The question asks about the primary objective or focus of the "Unnat Bharat Abhiyan" initiative. To answer this, one needs to recall the core mission and activities associated with this specific government program.
Correct Option: C) Developing rural India with the help of higher education institutions
The question asks to identify the British physicist who discovered electrons and received the Nobel Prize in Physics in 1906. This requires knowledge of key historical scientific discoveries and Nobel laureates.
Correct Option: B) J J Thomson
UN was founded as a successor to the League of Nations on 24th October ______.
The question asks for the year the United Nations (UN) was founded. This is a factual question related to international organizations and their history, which is a common topic in competitive exams.
Correct Option: C) The United Nations was officially founded on October 24, 1945, when the UN Charter came into force. This date is celebrated annually as United Nations Day.
The problem asks us to identify the odd one out from a list of abbreviations. This is a classification-based question where we need to find a common characteristic among three items and identify the one that does not share that characteristic.
Upon examining these, BHEL, SAIL, and NTPC are all Public Sector Undertakings (PSUs) that operate in industrial or commercial sectors (manufacturing, steel production, power generation). CRPF, on the other hand, is a paramilitary force responsible for law enforcement and internal security, not a commercial or industrial PSU.
C) CRPF is the odd one out because it is a Central Armed Police Force (a paramilitary organization) responsible for law and order and internal security, whereas BHEL, SAIL, and NTPC are all Public Sector Undertakings (PSUs) involved in commercial/industrial activities.
The question asks to identify India's first female para-athlete to win a Paralympic medal, specifically mentioning a silver medal in shot put at the Rio 2016 Paralympic Games. This requires knowledge of prominent Indian para-athletes and their achievements.
Correct Option: C) Deepa Malik
The question asks to identify the popular sword dance from the Kumaun region of Uttarakhand among the given options. This requires knowledge of traditional Indian folk dances and their associated regions.
D) Chholiya — Chholiya is a traditional folk dance form from the Kumaun region of Uttarakhand, India. It is a sword dance, performed during weddings and other auspicious occasions, often by Rajput men. The dancers wear traditional Kumauni attire and carry swords and shields, enacting mock battles.
This problem can be solved by setting up a system of two linear equations based on the initial population and the population after an increase in the number of males and females. We will use variables to represent the initial number of males and females and then solve for these variables.
The number of males in the village prior to the new members coming in was 3000.
A) 3000 is the correct answer, as calculated by solving the system of equations.
If a cos θ − b sin θ = c, then find the value of a sin θ + b cos θ.
\(\sqrt{a^2+b^2+c^2}\)
\(\pm\sqrt{a^2+b^2-c^2}\)
\(\sqrt{b^2+c^2-a^2}\)
\(\pm\sqrt{a^2+c^2-b^2}\)
This problem involves trigonometric identities and algebraic manipulation. We are given an equation and asked to find the value of another expression. The key idea is to square both the given equation and the expression we need to find, and then use the identity \(\sin^2\theta + \cos^2\theta = 1\).
Let the given equation be:
\[ a \cos \theta - b \sin \theta = c \quad \ldots (1) \]Let the expression we need to find be \(x\):
\[ a \sin \theta + b \cos \theta = x \quad \ldots (2) \]Square both equation (1) and equation (2):
From (1):
\[ (a \cos \theta - b \sin \theta)^2 = c^2 \] \[ a^2 \cos^2 \theta + b^2 \sin^2 \theta - 2ab \sin \theta \cos \theta = c^2 \quad \ldots (3) \]From (2):
\[ (a \sin \theta + b \cos \theta)^2 = x^2 \] \[ a^2 \sin^2 \theta + b^2 \cos^2 \theta + 2ab \sin \theta \cos \theta = x^2 \quad \ldots (4) \]Add equation (3) and equation (4):
\[ (a^2 \cos^2 \theta + b^2 \sin^2 \theta - 2ab \sin \theta \cos \theta) + (a^2 \sin^2 \theta + b^2 \cos^2 \theta + 2ab \sin \theta \cos \theta) = c^2 + x^2 \]Notice that the \(-2ab \sin \theta \cos \theta\) and \(+2ab \sin \theta \cos \theta\) terms cancel out:
\[ a^2 \cos^2 \theta + b^2 \sin^2 \theta + a^2 \sin^2 \theta + b^2 \cos^2 \theta = c^2 + x^2 \]Group terms with \(a^2\) and \(b^2\):
\[ a^2 (\cos^2 \theta + \sin^2 \theta) + b^2 (\sin^2 \theta + \cos^2 \theta) = c^2 + x^2 \]Apply the trigonometric identity \(\sin^2\theta + \cos^2\theta = 1\):
\[ a^2 (1) + b^2 (1) = c^2 + x^2 \] \[ a^2 + b^2 = c^2 + x^2 \]Solve for \(x^2\):
\[ x^2 = a^2 + b^2 - c^2 \]Take the square root to find \(x\):
\[ x = \pm\sqrt{a^2 + b^2 - c^2} \]Correct Option: B) \(\pm\sqrt{a^2+b^2-c^2}\)
An E-Way Bill is related with which of the following?
Pre-payment of goods and services
Supply of goods from one place to another
Post-payment of goods and services
Making toll payments on national highways
The question asks about the purpose of an E-Way Bill. We need to identify the core function of this document in the context of goods movement and taxation, specifically under the Goods and Services Tax (GST) regime in India.
B) Supply of goods from one place to another — An E-Way Bill is a document required for the movement of goods worth more than a specified amount from one place to another, under the GST regime in India. It serves as proof of compliance with GST regulations during transit.