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Question : The following pie chart represents the units of electricity sold to various categories in a month by an Electricity Supplier. Electricity sold to various categories of a town
The central angle of the sector corresponding to supply for Industries is:
Option 1: $48^\circ$
Option 2: $25^\circ$
Option 3: $46^\circ$
Option 4: $90^\circ$
Correct Answer: $90^\circ$
Solution : Given: Percentage of industries = 25% Central angle $=\frac{\text{Given value of Industries}}{100}\times360^\circ=\frac{25}{100}\times360^\circ=90^\circ$ Hence, the correct answer is $90^\circ$.
Question : Simplify the given equation: $\frac{0.09 \times 0.09+0.04 \times 0.04+0.16 \times 0.16+2 \times 0.09 \times 0.04+2 \times 0.04 \times 0.16+2 \times 0.09 \times 0.16}{0.3 \times 0.3+0.2 \times 0.2+0.4 \times 0.4}$
Option 1: 0.38
Option 2: 0.24
Option 3: 0.32
Option 4: 0.29
Correct Answer: 0.29
Solution : Use the algebraic identity, \((a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca\) Where \(a=0.09\), \(b=0.04\) and \(c=0.16\). Substituting these values into the formula, we get: $=\frac{0.09 \times 0.09+0.04 \times 0.04+0.16 \times 0.16+2 \times 0.09 \times 0.04+2 \times 0.04 \times 0.16+2 \times 0.09 \times 0.16}{0.3 \times 0.3+0.2 \times 0.2+0.4 \times 0.4}$
Question : $\frac{\sec A(\sec A+\tan A)(1-\sin A)}{\left(\operatorname{cosec}^2 A-1\right) \sin ^2 A}$ is equal to:
Option 1: $\cot A$
Option 2: $\cos A$
Option 3: $\sec ^2 A$
Option 4: $\cos ^2 A$
Correct Answer: $\sec ^2 A$
Solution : $\frac{\sec A(\sec A+\tan A)(1-\sin A)}{\left(\operatorname{cosec}^2 A-1\right) \sin ^2 A}$ = $\frac{\frac{1}{\cos A}(\frac{1}{\cos A}+\frac{\sin A}{\cos A})(1-\sin A)}{\left(\operatorname{cot}^2 A\right) \sin ^2 A}$ = $\frac{\frac{1}{\cos^2 A}(1+\sin A)(1-\sin A)}{\left(\frac{\cos^2A}{\sin^2A}\right) \sin ^2 A}$ = $\frac{(1-\sin^2 A)}{\cos^4 A}$ = $\frac{\cos^2 A}{\cos^4 A}$ = $\frac{1}{\cos^2A}$ = $\sec^2A$ Hence, the correct
Question : Select the correctly spelt word.
Option 1: Deifinatn
Option 2: Defination
Option 3: Definition
Option 4: Definasion
Correct Answer: Definition
Solution : The third option is correct.
The correct spelling is definition. The other options (deifinatn, defination, and definasion) contain spelling errors.
Definition is about clarifying the meaning of words and providing clear explanations of concepts or ideas.
Therefore, the correct answer will be definition.
Question : Directions: In a certain code language, GHOST is written as VVSMM, and EATER is written as THXFK. How will HANDS be written in that language?
Option 1: UGRFN
Option 2: NFRGV
Option 3: WHRGN
Option 4: VGRGN
Correct Answer: UGRFN
Solution : Given: GHOST is written as VVSMM, and EATER is written as THXFK.
Add the consecutive natural numbers, in decreasing order (starting from 6) to the place value of the letters of the given words, and then reverse the order of the letters to get the
Question : Directions: Select the missing number from the given responses.
Option 1: 10
Option 2: 20
Option 3: 22
Option 4: 110
Correct Answer: 20
Solution : In a column, determine the square root of the first number to get the second number, and then multiply the second number by 2 to get the third number.
In the first column: $\sqrt36$ = 6 and 6 × 2 = 12 In the second
Question : Directions: Select the option related to the fourth term in the same way as the first term is related to the second term and the fifth term is related to the sixth term. 11 : 132 :: ? : 342 :: 22 : 506
Option 1: 17
Option 2: 19
Option 3: 18
Option 4: 20
Correct Answer: 18
Solution : Given: 11 : 132 :: ? : 342 :: 22 : 506
Add one to the first number and multiply the resultant by the first number – Like, 11 : 132→11 × (11 + 1) = 132 And, 22 : 506→22 × (22 + 1)
Question : Select the option that expresses the given sentence in active voice.
Were the cakes being baked by them?
Option 1: Were they baking the cakes?
Option 2: Did the cakes baked by them?
Option 3: Were they baking the cake?
Option 4: Was cakes being baked by them?
Correct Answer: Were they baking the cakes?
Solution : The correct option is the first option.
Active voice emphasises the doer of the action, while passive voice emphasises the receiver. To convert passive to active, we make the subject perform the action and rephrase the verb.
The structure of
Question : Directions: In the following question, two statements are given followed by two conclusions I and II. You have to consider the two statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow from the given statements. Statements: Some schools are Laboratories. All Laboratories are theatres. Conclusions: I. Some theatres are schools. II. No school is a theatre.
Option 1: Only Conclusion II follows
Option 2: Both Conclusions I and II follow
Option 3: Neither Conclusion I nor II follows
Option 4: Only Conclusion I follows
Correct Answer: Only Conclusion I follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse each conclusion – Conclusion (I): Some theatres are schools – From the Venn diagram, it is evident that the circles representing schools and theatres overlap and have
Question : What is the Atomic Number of the element Einsteinium?
Option 1: 98
Option 2: 101
Option 3: 99
Option 4: 100
Correct Answer: 99
Solution : The correct option is 99.
The atomic number of Einsteinium is 99. A synthetic element, Einsteinium (Es), is a member of the actinide series and is produced artificially in nuclear reactors. Named after Albert Einstein, it is radioactive and has no significant practical applications,
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