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Question : What is the value of $p$, if, $25(4+3 p) \div 5-3 \times 8=26$?
Option 1: 5
Option 2: 4
Option 3: 7
Option 4: 2
Correct Answer: 2
Solution : $25(4+3 p) \div 5-3 \times 8=26$ ⇒ $ 5(4+3 p)-24=26$ ⇒ $20+15p=50$ ⇒ $15p=30$ $\therefore p=2$ Hence, the correct answer is 2.
Question : Select the most appropriate antonym of the given word.
OPAQUE
Option 1: PELLUCID
Option 2: PARAGON
Option 3: GLORIFY
Option 4: DARK
Correct Answer: PELLUCID
Solution : The correct choice is the first option.
Explanation:
The word opaque means not transparent or not allowing light to pass through. To find the antonym, we need a word that means transparent or allowing light to pass through. Pellucid fits this definition and
Question : Matter waves are:
Option 1: De Broglie waves
Option 2: Electromagnetic waves
Option 3: Transverse waves
Option 4: Longitudinal waves
Correct Answer: De Broglie waves
Solution : The correct answer is De Broglie waves.
De Broglie waves, also known as matter waves, were introduced by the French physicist Louis de Broglie in 1924. De Broglie proposed that particles, such as electrons, and other subatomic particles, can exhibit both particle-like and
Question : IVF (In Vitro Fertilization) Technique was first devised by
Option 1: Patrick Steptoe and Robert Edwards
Option 2: Dr. Henry Dixon
Option 3: Robertson
Option 4: Dr. Martin Cooper
Correct Answer: Patrick Steptoe and Robert Edwards
Solution : The correct answer is Patrick Steptoe and Robert Edwards
The invention of IVF is attributed to Sir Robert Edwards and Patrick Steptoe. When a woman's fallopian tubes were blocked in 1978, Dr. Steptoe treated her. Robert Edwards, a physiologist at Cambridge
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 3: 8
Option 4: 16
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.
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