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Question : Two alloys consist of copper and tin. The copper-to-tin ratio in the first alloy is 1 : 3, and in the second alloy, it is 2 : 5. What ratio should the two alloys be mixed in to create a new alloy with a tin-to-copper ratio of 8 : 3?
Option 1: 3 : 5
Option 2: 4 : 7
Option 3: 3 : 8
Option 4: 5 : 11
Correct Answer: 4 : 7
Solution : Given: The ratio of copper and tin in the first alloy is 1 : 3. And in the second alloy is 2 : 5. Let the alloys be mixed in the ratio of $x:y$. Copper in first alloy = $\frac{x}{4}$ Tin in first
Question : Directions: How many quadrilaterals are there in the given figure?
Option 1: 11
Option 2: 12
Option 3: 10
Option 4: 9
Correct Answer: 11
Solution : The given figure can be labelled as shown below –
In the above-labelled figure, there are a total of 11 quadrilaterals. They are ABJH, BCIJ, ACIH, HIFG, ACFG, CDEF, ABJG, BJFC, GJIF, GHJF, ADEG.
Hence, the first option is correct.
Question : If $D$ and $E$ are points on sides $AB$ and $AC$ of $\Delta ABC$. $DE$ is parallel to $BC$. If $AD: DB = 2:3$ and the area of $\Delta ADE$ is 4 sq. cm, what is the area (in sq. cm) of quadrilateral $BDEC$?
Option 1: 25
Option 2: 21
Option 3: 5
Correct Answer: 21
Solution : We have, $AD:DB = 2:3$, area($\triangle ADE$) = 4 sq. cm Let $AD = 2x$ and $DB = 3x$ So, $AB = AD + DB = 2x + 3x = 5x$ Two triangles $ABC$ and $ADE$ such that $\triangle ABC$ ∼$\triangle ADE$ So, $\frac{\text{area of}
Question : The height of a right circular cone is 24 cm. If the diameter of its base is 36 cm, then what will be the curved surface area of the cone?
Option 1: $1444.6 \; \mathrm{cm^2}$
Option 2: $2400.9\; \mathrm{cm^2}$
Option 3: $1697.14 \; \mathrm{cm^2}$
Option 4: $2144.2\; \mathrm{cm^2}$
Correct Answer: $1697.14 \; \mathrm{cm^2}$
Solution : Given that the diameter of the base is 36 cm. So the radius is 18 cm. Height = 24 cm $l = \sqrt{r^2 + h^2} = \sqrt{(18)^2 + (24)^2}=30\; \text{cm}$ We know, the curved surface area of a cone $=\pi rl$, where $r$
Question : The table given below shows the number of students in 6 different schools.
What is the total number of students in all schools?
Option 1: 1340
Option 2: 1020
Option 3: 1230
Option 4: 1180
Correct Answer: 1230
Solution : The total number of students in all schools = 360 + 180 + 210 + 240 + 90 + 150 = 1230 Hence, the correct answer is 1230.
Question : Select the most appropriate option that can substitute the underlined segment in the given sentence. He was not able to adopt himself to the new environment of the hostel.
Option 1: able to adept himself to
Option 2: able for adopt himself to
Option 3: able to adopt himself with
Option 4: able to adapt himself to
Correct Answer: able to adapt himself to
Solution : The fourth option is correct.
Adopt should be changed to adapt to make the sentence grammatically accurate, as adapt means to adjust to new circumstances, which is the intended meaning whereas adopt means to start doing something new or in a
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. Some chocolates are toffees. II. All toffees are eclairs. Conclusions: I. Some eclairs are toffees. II. Some eclairs are chocolates.
Option 1: Both conclusions I and II follow
Option 2: Only conclusion II follows
Option 3: Only conclusion I follows
Option 4: Neither conclusion I nor II follows
Correct Answer: Both conclusions I and II follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some eclairs are toffees – From the Venn diagram, the circle of toffee is completely inside the circle of eclairs.
Question : When N is divided by 6, the remainder is 4. When 2N is divided by 6, the remainder is:
Option 1: 2
Option 2: 0
Option 3: 3
Option 4: 1
Correct Answer: 2
Solution : Dividend = N, Divisor = 6, Remainder = 4, Quotient = Q Dividend = (Divisor × Quotient) + Remainder Case 1: N = (6 × Q) + 4............................(1) Multiply equation (1) by 2 ⇒ 2N = 2(6 × Q) + 8 ⇒ 2N = 12Q
Question : Comprehension: In the following passage, some of the words have been deleted. Read the passage carefully and select the correct answer for the given blank out of the four alternatives.
The "Sesame Street" spin off (1)__________ to be the first Russian-language educational TV (2)__________ aimed specifically at preschoolers. The project (3)__________ support from both American and Russian government officials. "If we do not reform our (4)__________, we can hardly hope that we will reform our society," (5)_________ Elena Lenskaya, a director in Russia's Ministry of Education, during a 1992 U.S. congressional hearing on the planned adaptation.
Question: Select the most appropriate option to fill in the blank number. 5
Option 1: told
Option 2: ordered
Option 3: said
Option 4: muted
Correct Answer: said
Solution : The third option is correct.
Said is the best fit here because it indicates the act of speaking, which is what Elena Lenskaya did during the 1992 U.S. congressional hearing. It's a neutral term that accurately represents the action of speaking.
The meanings of the
Question : Which river flows between the Satpuras and the Vindhyas?
Option 1: Godavari
Option 2: Gandak
Option 3: Tapti
Option 4: Narmada
Correct Answer: Narmada
Solution : The correct answer is Narmada.
Satpura, and Vindhya Ranges are mountains in central India in the state of Madhya Pradesh, and Maharashtra. Narmada River flows between Satpura and Vindhya Ranges. Narmada River originates from Amarkantak Hills in the state of Madhya Pradesh, and drains
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