The problem asks us to identify the odd one out from a given list of words: Pyramid, Cylinder, Cuboid, and Circle. We need to find a common characteristic shared by three of the words and identify the one that does not share that characteristic.
Correct Option: D) Circle is the odd one out because it is a two-dimensional shape, whereas Pyramid, Cylinder, and Cuboid are all three-dimensional shapes.
The problem describes a coding pattern where the letters of a word are rearranged to form a new word. We need to identify this pattern by comparing the original word 'MUFASA' with its coded form 'UMAFAS' and then apply the same pattern to code the word 'SONNET'.
Correct Option: D) OSNNTE is the correct coded word for 'SONNET' based on the identified pattern.
Six family members, A, B, C, D, E and F, are working as a team on a family project of renovating a house. Each person has been given a single task. A is B’s son and is in charge of ‘flooring’. B is C’s sister and is in charge of ‘water issues’. C is D’s wife and is in charge of ‘electrical work’. D is in charge of ‘foundation related work’ and his son E is in charge of ‘interior decoration’. F, who is D’s brother, is in charge of ‘roof’. What work is assigned to A’s cousin?
Interior decoration
Roof
Electrical work
Foundation related work
To solve this problem, we need to establish the family relationships between all members and then identify who A's cousin is. Once the cousin is identified, we can determine the task assigned to them.
Correct Option: A) Interior decoration
This question tests general knowledge about famous quotes and their attribution, specifically focusing on historical figures who acknowledged India's contributions to mathematics and science.
Correct Option: D) Albert Einstein
The question asks to identify which option is NOT considered a pillar of human development. Human development, as defined by the United Nations Development Programme (UNDP), emphasizes expanding people's choices and capabilities. It is built upon certain fundamental pillars.
Correct Option: B) Justice is not explicitly listed as one of the four main pillars of human development (Equity, Sustainability, Productivity, Empowerment) by the UNDP. While closely related and essential for societal well-being, it is considered a broader concept or an outcome rather than a foundational pillar in this specific context.
This question tests knowledge of basic human sensory biology, specifically the function of different types of receptors. To answer correctly, one must know the specific sense associated with "gustatory receptors."
Correct Option: D) taste
Gustatory receptors are specialized sensory cells found in taste buds, primarily on the tongue. Their function is to detect chemicals dissolved in saliva, which the brain then interprets as different tastes (sweet, sour, salty, bitter, umami).
The question asks to identify the Vice-President of the Constituent Assembly elected in 1946. This requires knowledge of the key figures and their roles in the formation of the Indian Constituent Assembly.
Correct Option: C) HC Mookherjee was elected as the Vice-President of the Constituent Assembly in 1946. He was a prominent Indian Christian leader and educationist.
If x =\(\frac{\sqrt{3}+1}{\sqrt{3}-1}\) and y =\(\frac{\sqrt{3}-1}{\sqrt{3}+1}\), then the value of \( x^{2} + y^{2} \) is:
To find the value of \(x^2 + y^2\), we first simplify the expressions for \(x\) and \(y\) by rationalizing their denominators. Then, we can either calculate \(x^2\) and \(y^2\) separately and add them, or use the algebraic identity \((x+y)^2 = x^2 + y^2 + 2xy\) which implies \(x^2 + y^2 = (x+y)^2 - 2xy\). The latter approach is often more efficient.
Given \(x = \frac{\sqrt{3}+1}{\sqrt{3}-1}\). Multiply the numerator and denominator by the conjugate of the denominator, which is \(\sqrt{3}+1\).
\[ x = \frac{\sqrt{3}+1}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1} \]\[ x = \frac{(\sqrt{3}+1)^2}{(\sqrt{3})^2 - (1)^2} \]\[ x = \frac{3 + 1 + 2\sqrt{3}}{3 - 1} \]\[ x = \frac{4 + 2\sqrt{3}}{2} \]\[ x = 2 + \sqrt{3} \]Given \(y = \frac{\sqrt{3}-1}{\sqrt{3}+1}\). Multiply the numerator and denominator by the conjugate of the denominator, which is \(\sqrt{3}-1\).
\[ y = \frac{\sqrt{3}-1}{\sqrt{3}+1} \times \frac{\sqrt{3}-1}{\sqrt{3}-1} \]\[ y = \frac{(\sqrt{3}-1)^2}{(\sqrt{3})^2 - (1)^2} \]\[ y = \frac{3 + 1 - 2\sqrt{3}}{3 - 1} \]\[ y = \frac{4 - 2\sqrt{3}}{2} \]\[ y = 2 - \sqrt{3} \]Now that we have simplified \(x\) and \(y\), let's find their sum.
\[ x+y = (2 + \sqrt{3}) + (2 - \sqrt{3}) \]\[ x+y = 2 + 2 + \sqrt{3} - \sqrt{3} \]\[ x+y = 4 \]Next, find their product.
\[ xy = (2 + \sqrt{3})(2 - \sqrt{3}) \]\[ xy = (2)^2 - (\sqrt{3})^2 \]\[ xy = 4 - 3 \]\[ xy = 1 \]Using the identity \(x^2 + y^2 = (x+y)^2 - 2xy\):
\[ x^2 + y^2 = (4)^2 - 2(1) \]\[ x^2 + y^2 = 16 - 2 \]\[ x^2 + y^2 = 14 \]Alternatively, we could calculate \(x^2\) and \(y^2\) directly:
Both methods yield the same result.
A) 14
The problem asks us to identify the odd word out of four given words. We need to find a common characteristic shared by three words and identify the one that does not share that characteristic.
Correct Option: A) Pedestal is the odd one out because Road, Highway, and Street are all types of thoroughfares or paths for travel, whereas a Pedestal is a base or support for an object.
To determine the time difference between Indian Standard Time (IST) and Greenwich Mean Time (GMT), we need to understand the concept of longitudes and their relation to time zones. The Earth rotates 360 degrees in 24 hours. This means for every 1 degree of longitude, there is a time difference. We will calculate this difference and then apply it to India's standard meridian.
D) 5 hours and 30 minutes - This is the correct time difference calculated based on India's standard meridian of \(82.5^\circ\) East longitude.