Staff Selection Commission Combined Higher Secondary Level Exam
Question : Which of the following is an identity?
Option 1: $(a-b)^2=a^2-b^2$
Option 2: $(a+b)^2=a^2+b^2+2ab$
Option 3: $(a+b)^2=a^2+b^2$
Option 4: $(a-b)^2=a^2-b^2-2ab$
Correct Answer: $(a+b)^2=a^2+b^2+2ab$
Solution : $(a+b)^2=a^2+b^2+2ab$ is an identity. Hence, the correct answer is $(a+b)^2=a^2+b^2+2ab$.
Question : Directions: Select the option that is related to the fifth word in the same way as the second word is related to the first word and the fourth word is related to the third word. Dentist : Teeth :: Orthopedician : Bones :: Cardiologist : ?
Option 1: Ears
Option 2: Heart
Option 3: Brain
Option 4: Eyes
Correct Answer: Heart
Solution : Given: Dentist : Teeth :: Orthopedician : Bones :: Cardiologist : ?
Like, Dentist : Teeth→Dentist treats or specializes in the teeth. And, Orthopedician : Bones→Orthopedician treats or specializes in bones. Similarly, follow the same pattern for Cardiologist : ?→Cardiologist treats or specialize in the
Question : The previous name of Zaire was
Option 1: Benin
Option 2: Liberia
Option 3: Congo
Option 4: Sierra Leone
Correct Answer: Congo
Solution : The correct answer is Congo.
It is an African place name that derives from a Congo phrase that means the river that swallows all rivers. From 1960 to 1971, it was referred to as the (Democratic) Republic of Congo, and from 1971 to 1996,
Question : Directions: Read the following graph and answer questions
Trade Deficit of a Country (in Crores of Rupees)
The deficit in 1993-94 was roughly how many times the deficit in 1990-91?
Option 1: 1.4
Option 2: 1.5
Option 3: 2.5
Option 4: 0.5
Correct Answer: 1.5
Solution : Deficit in 1993-94 = 4200 Deficit in 1990-91 = 2800 Required value = $\frac{4200}{2800}$ = $\frac{3}{2}$ = $1.5$ Hence, the correct answer is 1.5.
Question : $\triangle \mathrm{ABC}$ is an isosceles triangle with $\angle \mathrm{ABC}=90^{\circ}$ and $\mathrm{AB}=\mathrm{BC}$. If $\mathrm{AC}=12 \mathrm{~cm}$, then the length of $\mathrm{BC}$ (in $\mathrm{cm}$) is equal to:
Option 1: $6 \sqrt{2}$
Option 2: $8$
Option 3: $6$
Option 4: $8 \sqrt{2}$
Correct Answer: $6 \sqrt{2}$
Solution : Given, $\triangle \mathrm{ABC}$ is an isosceles triangle with $\angle \mathrm{ABC}=90^{\circ}$, $\mathrm{AB}=\mathrm{BC}$, and $\mathrm{AC}=12 \mathrm{~cm}$ According to Pythagoras theorem, $AC^2=AB^2+BC^2$ ⇒ $12^2=2\times BC^2$ ⇒ $BC^2= 72$ ⇒ $BC=6\sqrt2$ cm Hence, the correct answer is $6\sqrt2$.
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
Your son (will) have looked smart in a kurta.
(1) shall
(2) can
(3) would
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The third option is the correct choice.
This is because ''will'' should be replaced with ''would''. There is an error in the use of the modal verb. Modal verbs in the simple tense are always followed by the base form of the verb. Thus, in
Question : The value of the expression $\frac{(a-b)^{2}}{(b-c)(c-a)}+\frac{(b-c)^{2}}{(a-b)(c-a)}+\frac{(c-a)^{2}}{(a-b)(b-c)}$ is:
Option 1: $0$
Option 2: $3$
Option 3: $\frac{1}{3}$
Option 4: $2$
Correct Answer: $3$
Solution : Given: $\frac{(a-b)^{2}}{(b-c)(c-a)}+\frac{(b-c)^{2}}{(a-b)(c-a)}+\frac{(c-a)^{2}}{(a-b)(b-c)}$ Multiplying the numerator and denominator of each fraction by $(a-b)$, $(b-c)$ and $(c-a)$ respectively: $\frac{(a-b)^{2}×(a-b)}{(b-c)(c-a)(a-b)}+\frac{(b-c)^{2}(b-c)}{(a-b)(c-a)(b-c)}+\frac{(c-a)^{2}(c-a)}{(a-b)(b-c)(c-a)}$ = $\frac{(a-b)^{3}+(b-c)^{3}+(c-a)^{3}}{(a-b)(b-c)(c-a)}$ We know that $A^3+B^3+C^3=3ABC$ when $A + B + C = 0$ = ${\frac{3(a-b)(b-c)(c-a)}{(a-b)(b-c)(c-a)}}$ = $3$ Hence, the correct answer is $3$.
Question : Directions: In the following question, the sentence given with a blank is to be filled in with an appropriate word. Select the correct alternative out of the four.
The teacher accused Jeetu of ___ because she knew he could never write such an exceptional paper.
Option 1: borrowing
Option 2: plagiarism
Option 3: piracy
Option 4: theft
Correct Answer: plagiarism
Solution : The second option is the correct answer.
Plagiarism refers to the act of copying someone else's work and presenting it as one's own without proper permission, which fits perfectly in the sentence.
The meanings of the other options are as follows:
Question : Which of the following hypotheses was propounded by Harry Hammond Hess in 1962?
Option 1: Continental Drift hypothesis
Option 2: Seafloor spreading hypothesis
Option 3: Gaia hypothesis
Option 4: Geographical cycle hypothesis
Correct Answer: Seafloor spreading hypothesis
Solution : The correct answer is the Seafloor spreading hypothesis.
The hypothesis propounded by Harry Hammond Hess in 1962 is known as the "seafloor spreading" hypothesis. This groundbreaking idea suggested that the oceanic crust is constantly in motion, being created at mid-ocean ridges and then
Question : Directions: If 12 @ 2 = 145 and 15 @ 2 = 226, then 24 @ 2 = ?
Option 1: 577
Option 2: 676
Option 3: 575
Option 4: 576
Correct Answer: 577
Solution : Given: 12 @ 2 = 145; 15 @ 2 = 226
The logic here is – Like, 12 @ 2 = 145→122+ 1 = 144 + 1 = 145 And, 15 @ 2 = 226→152 + 1 = 225 + 1 =
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