Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $x=3+2\sqrt{2}$, then $\frac{x^{6}+x^{4}+x^{2}+1}{x^{3}}$ is equal to:
Option 1: 216
Option 2: 192
Option 3: 198
Option 4: 204
Correct Answer: 204
Solution : Given: $x=3+2\sqrt{2}$ -----------------(i) $\frac{x^{6}+x^{4}+x^{2}+1}{x^{3}}$ = $\frac{x^{6}}{x^{3}}$ + $\frac{x^{4}}{x^{3}}$ + $\frac{x^{2}}{x^{3}}$ + $\frac{1}{x^{3}}$ = $x^{3} + x + \frac{1}{x} + \frac{1}{x^{3}}$ = $x^{3} + \frac{1}{x^{3}} + x + \frac{1}{x}$ Using identity: $(a+b)^3 = a^3+b^3+3ab(a+b)$ Now, $\frac{x^{6}+x^{4}+x^{2}+1}{x^{3}}= (x + \frac{1}{x})^{3} - 3(x + \frac{1}{x})+(x + \frac{1}{x})$ =
Question : Directions: The second number in the given number pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) are followed in all the number pairs except one. Find that odd number pair. (NOTE: Operations should be performed on whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding/subtracting/multiplying, etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Option 1: 32 : 99
Option 2: 42 :123
Option 3: 24 : 75
Option 4: 64 : 195
Correct Answer: 42 :123
Solution : Let's check each option – First option: 32 : 99→(32 + 1) × 3 = 99 Second option: 42 : 123→(42 + 1) × 3 = 129 ≠ 123 Third option: 24 : 75→(24 + 1) × 3 = 75 Fourth option: 64 :
Question : The government is bound to ensure observance of social welfare and labour laws enacted to secure for workmen a life compatible with human dignity under____ of the Indian Constitution.
Option 1: Article 17
Option 2: Article 15
Option 3: Article 19
Option 4: Article 21
Correct Answer: Article 21
Solution : The correct answer is Article 21.
While Article 21 primarily deals with the protection of life and personal liberty, the Indian judiciary has interpreted it broadly to include aspects related to human dignity, and it has been used to uphold the rights and well-being
Question : A vertical pillar 42 cm long casts a 35 cm long shadow. At the same time, a tower casts a shadow 25 m long. Find the height of the tower.
Option 1: 28 m
Option 2: 35 m
Option 3: 32 m
Option 4: 30 m
Correct Answer: 30 m
Solution : Length of the vertical pole, AB = 42 cm = 0.42 m Length of the shadow of the pole, BC = 35 cm = 0.35 m Let the height of the tower be $h$ m. Length of the shadow of the tower, EF =
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
They congratulated me for my victory in the debate competition.
(1) About
(2) At
(3) On
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The sentence can be improved using the third option.
The preposition on is commonly used when expressing congratulations or well wishes for an achievement, success, or victory.
Therefore, the correct sentence is: "They congratulated me on my victory in the debate competition."
Question : Directions: In a certain code language, A + B means A is the father of B; A – B means A is the brother of B; A × B means A is the mother of B; A ÷ B means A is the sister of B. Based on the above, how is I related to M if I + J ÷ K × L – M?
Option 1: Father
Option 2: Father's brother
Option 3: Mother's father
Option 4: Father's father
Correct Answer: Mother's father
Solution : Given: I + J means I is the father of J. L – M means L is the brother of M. K × L means K is the mother of L. J ÷ K means J is the sister of K.
According to the
Question : Directions: In a certain code language, PRIME is coded as 37862 and REMAP is coded as 87423. What is the code for A in the given code language?
Option 1: 3
Option 2: 7
Option 3: 2
Option 4: 4
Correct Answer: 4
Solution : Given: 1. PRIME ⇒ 37862 2. REMAP ⇒ 87423
By comparing the coded word, we find that – In words 1 and 2, the common letters are P, R, M, and E and the common codes are 3, 7, 8, and 2. The remaining letters
Question : The difference between the circumference and diameter of a circle is 150 m. The radius of that circle is:
Option 1: 25 m
Option 3: 30 m
Option 4: 40 m
Correct Answer: 35 m
Solution : Given: The difference between the circumference and diameter of a circle is 150 m. Let the radius of the circle be $r$. Its diameter = $2r$ and its circumference is $2\pi r$. According to the question, $2\pi r\ –\ 2r=150$ ⇒ $2r(\frac{22}{7}-1)=150$ ⇒ $r\times(\frac{22-7}{7})=\frac{150}{2}$
Question : A train starts from place S at 10: 00 a.m. and arrives at another place T at 2: 30 p.m. on the same day. If the speed of the train is 40 m/s, then what will be the distance covered by the train?
Option 1: 706 km
Option 2: 648 km
Option 3: 726 km
Option 4: 616 km
Correct Answer: 648 km
Solution : Start time = 10:00 a.m. End time = 2:30 p.m. Speed = 40 m/s ⇒ Time = 2:30 p.m. – 10:00 a.m. = 4.5 hours = 16200 seconds ⇒ Distance = Speed × Time = 40 × 16200 = 648,000 meters = 648 km
Question : Which gland in the human body regulates the secretion of hormones from the pituitary gland?
Option 1: Thymus gland
Option 2: Thyroid gland
Option 3: Adrenal gland
Option 4: Hypothalamus gland
Correct Answer: Hypothalamus gland
Solution : The correct answer is the Hypothalamus gland.
The hypothalamus is the gland in the human body that governs pituitary gland hormone release. The hypothalamus is a tiny brain area located underneath the thalamus. It regulates several biological activities, including hormone secretion, body temperature, hunger,
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