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Question : Directions: Three 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: Some if are but. All but are so. No so is a then. Conclusions: I. All if being then is a possibility. II. All then being if is a possibility.
Option 1: Only conclusion II follows
Option 2: Neither conclusion I nor II follows
Option 3: Both conclusions I and II follow
Option 4: Only conclusion I follows
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 if being then is a possibility – From the Venn diagram, it is evident that some if are but and all
Question : An aeroplane flying horizontally at a height of 3 km above the ground is observed at a certain point on earth to subtend an angle of $60^\circ$. After 15 seconds of flight, its angle of elevation is changed to $30^\circ$. The speed of the aeroplane (Take $\sqrt{3}=1.732$) is:
Option 1: 230.63 m/s
Option 2: 230.93 m/s
Option 3: 235.85 m/s
Option 4: 236.25 m/s
Correct Answer: 230.93 m/s
Solution : AB = CD = 3 km = 3000 m In $\triangle$AOB, $\tan60^{\circ}=\frac{AB}{OB}$ ⇒ $OB=\frac{3000}{\sqrt3}=1000\sqrt3$ m In $\triangle$COD, $\tan30^{\circ}=\frac{CD}{OC}$ ⇒ $OC=3000\sqrt3$ m So, BC = AD = ($3000\sqrt3–1000\sqrt3)=2000\sqrt3$ m Therefore, the speed of the aeroplane = $\frac{2000\sqrt3}{15}$ m/s = 230.93 m/s Hence, the correct answer
Question : Directions: Select the correct combination of mathematical signs to replace the * signs and to balance the given equation. 23 * 12 * 36 * 2 * 9 * 285
Option 1: –, =, ×, ×, ÷
Option 2: ×, +, ÷, –, =
Option 3: +, +, =, ×, ×
Option 4: =, +, +, ×, –
Correct Answer: ×, +, ÷, –, =
Solution : Given: 23 * 12 * 36 * 2 * 9 * 285
Replace * with the mathematical signs and solve the equations one by one using the BODMAS. Let's check the given options – First option: –, =, ×, ×, ÷
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the given set. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding/subtracting/multiplying etc to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (15, 45, 90) (8, 24, 48)
Option 1: (9, 27, 45)
Option 2: (7, 21, 24)
Option 3: (6, 18, 36)
Option 4: (12, 36, 68)
Correct Answer: (6, 18, 36)
Solution : Given: (15, 45, 90); (8, 24, 48)
Like, (15, 45, 90)→15 × 3 = 45 and 15 × 6 = 90 (8, 24, 48)→8 × 3 = 24 and 8 × 6 = 48
Let's check the options – First option: (9, 27,
Question : Fill in the blank with an appropriate option. Habitat loss received little attention from all Twitter ______.
Option 1: band
Option 2: users
Option 3: forces
Option 4: pools
Correct Answer: users
Solution : The correct choice is the second option.
The word "users" is the appropriate option to fill in the blank.
The sentence suggests that habitat loss didn't receive much attention from the collective group of people using Twitter. In the context of the sentence, the term
Question : Among the following Himalayan peaks, which is the easternmost?
Option 1: Kangchenjunga
Option 2: Trishul
Option 3: Nanda Devi
Option 4: Kamet
Correct Answer: Kangchenjunga
Solution : The correct option is Kangchenjunga.
Kangchenjunga is the third-highest mountain in the world and is located on the India-Nepal border. It's the tallest mountain in India and the easternmost Himalayan summit, situated on the border between Nepal and the Indian state of Sikkim.
Question : The bar chart given below shows the annual production (in 1000 tonnes) of coffee of a country for the years 2018 to 2022. What is the average production (in 1000 tonnes) of coffee for the years 2018, 2019, and 2020?
Option 1: 530
Option 2: 810
Option 3: 720
Option 4: 640
Correct Answer: 640
Solution : Production of coffee in 2018 = 700 (in 1000 tonnes) Production of coffee in 2019 = 550 (in 1000 tonnes) Production of coffee in 2020 = 670 (in 1000 tonnes) Average = $\frac{\text{Sum of yearly production}}{{\text{Total number of years}}}$ = $\frac{700+550+670}{3}$ = $\frac{1920}{3}$ = $640$
Question : Akham Lakshmi Devi, a recipient of the Sangeet Natak Akademi award, is renowned for which of the following dances?
Option 1: Kathak
Option 2: Odissi
Option 3: Sattriya
Option 4: Manipuri
Correct Answer: Manipuri
Solution : The correct option is Manipuri.
Akham Lakshmi Devi is renowned for the Manipuri dance form. She was a renowned Manipuri dancer and advocate, showcasing this traditional dance style from the northeastern state of Manipur. Akham Lakshmi Devi was conferred with the Sangeet Natak Akademi Award
Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?
Option 1: $\frac{1}{\sqrt{2}}$
Option 2: $\sqrt{3}$
Option 3: $1$
Option 4: $\frac{1}{\sqrt{3}}$
Correct Answer: $1$
Solution : Given: $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$ = $\frac{\sin (90^{\circ}-60^{\circ}) \sin (90^{\circ}-50^{\circ}) \sin (90^{\circ}-40^{\circ}) \sin (90^{\circ}-30^{\circ})}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$ = $\frac{\cos 60^{\circ} \cos 50^{\circ} \cos 40^{\circ} \cos 30^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos
Question : Which state of India has made rainwater harvesting compulsory for all houses?
Option 1: Haryana
Option 2: Maharashtra
Option 3: Tamil Nadu
Option 4: Punjab
Correct Answer: Tamil Nadu
Solution : The correct option is Tamil Nadu.
The first state in India that mandates rooftop rainwater harvesting systems for every home is Tamil Nadu. The act of collecting and storing rainwater as opposed to letting it run off is called rainwater harvesting. Rainwater is collected
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