Staff Selection Commission Sub Inspector Exam
Question : Find the value of $\left(\tan ^2 \theta+\tan ^4 \theta\right)$.
Option 1: $\cot ^2 \theta-\tan ^2 \theta$
Option 2: $\ {\sec}^4 \theta-\ {\sec}^2 \theta$
Option 3: $\ {\sec}^4 \theta-\ {\sec}^4 \theta$
Option 4: $ \ {\sec}^4 \theta+\ {\sec}^2 \theta$
Correct Answer: $\ {\sec}^4 \theta-\ {\sec}^2 \theta$
Solution : According to the question, $\left(\tan ^2 \theta+\tan ^4 \theta\right)$ $=(\tan^{2}\theta)^{2} + \tan^{2}\theta$ $=(\sec^{2}\theta - 1)^{2} + \sec^{2}\theta - 1$ $=\sec^{4}\theta - 2 \sec^{2}\theta + 1 + \sec^{2}\theta - 1$ $=\sec^{4}\theta - \sec^{2}\theta$ Hence, the correct answer is $\sec^{4}\theta - \sec^{2}\theta$.
Question : Comprehension: Read the given passage carefully and answer the questions that follow. Throughout history, the intricacies of the human mind have been the subject of fascination and inquiry. From ancient philosophers to modern-day neuroscientists, the workings of the brain have been studied and analysed in an attempt to unravel its mysteries. However, despite centuries of research, much remains unknown about the complexities of human cognition and consciousness. One of the most fascinating aspects of the human mind is its ability to create and imagine. The human mind has the capacity to conceptualise and bring into being ideas that were previously unknown or unimaginable, from artistic expression to scientific discovery. The process of creativity has captured the attention of scholars and laypeople alike and is both enigmatic and awe-inspiring. There have been many theories proposed to explain the process of creativity. Some suggest that it is a purely subconscious process, while others argue that creativity is a result of conscious effort and intentional problem-solving. Still others suggest that creativity arises from a combination of conscious and subconscious processes. Despite the ongoing debate over the nature of creativity, one thing is clear: it is a multifaceted and complex phenomenon. Creativity can manifest in a wide range of human activities, from the creation of art and literature to the development of scientific theories and inventions. It can occur in both individual and collective contexts and can be driven by a variety of factors such as curiosity, passion, or the desire for recognition. Creativity also has the potential to bring about positive change in the world. Throughout history, creative individuals and groups have used their talents to address social, political, and environmental challenges, often inspiring others to take action and make a difference. From the abolitionist movement to the civil rights movement to the environmental movement, creativity has played a crucial role in promoting social justice and positive change. Despite the many benefits of creativity, it is not without its challenges. The process of creative expression can be fraught with obstacles, from self-doubt and insecurity to external pressures and constraints. Moreover, not all creative ideas are successful or well-received, and many artists and innovators face rejection and criticism as they seek to bring their ideas to fruition. Despite these challenges, however, the human drive to create and imagine persists. Individuals and groups continue to harness the power of creativity to make a difference in the world. From the humblest amateur artist to the most celebrated innovator, the human capacity for creativity remains one of our greatest strengths and sources of inspiration. Question: Select the most appropriate ANTONYM for the word ‘fraught’.
Option 1: Tranquil
Option 2: Calm
Option 3: Beset
Option 4: Devoid
Correct Answer: Devoid
Solution : The fourth option is the correct answer.
The term fraught suggests being filled or laden with something undesirable, challenging, or burdensome. In the context of the passage, it refers to the challenges associated with the process of creative expression. On the other hand, 'devoid' means
Question : Find the amount of a sum of Rs. 7,500 invested on compound interest at 8% p.a. for 1.5 years when the interest is compounded half-yearly.
Option 1: Rs. 8,436.48
Option 2: Rs. 8,736.48
Option 3: Rs. 8,657.48
Option 4: Rs. 8,564.48
Correct Answer: Rs. 8,436.48
Solution : Given: Principal($P$) = Rs. 7500 Rate($R$) = 8% compounded half yearly = 4% annually Time 1.5 years, half-yearly($T$) = 3 years We know that, $ A= P(1+\frac{R}{100})^{T}$ $= 7500(1+\frac{4}{100})^{3}$ $= 7500\times\frac{26}{25}\times\frac{26}{25}\times\frac{26}{25}$ $=8436.48$ Hence, the correct answer is Rs. 8,436.48.
Question : Directions: Six friends are sitting in a circle. All of them are facing the centre. Kanak sits third to the right of Sona. Kapil is an immediate neighbour of Mani. Goldy sits second to the right of Mani. Sona is an immediate neighbour of Kapil and Suresh. Who sits second to the left of Kanak?
Option 1: Suresh
Option 2: Kapil
Option 3: Goldy
Option 4: Mani
Correct Answer: Kapil
Solution : Given: Six friends are sitting in a circle. All of them are facing the centre. Kanak sits third to the right of Sona.
II. Kapil is an immediate neighbour of Mani. Goldy sits second to the right of Mani. Sona is an immediate neighbour of
Question : In which year did King George V assume the crown of India?
Option 1: 1917
Option 2: 1906
Option 3: 1923
Option 4: 1911
Correct Answer: 1911
Solution : The correct answer is 1911
In 1911, King George V became the new ruler of India. He also declared that Delhi would become the new capital, replacing Calcutta. On December 31, 1926, he also formally renamed the capital New Delhi.
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No error".
His parents does not (1) / approve of (2) / his business. (3) / No error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The error lies in the first part of the sentence.
"Parents" is a plural noun, so it should be paired with the plural form of the verb "do" rather than the singular form "does" to maintain the subject-verb agreement.
Therefore, the correct sentence is: "His
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.
Gender equality is not only a fundamental human right, but a necessary foundation for a peaceful, prosperous and sustainable world. There (1)_____ progress over the last decades: More girls are going to school, fewer girls are forced into early marriage, more women are serving in parliament and positions of leadership, and laws are being reformed to (2)_____ gender equality. Despite these gains, many challenges remain: discriminatory laws and social norms remain (3)_____, women continue to be underrepresented at all levels of political leadership, and 1 in 5 women and girls between the ages of 15 and 49 report experiencing physical or sexual violence by an intimate partner within a 12 -month period. The effects of the COVID-19 pandemic could reverse the limited progress that has been made on gender equality and women's rights. The coronavirus outbreak (4)_____ existing inequalities for women and girls across every sphere - from health and the economy to security and social protection. Women play a disproportionate role in responding to the virus, including as frontline healthcare workers and carers at home. Women's unpaid care work has increased significantly as a result of school closures and the increased needs of older people. Women are also harder hit by the economic (5)_____ of COVID-19, as they disproportionately work in insecure labour markets. Nearly 60 percent of women work in the informal economy, which puts them at greater risk of falling into poverty.
Question: Select the most appropriate option to fill in the blank 4.
Option 1: placate
Option 2: exacerbates
Option 3: appease
Option 4: aid
Correct Answer: exacerbates
Solution : The correct choice is the second option.
Exacerbate means to make something worse that is already bad. This helps convey the intended meaning that the pandemic worsened the already existing inequalities for women and girls.
Therefore, the correct answer is exacerbates.
Question : The value of $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}-\sec 35^{\circ} \cdot \sin 55^{\circ}}{\sec 60^{\circ}+\operatorname{cosec} 30^{\circ}}$ is equal to:
Option 1: $\frac{1}{8}$
Option 2: $-\frac{1}{4}$
Option 3: $\frac{1}{4}$
Option 4: $-\frac{1}{8}$
Correct Answer: $-\frac{1}{8}$
Solution : Given: $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}-\sec 35^{\circ} \cdot \sin 55^{\circ}}{\sec 60^{\circ}+\operatorname{cosec} 30^{\circ}}$ = $\frac{(\frac{1}{2})^2+(\frac{1}{2})^2 - \sec 35^{\circ} \cdot \sin (90-35)^{\circ}}{2+2}$ = $\frac{(\frac{1}{4})+(\frac{1}{4}) - \sec 35^{\circ} \cdot \cos 35^{\circ}}{2+2}$ = $\frac{(\frac{2}{4}) - (\frac{1}{ \cos 35^{\circ}}) \cdot \cos 35^{\circ}}{4}$ = $\frac{(\frac{2}{4}) - 1}{4}$ = $-\frac{1}{8}$ Hence, the
Question : Directions: If 1 / 4 / 3 = 254 and 3 / 6 / 8 = 479, then 5 / 2 / 7 = ?
Option 1: 416
Option 2: 461
Option 3: 368
Option 4: 638
Correct Answer: 638
Solution : Given: 1 / 4 / 3 = 254; 3 / 6 / 8 = 479
1 / 4 / 3→1 + 1 = 2; 4 + 1 = 5; 3 + 1 = 4→254 3 / 6 / 8→3 + 1 = 4; 6 +
Question : Directions: If + means ×, × means –, – means ÷ and ÷ means +, then what will come in place of the (?) in the following equation? 250 – 10 + 10 × 5 ÷ 2 = ?
Option 1: 247
Option 2: 167
Option 3: 320
Option 4: 234
Correct Answer: 247
Solution : Given: 250 – 10 + 10 × 5 ÷ 2 = ?
After interchanging the given mathematical signs, we get – ⇒ 250 ÷ 10 × 10 – 5 + 2 ⇒ 25 × 10 – 5 + 2 ⇒ 250 – 5 + 2
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