Staff Selection Commission Combined Higher Secondary Level Exam
Question : What is the value of $3 \tan 20° \tan 45°\tan 70°$?
Option 1: 2
Option 2: 3
Option 3: 1.5
Option 4: 4
Correct Answer: 3
Solution : $3 \tan 20°\tan 45° \tan70°$ $= 3 \tan 20°\tan 45° \tan (90° - 20°)$ [Using $\tan \theta = \cot (90° - \theta)$] $= 3 \tan 20°\tan 45°\cot 20°$ $= 3 \times \tan 45°$ $= 3 \times 1$ $= 3$ Hence, the correct answer is 3.
Question : Which of the following constitutional amendment acts made the right to education a fundamental right under Article 21A of the Indian constitution?
Option 1: 91st Amendment Act, 2003
Option 2: 86th Amendment Act, 2002
Option 3: 89th Amendment Act, 2003
Option 4: 19th Amendment Act, 1966
Correct Answer: 86th Amendment Act, 2002
Solution : The correct answer is the 86th Amendment Act, of 2002.
The 86th Amendment Act, 2002 came during the Atal Bihari Vajpayee government. This act makes it obligatory on the part of the government to ensure admission, attendance, and completion of elementary
Question : ______ won the gold medal in the Women's event in the 44th Chess Olympiad 2022 held in India.
Option 1: Georgia
Option 2: Armenia
Option 3: Ukraine
Option 4: India
Correct Answer: Ukraine
Solution : The correct option is Ukraine.
The 44th Chess Olympiad, orchestrated by the International Chess Federation, also known as the World Chess Federation (FIDE), took place in Chennai, India, spanning from July 28 to August 9, 2022. In the women's section of the 44th Chess
Question : AB is the diameter of a circle with centre O. P is a point on it. If $\angle$POA = 120°. Then $\angle$PBO = ?
Option 1: 60°
Option 2: 120°
Option 3: 45°
Option 4: 50°
Correct Answer: 60°
Solution : $\angle$AOB = 180° $\angle$AOP = 120° we know that , $\angle$AOP + $\angle$POB = 180° ∴ $\angle$POB = 180° – 120° = 60° OP = OB = radius ∴ $\angle$OPB = $\angle$PBO = $\frac{120°}{2}=60°$ ($\because $ OP = OB) Hence, the correct answer is 60°.
Question : Directions: The bar graph provided below gives the data on the production of paper (in lakh tonnes) by three different companies X, Y and Z over the years. Study the bar chart and answer the following questions.
The percentage increase in the production of company Y from 1996 to 1999 is:
Option 1: 60%
Option 2: 50%
Option 3: 55%
Option 4: 40%
Correct Answer: 60%
Solution : Production of company Y in 1996 = 25 (in lakh tonnes) Production of company Y in 1999 = 40 (in lakh tonnes) Increment in production = 40–25 = 15 (in lakh tonnes) Percentage increased = $\frac{\text{Increment in production}}{\text{Previous production}}$ × 100 = $\frac{15}{25}$ × 100
Question : Sodium Calcium Silicate is called________.
Option 1: hard glass
Option 2: borosilicate glass
Option 3: soft glass
Option 4: jena glass
Correct Answer: soft glass
Solution : The correct option is soft glass.
Soft glass refers to soda-lime glass and is the most common type. It is used in daily objects such as windows, bottles, and glasses. The chemical formula of soda-lime glass is Na2O.CaO.6SiO2. It is
Question : Harshavardhan's Vallabhi conquest is found in which of the following inscriptions?
Option 1: Aihole pillar inscription
Option 2: Junagadh inscription
Option 3: Navsari copper plate inscription
Option 4: Damodarpur copper plate inscription
Correct Answer: Navsari copper plate inscription
Solution : The correct option is the Navsari copper plate inscription.
The Navsari copper plate inscription at Nausasi(Navsari) shows Harshavardhan conquering the kingdom of Vallabhi. He also defeated the king of Vallabhi, Dhruvasena II, according to the Navsari copper plate inscription. Harsha, however,
Question : Directions: Select the word pair that best represents a similar relationship to the one expressed in the pair of words given below: (The words must be considered meaningful English words and must not be related to each other based on the number of letters/consonants/vowels in the word.) Bitter : Pungent
Option 1: Boggle : Wonder
Option 2: Digitise : Digress
Option 3: Cider : Cine
Option 4: Cite : Cirrus
Correct Answer: Boggle : Wonder
Solution : Given: Bitter : Pungent (Bitter and Pungent are synonyms where the meaning of bitter is having a sharp pungent taste or smell.)
First option: Boggle : Wonder; Boggle and wonder are synonyms where wonder refers to a feeling of amazement or admiration. Second
Question : If $(a+b+c) \neq 0$, then $(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$ is equal to:
Option 1: $a^3+b^3-c^3-3abc$
Option 2: $a^3-b^3+c^3-3abc$
Option 3: $a^3+b^3+c^3-3abc$
Option 4: $a^3+b^3+c^3+3abc$
Correct Answer: $a^3+b^3+c^3-3abc$
Solution : Given: $(a+b+c)\left(a^2+b^2+c^2-ab-bc-ca\right)$ Simplifying this expression, we have: $(a^3+ab^2+ac^2–a^2b–abc–ca^2+a^2b+b^3+bc^2–ab^2–b^2c–abc+a^2c+b^2c+c^3–abc–bc^2–c^2a)$ = $(a^3+b^3+c^3–3abc)$ Hence, the correct answer is $(a^3+b^3+c^3–3abc)$.
Question : Directions: Select the option in which the numbers share the same relationship in the set as that shared by the numbers in the given sets. (NOTE: Operations should be performed on the 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.) (8, 6, 50) (24, 4, 98)
Option 1: (2, 48, 100)
Option 2: (12, 8, 100)
Option 3: (32, 3, 144)
Option 4: (18, 6, 110)
Correct Answer: (18, 6, 110)
Solution : Given: (8, 6, 50); (24, 4, 98)
Here, (8, 6, 50)→(8 × 6) + 2 = 48 + 2 = 50 (24, 4, 98)→(24 × 4) + 2 = 96 + 2 = 98
Let's check the options – First option: (2, 48,
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