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Question : In a triangle ABC, if $\angle B=90^{\circ}, \angle C=45^{\circ}$ and AC = 4 cm, then the value of BC is:
Option 1: $\sqrt{2} \mathrm{~cm}$
Option 2: $4 \mathrm{~cm}$
Option 3: $2 \sqrt{2} \mathrm{~cm}$
Option 4: $4 \sqrt{2} \mathrm{~cm}$
Correct Answer: $2 \sqrt{2} \mathrm{~cm}$
Solution : AC = 4 cm $\angle B=90^{\circ}$ $\angle C=45^{\circ}$ $\therefore \angle A = 180^{\circ}-(90^{\circ}+45^{\circ}) = 45^{\circ}$ Since $\angle A= \angle C$, $AB = BC$ -----------(i) By Pythagoras theorem, $AB^2 + BC^2 = AC^2$ ⇒ $BC^2 + BC^2 = 4^2$ ⇒ $2BC^2 = 16$ ⇒
Question : In the higher latitudes (50°–70°) of the northern hemisphere, spectacular coniferous forests are found. These are also called _____________.
Option 1: Veld
Option 2: Tundra
Option 3: Llanos
Option 4: Taiga
Correct Answer: Taiga
Solution : The correct option is Taiga.
In the higher latitudes (50°–70°) of the Northern Hemisphere, the spectacular coniferous forests are often referred to as "taiga." These forests are characterised by coniferous trees such as spruce, fir, and pine, and they play a crucial role in the
Question : A big cube is formed by arranging the 160 coloured and 56 non-coloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimal. The percentage of exposed area that is coloured is:
Option 1: 25.9%
Option 2: 44.44%
Option 3: 35%
Option 4: 46%
Correct Answer: 44.44%
Solution : Total number of cubes = 160 + 56 = 216 Thus, side of cube = $\sqrt[3]{216}$ = 6 unit No. of cubes without exposure = (6 – 2)3 = 64 Thus, 64 coloured cubes will not be exposed. Now, Number of coloured cubes on
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the following set. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits.) (5, 41, 4) (2, 68, 8)
Option 1: (6, 100, 8)
Option 2: (5, 18, 4)
Option 3: (5, 100, 4)
Option 4: (4, 49, 3)
Correct Answer: (6, 100, 8)
Solution : Given: (5, 41, 4); (2, 68, 8)
Here, (5, 41, 4)→(5)2 + (4)2 = 25 + 16 = 41 (2, 68, 8)→(2)2 + (8)2 = 4 + 64 = 68
Let's check the options – First option: (6, 100,
Question : A drink of chocolate and milk contains 8% pure chocolate by volume. If 10 litres of pure milk are added to 50 litres of this drink, the percentage of chocolate in the new drink is:
Option 1: $6 \frac{2}{3}$
Option 2: $5 \frac{2}{3}$
Option 3: $5 \frac{1}{3}$
Option 4: $6 \frac{1}{3}$
Correct Answer: $6 \frac{2}{3}$
Solution : A drink of chocolate and milk contains 8% pure chocolate. 10 litres of pure milk are added to 50 litres of this drink. Let $x$ be the percentage of chocolate in the new drink. Using the above data in the alligation method, we have:
Question : Directions: Arrange the given words in the sequence in which they occur in the dictionary. 1. Temple 2. Trained 3. Training 4. Troupe 5. Tented
Option 1: 15234
Option 2: 15243
Option 3: 15432
Option 4: 14532
Correct Answer: 15234
Solution : Given: 1. Temple 2. Trained 3. Training 4. Troupe 5. Tented
Step 1: Compare the first letter of each word. Since all the words start with the same letter T, then move to the next letter. Step 2: The second letter of each word
Question : Kajal can do a piece of work alone in 24 days, while Neha can do the same work alone in 40 days. Kajal started the work alone, and then after 12 clays, Neha joined her till the completion of the work. How long did the work take to be completed since Kajal started to work on it?
Option 1: $\frac{37}{4}$ days
Option 2: $\frac{39}{2}$ days
Option 3: $\frac{37}{2}$ days
Option 4: $\frac{39}{4}$ days
Correct Answer: $\frac{39}{2}$ days
Solution : LCM of 24 and 40 = 120 Let the total work = 120 units Now, Kajal completes work in = 24 days Efficiency of Kajal = $\frac{120}{24}$ = 5 units/day Efficiency of Neha = $\frac{120}{40}$ = 3 units/day Kajal worked for 12 days before
Question : Select the most appropriate option to fill in the blanks.
As cattle are to herd so are birds to ________.
Option 1: flock
Option 2: litter
Option 3: pack
Option 4: streak
Correct Answer: flock
Solution : The correct choice is the first option.
Flock: A group of birds, typically of the same species, that fly, move, or feed together.
The meanings of the other options are as follows:
Question : The sum of the perfect squares between 120 and 300 is:
Option 1: 1400
Option 2: 1296
Option 3: 1024
Option 4: 1204
Correct Answer: 1400
Solution : Perfect squares between 120 and 300 are 121, 144, 169, 196, 225, 256 and 289. The sum = (121 + 144 + 169 + 196 + 225 + 256 + 289) = 1400 Hence, the correct answer is 1400.
Question : The percentage of the earth's water found in the oceans is ______.
Option 1: 94%
Option 2: 97.2%
Option 3: 90.2%
Option 4: 92.2%
Correct Answer: 97.2%
Solution : The correct option is 97.2%.
The vast majority of Earth's water, around 97.2%, is saline and found in the oceans. Only about 2.5% of Earth's water is freshwater, and the majority of that is locked in ice caps, glaciers, and underground aquifers.
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