Staff Selection Commission Combined Graduate Level Exam
Question : a and b are two sides adjacent to the right angle of a right-angled triangle and p is the perpendicular drawn to the hypotenuse from the opposite vertex. Then p2 is equal to:
Option 1: $a^{2}+b^{2}$
Option 2: $\frac{1}{a^{2}}+\frac{1}{b^{2}}$
Option 3: $\frac{a^{2}b^{2}}{a^{2}+b^{2}}$
Option 4: $a^{2}-b^{2}$
Correct Answer: $\frac{a^{2}b^{2}}{a^{2}+b^{2}}$
Solution : In triangle ABC, The hypotenuse of the triangle, $AC=\sqrt{a^2+b^2}$ The area of triangle ABC, $\frac{1}{2}\times AB \times BC=\frac{1}{2}\times AC\times BD$ $⇒\frac{1}{2}ab=\frac{1}{2}p\sqrt{a^2+b^2}$ $⇒ab=p\sqrt{a^2+b^2}$ Squaring both sides, $⇒a^2b^2=p^2(a^2+b^2)$ $⇒p^2=\frac{a^{2}b^{2}}{a^{2}+b^{2}}$ Hence, the correct answer is $\frac{a^{2}b^{2}}{a^{2}+b^{2}}$.
Question : In an examination, the average marks obtained by the girls of a class is 85 and the average marks obtained by the boys of the same class is 87. If the girls and boys are in the ratio of 4 : 5, the average marks of the whole class (approximately) are closest to:
Option 1: 85.9
Option 2: 86.1
Option 3: 86.4
Option 4: 86.5
Correct Answer: 86.1
Solution : Given: Ratio of girls : boys = 4 : 5 Average marks obtained by the girls = 85 Average marks obtained by the boys = 87 Required average $=\frac{(4×85)+(5×87)}{4+5}= \frac{340 + 435}{9}= \frac{775}{9} = 86.1$ Hence, the correct answer is 86.1.
Question : The sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful and coherent paragraph. A. Many species of bamboo flower once in several years and then die. B. The stem itself is hollow and is connected to a network of rhizomes, which spreads out beneath the surface of the soil. C. Roots grow out of this network of rhizomes and help the plants absorb and distribute food and water from the soil. D. The bamboo is a variety of grass, with a woody, many-jointed stem.
Option 1: ADCB
Option 2: DBCA
Option 3: BCAD
Option 4: CADC
Correct Answer: DBCA
Solution : The correct choice is the second option.
The statement (D) is the subject, which discusses the bamboo plant. It is followed by statement (B), in which the action of rhizomes under the soil is discussed. This, in turn, is followed by statement (C), which
Question : Select the wrongly spelt word.
Option 1: incorrect
Option 2: increament
Option 3: incubate
Option 4: incorporate
Correct Answer: increament
The given word "increament" is incorrectly spelt, which contains an extra letter "a". The correct spelling of the word is increment.
Increment refers to an increase or addition, especially a small, gradual one. It signifies a step-by-step
Question : Which of the four Vedas contains a collection of magic spells and charms to fend off evil spirits and diseases?
Option 1: Rigveda
Option 2: Samaveda
Option 3: Yajurveda
Option 4: Atharvaveda
Correct Answer: Atharvaveda
Solution : The correct answer is Atharvaveda.
The fourth and final Veda is the Atharvaveda, which offers a compendium of magical spells and charms to ward off bad spirits and ailments. It consists of 730 hymns and over 6,000 mantras, separated into 20 books. Many Atharvavedic hymns
Question : Two buses travel to a place at 45 km/hr and 60 km/hr, respectively. If the second bus takes $5\frac{1}{2}$ hours less than the first for the journey, then the length of the journey is:
Option 1: 900 km
Option 2: 945 km
Option 3: 990 km
Option 4: 1350 km
Correct Answer: 990 km
Solution : Given: The speeds of the two buses are 45 km/hr and 60 km/hr, respectively. The second bus takes $5\frac{1}{2}$ hours less than the first bus. Let the length of the journey be $x$ km. According to the given condition, $⇒ \frac{x}{45}-\frac{x}{60}=\frac{11}{2}$ $⇒ \frac{4x-3x}{180}=\frac{11}{2}$ $⇒
Question : Direction: 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
1. All goats are cows.
2. All cows are animals.
Conclusions
I. All goats are animals.
II. All animals are goats.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: Both conclusion I and conclusion II follow
Option 4: Neither conclusion I nor conclusion II follows
Correct Answer: Only conclusion I follows
Solution : Let's evaluate the conclusions based on the given statements:
Venn diagram
Now, let's consider each conclusion:
Question : The common tree species in Nilgiri hills is
Option 1: Sal
Option 2: Pine
Option 3: Eucalyptus
Option 4: Teak
Correct Answer: Eucalyptus
Solution : The correct answer is Eucalyptus.
Eucalyptus is quite prevalent. Eucalyptus trees have a rapid growth rate and may grow as tall as 100 metres. They are renowned for their capacity to adjust to various soils and climatic conditions. However, the Nilgiri Hills are well-known for
Question : Select the most appropriate meaning of the given idiom.
Treading on thin ice
Option 1: Playing with a sharp icicle
Option 2: To be in a dangerous risky position
Option 3: Skating on ice fallen in a hailstorm
Option 4: Making a thin ice sculpture
Correct Answer: To be in a dangerous risky position
The idiom "treading on thin ice" means "doing something risky that may have serious or unpleasant consequences".
Therefore, the option that best matches the meaning is the second option.
Question : The first Mysore War fought between the British and Hyder Ali in 1767 - 69 A.D., came to an end by the
Option 1: Treaty of Pondicherry
Option 2: Treaty of Madras
Option 3: Treaty of Mysore
Option 4: Treaty of Aix - la - Chapelle
Correct Answer: Treaty of Madras
Solution : The correct option is treaty of Madras.
The first Mysore War ended in 1769 with the Treaty of Madras. It was a temporary agreement between the British and Hyder Ali, restoring things to how they were before the war. However, it didn't provide
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