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Question : Which of the following statements is FALSE?
Option 1: Two triangles are congruent if the size and shape of the triangles may or may not be equal.
Option 2: SAS and SSS are both conditions of congruency of triangles.
Option 3: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, the triangles are congruent.
Option 4: If two triangles are congruent, one of them can be superimposed on the other triangle.
Correct Answer: Two triangles are congruent if the size and shape of the triangles may or may not be equal.
Solution : Two triangles are congruent if they have the same shape and size. In other words, the corresponding angles and sides of the two triangles are equal. Congruent triangles
Question : Five bells commence tolling together and toll at intervals of 5, 10, 15, 20, and 25 seconds respectively. In 1 hour 20 minutes, how many times do they toll together?
Option 1: 20
Option 2: 15
Option 3: 14
Option 4: 17
Correct Answer: 17
Solution : Time after which the 5 bells will toll together = LCM of 5, 10, 15, 20, and 25 = 5 × 5 × 3 × 2 × 2 = 300 seconds = 5 minutes Total time = 1 hour 20 minutes = 60 + 20
Question : If $\cos3A = \sin (A-18°)$, where 3A is an acute angle, what is the value of A?
Option 1: 110°
Option 2: 108°
Option 3: 54°
Option 4: 27°
Correct Answer: 27°
Solution : Given, $\cos3A = \sin (A-18°)$ We know, $\cos A = \sin(90°-A)$ ⇒ $\sin(90°-3A)=\sin(A-18°)$ ⇒ $90°-3A=A-18°$ ⇒ $90°+18 = A+3A$ ⇒ $4A=108°$ ⇒ $A=27°$ Hence, the correct answer is 27°.
Question : Directions: In the following question, which one set of letters/numbers when sequentially placed at the gaps in the given letter series shall complete it? _ _ babbba_a_ _
Option 1: baaab
Option 2: babbb
Option 3: ababb
Option 4: bbaba
Correct Answer: babbb
Solution : Given: _ _ babbba_a_ _
To fill the series we have to divide the series – _ _ b/abb/ba _/a_ _ Let's check each option – First option: baaab; bab/abb/baa/aab (No repeated pattern has been found) Second option: babbb; bab/abb/ba
Question : Simplify the following expression. 25 + 12 – 2 + (4 + 2)
Option 1: 41
Option 2: 37
Option 3: 35
Option 4: 44
Correct Answer: 41
Solution : Given: 25 + 12 – 2 + (4 + 2) = 25 + 12 – 2 + 6 = 41 Hence, the correct answer is 41.
Question : If $x^{2}+y^{2}+\frac{1}{x^{2}}+\frac{1}{y^{2}}=4$, then the value of $x^{2}+y^{2}$ is:
Option 1: 2
Option 2: 4
Option 3: 8
Option 4: 16
Correct Answer: 2
Solution : $x^{2}+y^{2}+\frac{1}{x^{2}}+\frac{1}{y^{2}}-4=0$ $⇒x^{2}+\frac{1}{x^{2}}-2+y^{2}+\frac{1}{y^{2}}-2=0$ $⇒(x-\frac{1}{x})^2+(y-\frac{1}{y})^2 = 0$ So, $x-\frac{1}{x}=0$ and $y-\frac{1}{y}=0$ ⇒ $x^2-1=0$ and $y^2-1=0$ ⇒ $x^2 = 1$ and $y^2 = 1$ $\therefore x^{2}+y^{2}= 1 + 1 = 2$ Hence, the correct answer is 2.
Question : Directions: The sequence of folding a piece of paper and the manner in which the folded paper is cut is shown in the following figures. How would this paper look when unfolded?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : When the given folded paper is unfolded, it will look like –
Hence, the second option is correct.
Question : Directions: Among the four answer figures, which one can be formed from the cutout pieces given below in the question figure?
Solution : The given figure can be numbered as shown below –
The parts can be arranged in the following manner –
The above-compiled figure matches the figure given in the second option. Hence, the second option is correct.
Question : Fill in the blank with an appropriate option. Participants were ______ a meal of steak and French fries under dim light.
Option 1: served
Option 2: nerved
Option 3: cured
Option 4: calmed
Correct Answer: served
Solution : The first option is correct.
In the context of the sentence, the word that fits best is served, which means to present food or drink for people to have.
Question : Direction: In the following question a series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
3, 8, 18, 35, ?, 98
Option 1: 60
Option 2: 61
Option 3: 62
Option 4: 63
Correct Answer: 61
Solution : Given: 3, 8, 18, 35, ?, 98
Here, the pattern is:
So, the series becomes → 3, 8, 18, 35, 61, 98
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