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Question : If the numerical values of the height and the area of an equilateral triangle are the same, then the length of each side of the triangle is:
Option 1: 2 units
Option 2: 4 units
Option 3: 5 units
Option 4: 8 units
Correct Answer: 2 units
Solution : Let the side of an equilateral triangle be $a$ units. Let its height be $h$. Using Pythagoras theorem, we get, $a^2 = h^2+(\frac{a}2)^2$ ⇒ $h=\frac{\sqrt{3}}2a$ Area of equilateral triangle = $\frac{\sqrt{3}}{4}a^2$ sq. units According to the question, $\frac{\sqrt{3}}2a=\frac{\sqrt{3}}{4}a^2$ ⇒ $a=2$ units Hence, the correct
Question : Directions: There are eight persons, A, B, C, D, E, F, G and H, all having different weights. Only two persons are lighter than F. F is heavier than A but lighter than B. D is lighter than E but heavier than G. H is lighter than A. C is heavier than E. C is not the heaviest person. The weights of the second heaviest and the second lightest persons are 78 kg and 48 kg, respectively. How many persons are lighter than the person who is just lighter than D?
Option 1: One
Option 2: Three
Option 3: Four
Option 4: Two
Correct Answer: Three
Solution : Given: (I) Only two persons are lighter than F. F is heavier than A but lighter than B. B > F > A > _ (II) D is lighter than E but heavier than G. H is lighter than A. C is heavier than E.
Question :
Directions: In the following question, select the related word from the given alternatives. Forecast : Future :: Regret : ?
Option 1: Present
Option 2: Sins
Option 3: Life
Option 4: Past
Correct Answer: Past
Solution : Given: Forecast : Future :: Regret : ?
Forecast stands for the prediction of future. Regret is a feeling about something bad or wrong which is already made in the past.
Hence, the fourth option is correct.
Question : A copper sphere of diameter 18 cm is drawn into a wire of diameter 6 mm. Find the length of the wire.
Option 1: 143 m
Option 2: 108 m
Option 3: 324 m
Option 4: 234 m
Correct Answer: 108 m
Solution : Diameter of sphere = 18 cm Radius of sphere, $R$ = 9 cm Diameter of wire = 6 mm The radius of wire, $r$ = 3 mm = 0.3 cm Let $l$ be the length of the wire. Volume of sphere = volume of
Question : A sum of Rs. 11064 gives an interest of Rs. 2766 in $x$ years at 5% per annum simple interest. What will be the value of $x$?
Option 1: 3
Option 2: 2
Option 3: 4
Option 4: 5
Correct Answer: 5
Solution : Given: Principal = Rs. 11064 Simple interest = Rs. 2766 Time = $x$ years Rate = 5% We know that, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ ⇒ $2766=\frac{11064 × 5 × x}{100}$ ⇒ $x=\frac{2766\times100}{11064 × 5}$ $\therefore x=5$ years Hence, the correct answer
Question : In a triangle ABC, $\angle A = 70^{\circ}, \angle B = 80^{\circ}$ and D is the incentre of $\triangle ABC. \angle ACB = 2 x^{\circ}$ and $\angle BDC = y^{\circ}$ The values of x and y, respectively, are:
Option 1: 15 and 130
Option 2: 15 and 125
Option 3: 35 and 40
Option 4: 30 and 150
Correct Answer: 15 and 125
Solution : Given: $\angle A=70^{\circ},\angle B=80^{\circ}$, $\angle ACB = 2x^{\circ},$ and $\angle BDC = y^{\circ}$ $\angle C = 180^{\circ}-70^{\circ}-80^{\circ}=30^{\circ}$ $\therefore \angle ACB = 2x^{\circ} = 30^{\circ}$ $⇒x=15^{\circ}$ Now, $\angle BDC=90^{\circ}+\frac{1}{2}\angle A^{\circ}$ ⇒ $y=90^{\circ}+\frac{1}{2}\angle 70^{\circ}$ $\therefore y=125^{\circ}$ Hence, the correct answer is 15 and 125.
Question : Directions: Select the option figure that is embedded in the given figure (rotation is NOT allowed).
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Since the rotation is restricted. So, the embedded figure will have the same orientation as the main figure. By comparison of all the option figures, only the third option figure is embedded in the given question figure.
Hence, the third option is correct.
Question : Directions: In the following question, a series is given with one number missing. Select the missing number from the given alternatives. 3, 8, 5, 27, 8, 64, 12, 125, 17, ?
Option 1: 216
Option 2: 361
Option 3: 625
Option 4: 441
Correct Answer: 216
Solution : Given: 3, 8, 5, 27, 8, 64, 12, 125, 17, ?
The series follows an alternative pattern, where every other number, starting from the first, is obtained by adding consecutive numbers in each previous term to get the next term. On the other hand, every
Question : Directions: Select the option figure in which the given figure (X) is embedded as its part. (Rotation is not allowed.)
Solution : As there is a restriction on the rotation of the figure, we will check where the question figure can exactly fit itself in the given option figures. By comparison of all the option figures, the given question figure is embedded only in the second option figure.
Question : Which among the following is not a component of Lion Capital at Sarnath, India?
Option 1: Carved cow representing the South direction
Option 2: Figures of 4 lions
Option 3: Dharma Chakras
Option 4: Lotus base bell
Correct Answer: Carved cow representing the South direction
Solution : The correct answer is the Carved cow representing the South direction.
The component that is not part of the Lion Capital at Sarnath, India, is the "carved cow representing the south direction." The Lion Capital consists of four lions
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