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Question :
Which of the following has no blood, but respires?
Option 1:
Fish
Option 2:
Earthworm
Option 3: Hydra
Option 4: Cockroach
Correct Answer: Hydra
Solution : The correct answer is Hydra.
The Genus Hydra falls under the Phylum Cnidaria and is a small group of freshwater Hydrozoans. The body of Hydra is cylindrical and radially symmetrical. The body of Hydra does not contain blood instead, they have Mesenchymal stem cells.
Question : From a point 12 m above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. What is the height (in m) of the hill?
Option 1: $48 \sqrt{3}$
Option 2: $36$
Option 3: $36 \sqrt{3}$
Option 4: $48$
Correct Answer: $48$
Solution : Given : Point 12 m above the water level The angle of elevation of the top of a hill = $60^\circ$ The angle of depression of the base of the hill = $30^\circ$ Now, In triangle ABE $\Rightarrow \tan 30^\circ\ =\ \frac{AB}{BE}$ $\Rightarrow \frac{1}{\sqrt{3}}\ =\
Question : Assume that a drop of water is spherical and that its diameter is one-tenth of a cm. A conical glass has a height equal to the diameter of its rim. If 32,000 drops of water fill the glass completely, then the height of the glass (in cm) is:
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 4
Solution : Height of the glass $=h$ cm Radius of the glass $=\frac{h}{2}$ Volume of the glass $=\frac{1}{3}\pi r^2 h=\frac{1}{3}\pi (\frac{h}{2})^2 h$ Radius of the spherical drop $=\frac{1}{2\times10}=\frac{1}{20}$ cm Volume of a spherical drop $=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (\frac{1}{20})^3$ Volume of 32,000 spherical drops $=32000\times\frac{4}{3}\pi (\frac{1}{20})^3$ Now, the volume
Question : If $\tan^4\theta + \tan^2\theta=1$, what is the value of $11(\cos^4\theta+\cos^2\theta)$?
Option 1: – 11
Option 2: 8
Option 3: 0
Option 4: 11
Correct Answer: 11
Solution : Given: $\tan^4\theta + \tan^2\theta=1$ ⇒ $\tan^2\theta(\tan^2\theta+1)=1 [\because \sec^2\theta-\tan^2\theta=1]$ ⇒ $\tan^2\theta \sec^2\theta=1$ $\therefore \tan^2\theta=\cos^2\theta$ $11(\cos^4\theta+\cos^2\theta)$ = $11[(\cos^2\theta)^2+\cos^2\theta]$ = $11(\tan^4\theta + \tan^2\theta)$ = $11×1$ = $11$ Hence, the correct answer is 11.
Question : If $\cos A=\frac{1}{2}, 0 \leq A \leq 90^{\circ}$, then what is the value of sin (180 - A)?
Option 1: $\frac{1}{2}$
Option 2: $\frac{\sqrt{3}}{2}$
Option 3: $\frac{1}{\sqrt{3}}$
Option 4: $1$
Correct Answer: $\frac{\sqrt{3}}{2}$
Solution : According to the question sin2A + cos2A = 1 ⇒ sin$^{2} A + \frac{1}{2}^{2}$ = 1 ⇒ sin$^{2} A + \frac{1}{4}$ = 1 ⇒ sin$^{2} A = 1 - \frac{1}{4}$ = $\frac{3}{4}$ ⇒ Sin A = $\frac{\sqrt{3}}{2}$ Now, ⇒ sin(180 −
Question : Find the length of the arc if the angle at the centre of the circle of radius 7 units is 60°.
Option 1: $4$ units
Option 2: $\frac{11}{4}$ units
Option 3: $\frac{22}{3}$ units
Option 4: $21$ units
Correct Answer: $\frac{22}{3}$ units
Solution : Given: The radius of the circle: 7 units The angle at the centre is 60°. Length of arc = $\frac{θ}{360°} × 2πr$, here $r$ is the radius and $\theta$ is the angle at centre. ⇒ Length of the arc = $\frac{60°}{360°} × 2 ×
Question : If $\frac{xy}{x+y}=a$, $\frac{xz}{x+z}=b$ and $\frac{yz}{y+z}=c$, where $a,b,c$ are all non-zero numbers, $x$ equals to:
Option 1: $\frac{2abc}{ab+bc–ac}$
Option 2: $\frac{2abc}{ab+ac–bc}$
Option 3: $\frac{2abc}{ac+bc–ab}$
Option 4: $\frac{2abc}{ab+bc+ac}$
Correct Answer: $\frac{2abc}{ac+bc–ab}$
Solution : Given: $\frac{xy}{x+y}=a$, $\frac{xz}{x+z}=b$ and $\frac{yz}{y+z}=c$, where $a,b,c$ are all non-zero numbers. We can write $\frac{xy}{x+y}=\frac{1}{\frac{1}{x}+\frac{1}{y}}$ ⇒ $\frac{1}{a}=\frac{1}{x}+\frac{1}{y}$ -------------------------------(1) Similarly, we can write, $\frac{xz}{x+z}=\frac{1}{\frac{1}{x}+\frac{1}{z}}$ ⇒ $\frac{1}{b}=\frac{1}{x}+\frac{1}{z}$ --------------------------------(2) Similarly, $\frac{1}{c}=\frac{1}{y}+\frac{1}{z}$ ----------------------(3) Adding equation (1) and equation (2), ⇒ $\frac{1}{a}+\frac{1}{b}=\frac{2}{x}+\frac{1}{y}+\frac{1}{z}$ ⇒ $\frac{1}{a}+\frac{1}{b}=\frac{2}{x}+\frac{1}{c}$ ⇒ $\frac{1}{a}+\frac{1}{b}–\frac{1}{c}=\frac{2}{x}$ ⇒ $\frac{(bc+ac–ab)}{abc}=\frac{2}{x}$ $\therefore x=\frac{2abc}{(bc+ac–ab)}$
Question : Select the most appropriate ANTONYM of the given word.
Hostile
Option 1: Hospitable
Option 2: Bitter
Option 3: Nasty
Option 4: Aggressive
Correct Answer: Hospitable
Solution : The most appropriate option is the first option.
"Hospitable" is the direct antonym of "hostile". While "hostile" means unfriendly or antagonistic, "hospitable" means welcoming and friendly.
The meanings of the other options are as follows:
Question : The radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 8 : 5. The ratio of their volumes is equal to:
Option 1: 9 : 10
Option 2: 8 : 9
Option 3: 9 : 11
Option 4: 7 : 10
Correct Answer: 9 : 10
Solution : Given: The radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 8 : 5. Let the radii of two cylinders be $3x$ and $4x$ and their heights be $8y$ and $5y$. Use the formulas,
Question : Directions: In a certain code language, PLIERS is coded as MMAFJO, and SHOVEL is coded as FZRLFR. How will WRENCH be coded in the same language?
Option 1: CXJBQU
Option 2: BXJBPV
Option 3: BXJBQU
Option 4: CXIBPV
Correct Answer: BXJBPV
Solution : Given: PLIERS is coded as MMAFJO and SHOVEL as FZRLFR.
Like, PLIERS; PLIERS→SREILP (Reverse the letters); S – 6 = M; R – 5 = M; E – 4 = A; I – 3 = F; L – 2 = J; P – 1 =
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