Staff Selection Commission Sub Inspector Exam
Question : In the given figure, O is the centre of the circle, $\angle PQO=30^{\circ}$ and $\angle QRO=45^{\circ}$. What is the value (in degrees) of $\angle POR$?
Option 1: $150^{\circ}$
Option 2: $110^{\circ}$
Option 3: $160^{\circ}$
Option 4: $130^{\circ}$
Correct Answer: $150^{\circ}$
Solution : Given: $\angle PQO=30^{\circ}$ and $\angle QRO=45^{\circ}$ Since $OQ$ and $OR$ is the radius, So, $\angle OQR=45^{\circ}$ $⇒\angle POR=2(\angle PQO+\angle OQR)$ (By angle subtended by minor arc.) $\therefore \angle POR=2(30^{\circ}+45^{\circ})=2×75^{\circ}=150^\circ$ Hence, the correct answer is $150^\circ$.
Question : The following table shows the production of different types of two-wheelers from 1993 to 1998. (No. of two-wheelers is in 1000s)
What is the approximate percentage increase in the total production of all types of two-wheelers in 1998 in comparison to 1994?
Option 1: 42
Option 2: 45
Option 3: 40
Option 4: 41
Correct Answer: 41
Solution : Total production of all types of two-wheelers in 1998 = 334 Total production of all types of two-wheelers in 1994 = 237 Difference = 334 – 237 = 97 $\therefore$ Required percentage increment = $\frac{\text{Difference}}{\text{Total production of all types of two-wheelers in 1994}}\times 100$ =
Question : In the sentence identify the segment which contains the grammatical error.
'Plogging' is an international trend, in which someone picking up trash while jogging or brisk walking.
Option 1: in which someone
Option 2: picking up trash
Option 3: 'Plogging' is an international trend
Option 4: while jogging or brisk walking
Correct Answer: picking up trash
Solution : The error lies in the second option.
The error lies in the verb tense inconsistency, as the verb is in the present participle form, while the verb "is" in the main clause suggests a need for a simple present tense verb. Thus,
Question : Directions: Select the figure that will come next in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the given figure series – Each box is rotated by 90 degrees in an anticlockwise direction. So, following the above pattern, the required figure will be as follows –
Therefore, the figure in the first option is the required figure. Hence, the first option
Question : If $\frac{x^8+1}{x^4}=14$, then the value of $\frac{x^{12}+1}{x^6}$ is:
Option 1: 16
Option 2: 14
Option 3: 52
Option 4: 64
Correct Answer: 52
Solution : $\frac{x^8+1}{x^4}=14$ $⇒x^4+\frac{1}{x^4}=14$ $⇒x^4+\frac{1}{x^4}+2=14+2$ $⇒(x^2+\frac{1}{x^2})^2=(4)^2$ $⇒x^2+\frac{1}{x^2}=4$ Now, $\frac{x^{12}+1}{x^6}$ $=x^6+\frac{1}{x^6}$ $=(x^2)^3+\frac{1}{(x^2)^3}$ $=(x^2+\frac{1}{x^2})^3-3×x^2×\frac{1}{x^2}(x^2+\frac{1}{x^2})$ $=4^3-3(4)$ $=64-12=52$ Hence, the correct answer is 52.
Question : If the equation k(21x2 + 24) + rx + (14x2 – 9) = 0, k(7x2 + 8) + px + (2x2 – 3) = 0 have both roots common, then the value of $\frac{p}{r}$ is:
Option 1: $\frac{1}{3}$
Option 2: $\frac{2}{5}$
Option 3: $\frac{4}{3}$
Option 4: $\frac{7}{5}$
Correct Answer: $\frac{1}{3}$
Solution : Since the roots of the equation are common, the coefficients are in proportion. The equation 1 can be written as, (21k +14)x2 + rx + 24k – 9 = 0 The equation 2 can be written as, (7k + 2)x2 + px +
Question : In $\triangle \mathrm{ABC}, \angle \mathrm{A}=54^{\circ}$. If I is the incentre of the triangle, then the measure of $\angle \mathrm{BIC}$ is:
Option 1: 68o
Option 2: 54o
Option 3: 148o
Option 4: 117o
Correct Answer: 117o
Solution :
In $\triangle ABC$, $\angle A = 54^{\circ}$ $\angle BIC = 90^{\circ} + \frac{\angle A}{2}$ $= 90^{\circ} + \frac{54^{\circ}}{2}$ $= 90^{\circ} + 27^{\circ}$ $= 117^{\circ}$ Hence, the correct answer is 117º.
Question : Which of the following allows computers to transfer data using a telephone line?
Option 1: Keyboard
Option 2: CPU
Option 3: Modem
Option 4: Printer
Correct Answer: Modem
Solution : The correct option is Modem.
A Modem (short for "modulator-demodulator") is a device that converts digital data from a computer into analogue signals for transmission over a telephone line and demodulates incoming analogue signals back into digital data that the computer can comprehend.
Question : Which amongst the following films has won the minimum number of Oscars?
Option 1: Ben Hur
Option 2: Titanic
Option 3: The Lord of the Ring: Return of the King
Option 4: Jurassic Park
Correct Answer: Jurassic Park
Solution : The correct answer is Jurassic Park.
Ben Hur released in 1959, Titanic in 1997, and The Lord of Rings: The Return of the King in 2003 hold the record of having won most number of oscars ever. They have won 11 oscars each. Jurassic
Question : Directions: In the given figure, how many pages are either new or white but not both?
Option 1: 111
Option 2: 100
Option 3: 125
Option 4: 168
Correct Answer: 100
Solution : According to the question, in the below diagram, the shaded part shows the common region of pages that are either new or white but not both
In the Venn diagram, the number of pages that are new but not white is 43. Similarly, the number
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