Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $\theta$ is an acute angle and $\sin \theta=\frac{21}{25}$, then what is the value of $\tan \theta$?
Option 1: $\frac{2 \sqrt{46}}{21}$
Option 2: $\frac{25}{2 \sqrt{46}}$
Option 3: $\frac{21}{2 \sqrt{46}}$
Option 4: $\frac{2 \sqrt{46}}{25}$
Correct Answer: $\frac{21}{2 \sqrt{46}}$
Solution : Given, $\theta < 90°$ and $\sin \theta=\frac{21}{25}$ We know, $\sin\theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}}$ ⇒ Perpendicular = 21 and Hypotenuse = 25 Using Pythagoras theorem, Hypotenuse2 = Perpendicular2 + Base2 ⇒ 252 = 212 + Base2 ⇒ Base = $\sqrt{25^2-21^2}$
Question : Directions: If S denotes multiplied by, V denotes subtracted from, M denotes added to and L denotes divided by, then, 7 V 24 M 77 L 11 S 5 = ?
Option 1: 21
Option 2: 18
Option 3: 35
Option 4: 27
Correct Answer: 18
Solution : Given: 7 V 24 M 77 L 11 S 5 = ?
On replacing the letters with the assigned mathematical signs, the equation becomes – = 7 – 24 + 77 ÷ 11 × 5 = 7 – 24 + 7 × 5 = 7
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed at MN as shown below.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per mirror image properties, closer things appear closer to the mirror in reflection. Here, according to the information provided, if the mirror is placed on the right side of the figure (on line MN), the right of the reflected image will appear as the left,
Question : If $(r\cos \theta -\sqrt{3})^{2}+(r\sin \theta -1)^{2}=0$, then the value of $\frac{r\tan \theta +\sec \theta}{r\sec \theta +\tan\theta}$ is equal to:
Option 1: $\frac{4}{5}$
$\frac{5}{4}$
$\frac{\sqrt{3}}{4}$
$\frac{\sqrt{5}}{4}$
Correct Answer: $\frac{4}{5}$
Solution : $(r\cos \theta -\sqrt{3})^{2}+(r\sin \theta -1)^{2}=0$ $⇒(r\cos \theta -\sqrt{3})^{2}=0$ and $(r\sin \theta -1)^{2}=0$ $⇒r\cos\theta =\sqrt3$ and $r\sin \theta =1$ $\therefore\tan\theta = \frac{1}{\sqrt3}$ Now, $r^2\sin^2\theta + r^2\cos^2\theta =4$ $⇒r^2 (\sin^2\theta + \cos^2\theta) =4$ Using identity $\sin^2\theta + \cos^2\theta=1$, we get, $⇒r^2 =4$ $⇒r= 2$ Using identity: $1+\tan^2\theta
Question : Select the most appropriate SYNONYM of the underlined word.
Syam does not intervene in others' affairs.
Option 1: Meddle
Option 2: Speak
Option 3: Trouble
Option 4: Help
Correct Answer: Meddle
Solution : The correct choice is the first option.
Explanation: The aim is to find a word that conveys the idea of getting involved in or interfering in others' affairs. Meddle is the appropriate synonym, as it means to intrude or interfere in a situation without
Question : The International Criminal Police Organsiation (INTERPOL) has its headquarters at:
Option 1: London
Option 2: Paris
Option 3: Bonn
Option 4: Montreal
Correct Answer: Paris
Solution : The correct answer is Paris.
The headquarters of International Criminal Police Organisation is located at Lyon, France. It is also known as INTERPOL. It was established in 1923 and has 193 member states. It's main function is cross border police operations and controlling the illegal
Question : When the grains of sand are very fine and light, the wind can carry it over very long distances. When such sand is deposited in large areas, it is called ______.
Option 1: stacks
Option 2: loess
Option 3: moraines
Option 4: mushroom
Correct Answer: loess
Solution : The correct option is loess.
When very fine and light grains of sand are carried by the wind over long distances and then deposited in large areas, it is called loess. Loess is a type of sediment made up of fine-grained, silt-sized particles that are
Question : In a showroom. the marked prices of various items are displayed in such a manner that after giving a 10% discount to the customers, the owner of the showroom earns a profit of 20%. What is the ratio of the marked price and cost price of each item?
Option 1: 3 : 4
Option 2: 4 : 3
Option 3: 5 : 2
Option 4: 2 : 5
Correct Answer: 4 : 3
Solution : Let the cost price be Rs. 100. Final selling price after 20% profit = Rs. 120 (Discounted price) With a 10% discount, the selling price is 90% of the marked price. So, Marked price = $120\times \frac{100}{90}=\frac{400}{3}$ The ratio of marked price to
Question : The nineteenth century saw the golden age of Kathak under the patronage of____, the last Nawab of Awadh.
Option 1: Asaf-ud-Daula
Option 2: Siraj ud-Daulah
Option 3: Saadat Khan Burhan-ul-Mulk
Option 4: Wajid Ali Shah
Correct Answer: Wajid Ali Shah
Solution : The correct option is Wajid Ali Shah.
Under the patronage of Wajid Ali Shah, the final Nawab of Awadh, Kathak experienced its golden period in the nineteenth century. In addition to being a prominent politician, Wajid Ali Shah was a major supporter
Question : AB and BC are two chords of a circle with centre O. Both chords are on either side of the centre O. Point A and point C are connected to the centre O, such that $\angle B A O=36^{\circ}$ and $\angle B C O=48^{\circ}$. What is the degree measure of the angle subtended by the minor arc AC at the centre O?
Option 1: 136°
Option 2: 144°
Option 3: 120°
Option 4: 168°
Correct Answer: 168°
Solution : In $\triangle$BOC, OB = OC (since they are radii) $\angle$OBC = $\angle$OCB = 48° $\angle$BOC = 180° – (48° + 48°) = 84° In $\triangle$AOB, OA = OB (since they are radii) $\angle$OAB = $\angle$OBA = 36° ⇒ $\angle$AOB = 180° – (36° + 36°)
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