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Question : Directions: Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: I. All males are females. II. Some females are old. Conclusions: I. All males are old. II. Some males are old.
Option 1: Only II follows
Option 2: Neither I nor II follows
Option 3: Only I follows
Option 4: Both I and II follow
Correct Answer: Neither I nor II follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All males are old – From the Venn diagram, it is evident that there is no direct relation between males and
Question : Select the most appropriate option to fill in the blank. The police will regard it as an accident ______ any evidence to the contrary is found.
Option 1: still
Option 2: whenever
Option 3: otherwise
Option 4: unless
Correct Answer: unless
Solution : The fourth option is correct.
Question : Directions: Select a suitable figure from the answer figures that would replace the question mark (?).
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Given: Moving from Figure 1 to Figure 2, the lines with the symbol are rotated 90 degrees anti-clockwise.
Moving from Figure 2 to Figure 3, the lines with the symbol are rotated 90 degrees anti-clockwise. Moving from Figure 3 to Figure 4, the lines with the
Question : The selling price of 28 items is equal to the cost price of 17 items. What is the percentage of profit or loss?
Option 1: $39 \frac{2}{7} \%$ loss
Option 2: $39 \frac{2}{7} \%$ profit
Option 3: $33 \frac{2}{7} \%$ profit
Option 4: $33 \frac{2}{7} \%$ loss
Correct Answer: $39 \frac{2}{7} \%$ loss
Solution : Let the cost price of each item be Re. 1 ⇒ cost price of 28 items = Rs. 28 Also, Selling price of 28 items = Rs. 17 ⇒ Loss = 28 - 17 = Rs. 11 ⇒ Loss % = $\frac{11}{28}
Question : Which of the following does not belong to the physical environment?
Option 1: Hemisphere
Option 2: Atmosphere
Option 3: Lithosphere
Option 4: Hydrosphere
Correct Answer: Hemisphere
Solution : The correct option is Hemisphere.
The term hemisphere has no significance in the physical environment. The term hemisphere refers to the split of the Earth's surface into halves based on latitude lines, such as the Northern and Southern Hemispheres.
Question : In which of the following quadrilateral, opposite sides are not parallel?
Option 1: rectangle
Option 2: parallelogram
Option 3: rhombus
Option 4: kite
Correct Answer: kite
Solution : Opposite sides are parallel in rectangle, parallelogram and rhombus. Opposite sides are not parallel in a kite. Hence, the correct answer is kite.
Question : The value of $\cos^2 32^{\circ}-\sin^2 58^{\circ}$ is:
Option 1: $\frac{1}{2}$
Option 2: $-1$
Option 3: $1$
Option 4: $0$
Correct Answer: $0$
Solution : $\cos^2 32^{\circ}-\sin^2 58^{\circ}$ $= \cos^2 32^{\circ} - \sin^2 (90^{\circ}-32^{\circ})$ $= \cos^2 32^{\circ} - \cos^2 32^{\circ} = 0$ Hence, the correct answer is $0$.
Question : By which natural number should 5000 be divided so that it becomes a perfect square?
Option 1: 2
Option 2: 5
Option 3: 8
Option 4: 7
Correct Answer: 2
Solution : Find factors of 5000, 5000 = 2 × 5 × 5 × 10 × 10 Here, the factor of 2 doesn't come in a pair. Therefore, 5000, when divided by 2, will yield a perfect square. Hence, the correct answer is 2.
Question : PQR is an equilateral triangle inscribed in a circle. S is any point on the arc QR. Measure of $\frac{1}{2} \angle \mathrm{PSQ}$ is:
Option 1: 20°
Option 2: 15°
Option 3: 30°
Option 4: 60°
Correct Answer: 30°
Solution :
Since PQR is an equilateral triangle inscribed in a circle, each of its angles is 60°. $\angle PSQ=\angle QRP = $ 60° (Angles in the same segment) $\frac{1}{2}\times \angle PSQ=\frac{60°}{2}=30°$ Hence, the correct answer is 30°.
Question : Directions: A piece of paper is folded and punched as shown below in the question figures. From the given answer figures, indicate how it will appear when opened.
Solution : When the given folded paper is unfolded, it will look like –
Hence, the second option is correct.
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