement aimed at
Question : Directions: Five friends M, N, O, P and Q sit around a circular table facing away from the centre. O is sitting to the immediate left of P who sits third to the right of Q. M does not sit adjacent to P. Who sits to the immediate right of P?
Option 1: N
Option 2: Q
Option 3: O
Option 4: M
Correct Answer: N
Solution : Given: (I) Five friends M, N, O, P, and Q sit around a circular table facing away from the centre. O is sitting to the immediate left of P who sits third to the right of Q. (II) M does not sit adjacent to P.
Question : Parts of the following sentence are given as options. Identify the segment that contains a grammatical error. The bus broke down because we had to walk some distance.
Option 1: because we
Option 2: The bus broke down
Option 3: some distance
Option 4: had to walk
Correct Answer: because we
Solution : The first option is the correct choice.
When we read the sentence, we get to know that something happened because of which someone has to suffer. When the reason is given first and then the result or action, we must use "that is why",
Question : Directions: In the following question, find the odd letter cluster from the given alternatives.
Option 1: AEIM
Option 2: BFJN
Option 3: CGKO
Option 4: FDKN
Correct Answer: FDKN
Solution : Let's check the options – First option: AEIM; A + 4 = E; E + 4 = I; I + 4 = M Second option: BFJN; B + 4 = F; F + 4 = J; J + 4 = N Third option: CGKO; C
Question : Select the option that can be used as a one-word substitute for the given phrase. One who goes from place to place, begging
Option 1: Misogamist
Option 2: Malleable
Option 3: Meticulous
Option 4: Mendicant
Correct Answer: Mendicant
Solution : The correct answer is the fourth option.
The term "mendicant" is a one-word substitute that accurately represents the given phrase "one who goes from place to place, begging." A mendicant is an individual, often associated with a religious order, who survives by asking for alms
Question : Select the option that expresses the given sentence in passive voice. Who teaches her geography?
Option 1: By who geography is taught to her?
Option 2: By whom she is taught geography?
Option 3: By whom is she taught geography?
Option 4: By whom was she taught geography?
Correct Answer: By whom is she taught geography?
Solution : The correct answer is the third option.
In the original sentence, "Who teaches her geography?" is in the active voice, in which the subject who is performing the action as the subject is the doer in the active voice whereas
Question : What is the value of $3 \sin ^2 30^{\circ}+\frac{3}{5} \cos ^2 60^{\circ}–2 \sec ^2 45^{\circ} $?
Option 1: $-\frac{5}{2}$
Option 2: $-\frac{5}{8}$
Option 3: $-\frac{31}{10}$
Option 4: $-\frac{25}{17}$
Correct Answer: $-\frac{31}{10}$
Solution : Given: The trigonometric expression is $3 \sin ^2 30^{\circ}+\frac{3}{5} \cos ^2 60^{\circ}–2 \sec ^2 45^{\circ} $. We know the values of trigonometric ratios, $\sin 30^{\circ} =\frac{1}{2}$, $\cos 60^{\circ}=\frac{1}{2}$ and $\sec 45^{\circ}=\sqrt2$. ⇒ $3 \sin ^2 30^{\circ}+\frac{3}{5} \cos ^2 60^{\circ}–2 \sec ^2 45^{\circ}$ $= 3\times(\frac{1}{2})^2+\frac{3}{5}\times(\frac{1}{2})^2–2 \times
Question : If $a+b+c=13$ and $a b+b c+c a=45$, find $a^2+b^2+c^2$.
Option 1: 79
Option 2: 65
Option 3: 57
Option 4: 85
Correct Answer: 79
Solution : Given: $a+b+c=13$ and $ab+bc+ca=45$ $a^2 + b^2 + c^2 = (a + b + c)^2 - 2 (ab + bc + ca)$ $= 13^2-2\times 45$ $= 169-90 = 79$ Hence, the correct answer is 79.
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