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Question : A policeman sees a chain snatcher at a distance of 500 m. He starts chasing the chain snatcher who is running at a speed of 5 m/s, while the policemen are chasing him at a speed of 15 m/s. When the chain snatcher is caught by the policemen, what distance will the chain snatcher have covered?
Option 1: 200 m
Option 2: 180 m
Option 3: 150 m
Option 4: 250 m
Correct Answer: 250 m
Solution : Speed of the policeman = 15 m/s Speed of the snatcher = 5 m/s Relative speed of policeman with respect to snatcher= (15 – 5) m/s = 10 m/s Distance the policeman has to cover = 500 m Now, Time by which snatcher is
Question : The value of $x$ for which the expressions $15x+4$ and $13x-2$ become equal is:
Option 1: –1
Option 2: 1
Option 3: –3
Option 4: 3
Correct Answer: –3
Solution : Given: Value of $x$ for $15x+4=13x-2$. ⇒ $15x-13x=-2-4$ ⇒ $2x=-6$ ⇒ $x=\frac{-6}{2}$ ⇒ $x=-3$ Hence, the correct answer is –3.
Question : Directions: Select the option that is related to the third word in the same way as the second word is related to the first word. Rational : Illogical :: Scanty : ?
Option 1: Moving
Option 2: Abundant
Option 3: Nodding
Option 4: Less
Correct Answer: Abundant
Solution : Given: Rational : Illogical :: Scanty : ?
Like, Illogical is the the antonym of Rational. Similarly, the antonym for Scanty is abundant.
Hence, the second option is correct.
Question : Directions: Two statements are given, followed by three conclusions numbered I, II, and III. 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 colleges are schools. No ground is a college. Conclusions: I. No college is a ground. II. No school is a college. III. Some schools are colleges.
Option 1: Only conclusions II and III follow
Option 2: Only conclusions I and II follow
Option 3: Only conclusions I and III follow
Option 4: All of the conclusions follow
Correct Answer: Only conclusions I and III follow
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyze the conclusions – Conclusion (I): No college is a ground – From the Venn diagram, it is evident that there is a negative relation between
Question : In a triangle, if three altitudes are equal, then the triangle is:
Option 1: obtuse
Option 2: equilateral
Option 3: right-angled
Option 4: Isosceles
Correct Answer: equilateral
Solution : AD, BE and CF are the altitudes drawn on sides BC, CA and AB of $\triangle$ABC such that AD = BE = CF. Since area of triangle = $\frac{1}{2}$ × base × corresponding altitude, Area of $\triangle$ABC = $\frac{1}{2}$ × BC × AD = $\frac{1}{2}$
Question : Directions: Select the correct combination of mathematical signs to sequentially replace the * signs and to balance the given equation. 213 * 67 * 119 * (248 * 31) * 169
Option 1: –, ÷, =, –, ×
Option 2: +, –, +, ÷, =
Option 3: ×, –, =, +, ÷
Option 4: +, −, =, –, ×
Correct Answer: +, –, +, ÷, =
Solution : Given: 213 * 67 * 119 * (248 * 31) * 169
Replace * with the mathematical signs and solve the equations one by one. Let's check the given options – First option: −, ÷, =, −, × ⇒ 213 –
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bold part of the sentence. In case no improvement is needed, select "No Improvement".
A chance remark by her friend transported her life.
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 3
Solution : The correct option is the third option.
The appropriate answer is transformed. This word shows that her friend's comment influenced her life, which is the intended meaning.
The meanings of the other options are as follows:
Question : If the compound interest on a certain sum for 2 years at 4% per annum is Rs. 102, the simple interest on the same rate of interest for two years would be:
Option 1: Rs. 200
Option 2: Rs. 50
Option 3: Rs. 150
Option 4: Rs. 100
Correct Answer: Rs. 100
Solution : Given: Compound Interest = Rs. 102 Rate = 4% per annum Time = 2 years When compounded annually, Compound interest $CI= P(1+\frac{R}{100})^{T}-P$, where $A$ is the total amount, $P$ is the principal amount, $R$ is the rate of interest per annum and $T$ is
Question : Of the three numbers whose average is 40, the first is $\frac{1}{3}$rd of the sum of the other two. What is the first number?
Option 1: 20
Option 2: 50
Option 3: 25
Option 4: 30
Correct Answer: 30
Solution : Let the numbers be $x, y, z$. Their average is 40. Sum = $x + y + z = 40 × 3 = 120$ --(1) and given that $x = \frac{1}{3}(y+z)$ ⇒ $3x = y + z$ Putting the value of $y+z$ in equation 1,
Question : In $\triangle A B C, O$ is the point of intersection of the bisectors of $\angle B$ and $\angle A$. If $\angle B O C=108^{\circ}$, then $\angle B A O=$?
Option 1: 27°
Option 2: 40°
Option 3: 18°
Option 4: 36°
Correct Answer: 18°
Solution : In $\triangle$ABC, O is the point of intersection of the bisectors of $\angle$B and $\angle$A $\angle$BOC = 108° If the bisector of $\angle$ABC and $\angle$ACB of a triangle ABC meet at a point O then, $\angle$BOC = $90^\circ + \frac{1}{2}$$\angle$A ⇒ $108^\circ = 90^\circ +
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