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Question : If $\operatorname{cosec} A+\cot A=7$, then $\operatorname{cosec} A$ is equal to:
Option 1: $\frac{11}{7}$
Option 2: $\frac{16}{7}$
Option 3: $\frac{25}{7}$
Option 4: $\frac{19}{7}$
Correct Answer: $\frac{25}{7}$
Solution : We know if $\operatorname{cosec}x + \cot x = a$, then $\operatorname{cosec} x - \cot x = \frac{1}{a}$ Given, $\operatorname{cosec} A+\cot A=7$ ........(1) ⇒ $\operatorname{cosec} A-\cot A=\frac17$ .........(2) Solving these equations to get the value of $\operatorname{cosec} A$ (1) + (2), we get, ⇒ $\operatorname{cosec} A+\cot
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Question : PQRS is a cyclic quadrilateral. If $\angle$P is three times of $\angle$R and $\angle$S is four times of $\angle$Q, then the sum of $\angle$S + $\angle$R will be:
Option 1: $169^{\circ}$
Option 2: $171^{\circ}$
Option 3: $187^{\circ}$
Option 4: $189^{\circ}$
Correct Answer: $189^{\circ}$
Solution : $\angle$P = 3$\angle$R $\angle$S = 4$\angle$Q As PQRS is a cyclic quadrilateral, $\angle$P + $\angle$R = $180^{\circ}$ ⇒ 3$\angle$R + $\angle$R = $180^{\circ}$ ⇒ 4$\angle$R = $180^{\circ}$ $\therefore$ $\angle$R = $45^{\circ}$ ⇒ $\angle$P = 3 × $45^{\circ}$ = $135^{\circ}$ $\angle$S + $\angle$Q = $180^{\circ}$ ⇒
Question : The remainder when $19^{19}+20$ is divided by 18, is:
Option 1: 3
Option 2: 2
Option 3: 1
Option 4: 0
Correct Answer: 3
Solution : To find: The remainder when $19^{19}+20$ is divided by 18. Now, 19 $\equiv$ 1 (mod 18) ⇒ 1919 $\equiv$ 119 (mod 18) ⇒ 1919 $\equiv$ 1 (mod 18) ⇒ (1919 + 20) $\equiv$ (1 + 20) (mod 18) ⇒ (1919
Question : Directions: In the following question, some parts of the sentence may have errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No Error".
There are many inner voices that speak (1) / to us inside your head, and believe that (2) / they should not be trusted. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The correct choice is the second option.
It should be "our head" instead of "your head" the correct possessive pronoun to match the noun. Since the sentence refers to the inner voices speaking to "us" (which includes the speaker), it is more appropriate to
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the given sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (9, 7,189) (4, 13, 156)
Option 1: (5, 9, 160)
Option 2: (6, 9, 162)
Option 3: (8, 5,125)
Option 4: (7, 8, 188)
Correct Answer: (6, 9, 162)
Solution : Given: (9, 7,189); (4,13,156)
The product of the first and second numbers is multiplied by 3, to get the third number – ⇒ (9, 7,189)→(9 × 7) × 3 = 189 ⇒ (4, 13,156)→(4 × 13) × 3 = 156
Let's check each
Question : Directions: Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusions logically follow from the given statements. Statements: I. All papers are scissors. II. Some scissors are books. III. All books are animals. Conclusions: I. Some animals are books II. Some scissors are paper.
Option 1: Only conclusion (II) follows
Option 2: Only conclusion (I) follows
Option 3: Both conclusions (I) and (II) follow
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 animals are books – From the Venn diagram, we can see that the circle representing books is completely inside
Question : Select the option that expresses the given sentence in active voice. What information was shared with the school authority by the inspection team?
Option 1: What information has the inspection team shared with the school authority?
Option 2: What information did the inspection team share by the school authority?
Option 3: What information did the inspection team share with the school authority?
Option 4: What information the inspection team shared with the school authority?
Correct Answer: What information did the inspection team share with the school authority?
Solution : The third option is the correct choice.
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
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