Staff Selection Commission Combined Higher Secondary Level Exam
Question : Ram Babu donated 3% of his income to a charity and deposited 12% of the rest in the bank. If he has Rs. 12,804, then his income was:
Option 1: Rs. 17,640
Option 2: Rs. 15,000
Option 3: Rs. 7,500
Option 4: Rs. 14,550
Correct Answer: Rs. 15,000
Solution : Let us assume Ram Babu's income is $x$. According to the question, $x \times\frac{97}{100}\times \frac{88}{100} = 12804$ ⇒ $x$ = 15,000 Hence, the correct answer is Rs. 15,000.
Question : Directions: In a certain code language, READER is written as 123421 and DIRTY is written as 49178. How is DEARER written in that code language?
Option 1: 432121
Option 2: 423212
Option 3: 423121
Option 4: 412312
Correct Answer: 423121
Solution : Given: READER is written as 123421 and DIRTY is written as 49178.
On combining the letters of both the given words, the codes for each letter are – Like, READER is written as 123421; R→1; E→2; A→3; D→4; E→2; R→1 And, DIRTY is written as
Question : Directions: Arrange the given words in the sequence in which they occur in the dictionary. i. Irrelevant ii. Invincible iii. Irresistible iv. Invariable v. Investigate
Option 1: iv, ii, v, iii, i
Option 2: iv, v, i, iii, ii
Option 3: ii, v, iv, i, iii
Option 4: iv, v, ii, i, iii
Correct Answer: iv, v, ii, i, iii
Solution : Given: i. Irrelevant ii. Invincible iii. Irresistible iv. Invariable v. Investigate
Step 1: Compare the first letter of each word. Since all the words start with the same letter I, we move on to the next letter. Step 2: Let's
Question : Directions: Choose the related code from the given alternatives. AF : BE :: ? : DH
Option 1: CH
Option 2: CG
Option 3: DG
Option 4: CI
Correct Answer: CI
Solution : Given: AF : BE :: ? : DH
Subtract and add 1 alternatively to the letters of the second letter pair to get the first term. Like, B – 1 = A; E + 1 = F Similarly, D – 1 = C; H +
Question : What is the value of (a + b)3 – a3 – b3?
Option 1: – 3ab(a – b)
Option 2: 3ab(a + b)
Option 3: – 3ab(a + b)
Option 4: 3ab(a – b)
Correct Answer: 3ab(a + b)
Solution : (a + b)3 – a3 – b3 = a3 + b3 + 3ab(a + b) – a3 – b3 = 3ab(a + b) Hence, the correct answer is 3ab(a + b).
Question : If in $\triangle PQR$ and $\triangle DEF, \angle P=52^{\circ}, \angle Q=74^{\circ}, \angle R=54^{\circ}, \angle D=54^{\circ}, \angle E=74^{\circ}$ and $\angle F=52^{\circ}$, then which of the following is correct?
Option 1: $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$
Option 2: $\triangle \mathrm{RQP} \sim \triangle \mathrm{FED}$
Option 3: $\triangle \mathrm{PRQ} \sim \Delta \mathrm{FED}$
Option 4: $\triangle \mathrm{PQR} \sim \triangle \mathrm{DEF}$
Correct Answer: $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$
Solution : $\because$ $\angle P=\angle F=52^0$ $\angle Q=\angle E=74^0$ And $\angle R=\angle D=54^0$ By AAA criteria, triangles are similar. So, $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$. Hence, the correct answer is $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$.
Question : Who among the following has been accused of committing the judicial murder of Raja Nand Kumar?
Option 1: Lord Wellesley
Option 2: Lord Dalhousie
Option 3: Lord Cornwallis
Option 4: Warren Hastings
Correct Answer: Warren Hastings
Solution : The correct option is Warren Hastings.
Warren Hastings, the first Governor-General of British India, faced accusations of orchestrating the judicial murder of Raja Nand Kumar during the late 18th century. The trial of Raja Nand Kumar was marked by allegations of political motives
Question : If $\tan \theta=\frac{8}{19}$, find the value of $\sec ^2 \theta$.
Option 1: $\frac{11}{19} \\$
Option 2: $1 \frac{8}{19} \\$
Option 3: $\frac{297}{361} \\$
Option 4: $1 \frac{64}{361}$
Correct Answer: $1 \frac{64}{361}$
Solution : Given: $\tan \theta=\frac{8}{19}$ We know, $\sec ^2 \theta=1+\tan^2 \theta$ $⇒\sec ^2 \theta=1+(\frac{8}{19})^2$ $⇒\sec ^2 \theta=1+\frac{64}{361}$ $⇒\sec ^2 \theta=\frac{425}{361}$ $⇒\sec ^2 \theta=1\frac{64}{361}$ Hence, the correct answer is $1\frac{64}{361}$.
Question : Speed of stream is 4 km/hr and the speed of boat is 11 km/hr. In how much time will the boat cover a distance of 21 km upstream and 45 km downstream?
Option 1: 6 hours
Option 2: 3 hours
Option 3: 4 hours
Option 4: 7 hours
Correct Answer: 6 hours
Solution : The speed of the stream is 4 km/hr. The speed of the boat is 11 km/hr. Upstream Speed = Speed of boat –Speed of stream = 11 – 4 = 7 km/h Upstream distance = 21 km Time = $\frac{21}{7}$ = 3 hrs Downstream
Question : The average marks of 17 students in an examination was calculated as 71. However, it was later found that one student's mark had been wrongly entered as 65 instead of 56 and another as 24 instead of 50. The correct average is:
Option 1: 70
Option 2: 71
Option 3: 72
Option 4: 73
Correct Answer: 72
Solution : The total sum of marks was initially = 71 × 17 = 1207 The wrongly entered marks are 65 and 24, so subtract these from the total = 1207 – 65 – 24 = 1118 The correct marks are 56 and 50, so add these
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