Staff Selection Commission Combined Higher Secondary Level Exam
Question : The first term of an arithmetic progression is 22 and the last term is –11. If the sum is 66, the number of terms in the sequence is:
Option 1: 10
Option 2: 12
Option 3: 9
Option 4: 8
Correct Answer: 12
Solution : Let the first term as $a$, the last term as $l$, and the number of terms as $n$. Given: $a$ = 22, $l$ = –11 The sum of an arithmetic progression is given by $S = \frac{n}{2}(a + l)$ ⇒ 66 = $\frac{n}{2}$(22 – 11)
Question : In $\triangle$UVW measure of angle V is 90°. If $\tan U=\frac{12}{5}$ and UV = 10 cm, then what is the length (in cm) of side VW?
Option 1: 26
Option 2: 24
Option 3: 25
Option 4: 5
Correct Answer: 24
Solution : Given: In $\triangle$UVW measure of angle V is 90°. $\tan U=\frac{12}{5}$ and UV = 10 cm $\tan U=\frac{12}{5}$ $⇒\frac{VW}{UV}=\frac{12}{5}$ $⇒\frac{VW}{10}=\frac{12}{5}$ $\therefore VW = 24$ cm Hence, the correct answer is 24.
Question : Directions: Gurpreet is facing south. She turns right and walks 35 meters, then turns right again and walks 40 meters more. Finally, she turns left and walks 30 meters. In which direction is she facing now?
Option 1: South
Option 2: North
Option 3: West
Option 4: East
Correct Answer: West
Solution : Firstly, we will draw the diagram as per the given instructions –
Now, we have to find in which direction Gurpreet is facing in the final position.
Therefore, finally, Gurpreet is facing towards the West direction. Hence, the third option is correct.
Question : Which of the following pairs of "elements - valency" is correct? I. Boron - 2 II. Fluorine - 3
Option 1: Neither I nor II
Option 2: Both I and II
Option 3: Only II
Option 4: Only I
Correct Answer: Neither I nor II
Solution : The correct answer is Neither I nor II.
Although it might seem like Boron could have a valency of 2 because it has three valence electrons, it tends to form compounds by sharing those 3 electrons, achieving a stable octet for
Question : Directions: After arranging the given words according to dictionary order, which word will come in the third position? 1. Periwing 2. Perilad 3. Perimeter 4. Periodic 5. Perish
Option 1: Perilad
Option 2: Perimeter
Option 3: Periodic
Option 4: Perish
Correct Answer: Periodic
Solution : Given: 1. Periwing 2. Perilad 3. Perimeter 4. Periodic 5. Perish
Step I: Compare the first, second, third and fourth letters of each word. Since all the words start with the same letter P and are followed by e, r and i, then move on
Question : Directions: Study the following histogram of marks in mathematics (out of 50) of students in a class and answer the following question
If the students have got the marks out of 50 and if an A+ grade has been declared for above 90%, then the number of students who have got A+ grade is:
Option 2: 20
Option 3: 30
Option 4: 40
Correct Answer: 10
Solution : As per the given graph, The required class interval for the students has got 90% marks out of 50 marks = 90% of 50 marks = 45 marks From the graph, the required class interval is from 45 to 50. The number of students who
Question : If $ x+\frac{1}{x}=3,$ then the value of $x^{5}+\frac{1}{x^{5}}$ is:
Option 1: 110
Option 2: 132
Option 3: 122
Option 4: 123
Correct Answer: 123
Solution : $x+\frac{1}{x }=3$.........................................(1) Squaring both sides, we get, $⇒(x+\frac{1}{x })^2=3^2$ $⇒x^2+\frac{1}{x^2 } +2=9$ $⇒x^2+\frac{1}{x^2 } =7$..................................(2) Cubing both sides of equation (1), we get, $⇒(x+\frac{1}{x})^3=x^3 + \frac{1}{x^3}+3(x+\frac{1}{x})$ $⇒3^3=x^3 + \frac{1}{x^3}+3(3)$ $⇒x^3 + \frac{1}{x^3}=18$..................................(3) Multiplying (2) and (3), we get, $⇒\left ( x^2+\frac{1}{x^2} \right )\cdot \left (
Question : Out of the following Indian states, which state does not have any maritime boundary?
Option 1: Gujarat
Option 2: Goa
Option 3: Rajasthan
Option 4: Maharashtra
Correct Answer: Rajasthan
Solution : The correct option is Rajasthan.
Rajasthan is a landlocked state in northern India with no coastal boundaries. The state is landlocked if it is surrounded by land and has no direct connection to an ocean or sea. Rajasthan has borders with numerous other Indian states,
Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
If there was such a thing as perfect food, eggs would be a ________ (1)________. They are readily available, easy to cook, affordable, and packed ________ (2) ________ protein. An egg is meant to be something that has all the right ingredients to grow an organism, so obviously, it is very nutrient-dense. Eating eggs alongside other food can ________ (3) ________ our bodies absorb more vitamins too. For example, one study found that adding an egg to a salad can increase how much vitamin E we get from the salad. But for decades, eating eggs has also been controversial due to their ________ (4) ________ cholesterol content, which some studies have linked to an increased risk of heart disease. Cholesterol, a yellowish fat produced in our liver and intestines, can be found in every one of our body's cells. We ________ (5) ________ think of it as ‘bad’. But cholesterol is a crucial building block in our cell membranes. It is also needed for the body to make vitamin D and the hormones testosterone and oestrogen.
Select the most appropriate option to fill in the blank number 2.
Option 1: for
Option 2: with
Option 3: on
Option 4: at
Correct Answer: with
Solution : The correct choice is the second option.
Explanation: In this context, the phrase "packed with" is commonly used to describe something containing a high amount of a particular substance. For example, "packed with protein" means that the item has a high protein
Question : Directions: From the given answer figures, select the figure that is hidden/ embedded in the question figure.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Because there is no restriction on the rotation of the figure, we will check all the possible orientations of the question figure in which of the given option figures it can fit itself. By comparison of all option figures, the question figure is embedded only in
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