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Question : In $\triangle$ABC, the straight line parallel to the side BC meets AB and AC at the points P and Q, respectively. If AP = QC, the length of AB is 16 cm and the length of AQ is 4 cm, then the length (in cm) of CQ is:
Option 1: $(2 \sqrt{21}+2)$
Option 2: $(2 \sqrt{18}-2)$
Option 3: $(2 \sqrt{17}-2)$
Option 4: $(2 \sqrt{19}+2)$
Correct Answer: $(2 \sqrt{17}-2)$
Solution : In $ \triangle $APQ and $ \triangle $ABC, $ \angle $P = $ \angle $B (corresponding angle) $ \angle $Q = $ \angle $C (corresponding angle) $ \triangle $APQ $\sim$ $ \triangle $ABC, by AA similarity. Given that AP = QC, AB = 16
Question : Directions: Two statements are given followed by two conclusions numbered I and II. 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: All goods are services. No service is a delivery. Conclusions: I. No good is a delivery. II. Some goods are deliveries.
Option 1: Neither conclusion I nor II follows
Option 2: Both conclusions I and II follow
Option 3: Only conclusion 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 analyze the conclusions – Conclusion I: No good is a delivery – Since all goods are services and no service is delivery. Thus, it can be concluded that
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: I. All knives are guns. II. Some bullets are knives. Conclusions: I. Some guns are bullets. II. No bullet is a gun. III. Some guns are knives.
Option 1: Both conclusions II and III follow
Option 2: Both conclusions I and III follow
Option 3: Conclusions I, II and III follow
Option 4: Both conclusions I and II follow
Correct Answer: Both conclusions I and III follow
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some guns are bullets – From the Venn diagram, it is evident that the circles representing guns and bullets intersect
Question : The sigmoid colon is part of
Option 1: small intestine
Option 2: anal canal
Option 3: large intestine
Option 4: ileum
Correct Answer: large intestine
Solution : The correct option is the large intestine.
The sigmoid colon is a section of the large intestine, also known as the colon. Between the descending colon and the rectum, it is placed. The sigmoid colon's primary role is to store and transport faecal material
Question : Select the most appropriate option to fill in the blank.
The event promised to be a grand show, will see a display of grit, _______ and mettle.
Option 1: tyro
Option 2: zeal
Option 3: umbrage
Option 4: zenith
Correct Answer: zeal
Solution : The correct choice is the second option.
Explanation:
Zeal means great enthusiasm or passion. In the context of the sentence, it aligns well with the display of determination and strength implied by grit and mettle.
The meanings of the other options are as follows:
Question : Directions: Select the option figure that is embedded in the given figure (rotation is NOT allowed).
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Since the rotation is restricted. So, the embedded figure will have the same orientation as the main figure. By comparison of all the option figures, only the fourth option figure is embedded in the given question figure.
Hence, the fourth option is correct.
Question : If $a^2+1=9a$ and $a\neq0$, then the value of $a^2+\frac{1}{a^2}$ is:
Option 1: 81
Option 2: 18
Option 3: 79
Option 4: 83
Correct Answer: 79
Solution : Given: $a^2+1=9a, a\neq0$ Dividing both sides by $a$, we get $a+\frac{1}{a}=9$ Squaring both sides, we get $a^2+\frac{1}{a^2}+2×a×\frac{1}{a}=81$ ⇒ $a^2+\frac{1}{a^2}=81-2$ $\therefore a^2+\frac{1}{a^2}=79$ Hence, the correct answer is 79.
Question : Directions: Select the figure that will replace the question mark (?) in the following figure series.
Solution : According to the question figure – 1. The circle moves along the corners in a clockwise direction and changes its shade alternatively from shaded to unshaded and vice versa. 2. The star moves along the diagonals and alternates its shade from shaded to unshaded and vice
Question : Directions: In a certain code language, YOU is written as 7878 and GO is written as 108. How will SIT be written in that language?
Option 1: 3423
Option 2: 3419
Option 3: 3414
Option 4: 3420
Correct Answer: 3423
Solution : Given: YOU is written as 7878 and GO is written as 108.
Multiply the positional value of letters and add 3 to the resultant of YOU, to obtain the required code – Y→25; O→15; U→21 (25 × 15 × 21) + 3 = 7878 Thus,
Question : Select the INCORRECTLY spelt word.
Option 1: Bouquet
Option 2: Hygene
Option 3: Mortgage
Option 4: Champagne
Correct Answer: Hygene
Solution : The correct option is the second option.
Explanation: The correct spelling of the word is hygiene, as it refers to practices or conditions conducive to maintaining health and preventing diseases, especially through cleanliness. It encompasses various habits and routines that promote health, such as regular
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