The question asks to identify the element that does not belong to Group 11 of the Modern Periodic Table. To answer this, we need to recall the elements that constitute Group 11 and then compare them with the given options.
D) Hg (Mercury) does not belong to Group 11. Mercury is a Group 12 element, known as a post-transition metal, and is unique for being a liquid at standard temperature and pressure.
The given series is an alternating series where numbers are formed by squaring and cubing consecutive integers. We need to identify the pattern and apply it to find the missing number.
The series alternates between cubing and squaring consecutive integers starting from 2:
Following this pattern, the next number in the series should be the square of the next consecutive integer, which is 7.
\[ 7^2 = 49 \]Therefore, the number that replaces the question mark is 49.
Correct Option: C) 49
If α, β are the roots of the quadratic equation
2x² – 3x – 35 = 0,
then the value of α³ + β³ is:
\(\frac{757}{8}\)
\(\frac{657}{8}\)
\(\frac{857}{8}\)
\(\frac{957}{8}\)
To find the value of \(\alpha^3 + \beta^3\) for a quadratic equation, we first identify the coefficients of the given quadratic equation. Then, we use Vieta's formulas to find the sum (\(\alpha + \beta\)) and product (\(\alpha\beta\)) of the roots. Finally, we use the algebraic identity \(\alpha^3 + \beta^3 = (\alpha + \beta)(\alpha^2 - \alpha\beta + \beta^2)\) or \(\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha\beta(\alpha + \beta)\) to calculate the required value.
Identify coefficients:
The given quadratic equation is \(2x^2 - 3x - 35 = 0\).
Comparing it with the standard form \(ax^2 + bx + c = 0\), we have:
Find sum and product of roots:
For a quadratic equation \(ax^2 + bx + c = 0\) with roots \(\alpha\) and \(\beta\):
Sum of roots: \(\alpha + \beta = -\frac{b}{a}\)
Product of roots: \(\alpha\beta = \frac{c}{a}\)
Substitute the values of \(a, b, c\):
Use algebraic identity for \(\alpha^3 + \beta^3\):
We know the identity:
Substitute the values and calculate:
Substitute \(\alpha + \beta = \frac{3}{2}\) and \(\alpha\beta = -\frac{35}{2}\) into the identity:
Simplify the expression:
To add the fractions, find a common denominator, which is 8:
Correct Option: B) \(\frac{657}{8}\)
ZR 18 is related to UW 11 in a certain way. In the same way, YM 24 is related to TR 17. To which of the following is KJ 35 related following the same logic?
The problem presents a relationship between a pair of letter-number combinations. We need to identify the pattern in this relationship and apply it to a new combination to find the missing pair.
Correct Option: A) FO 28
The question asks to identify the southernmost district of Tamil Nadu based on its geographical location and given area. This requires knowledge of the geography of Tamil Nadu districts.
Correct Option: C) Kanniyakumari
Which of the following materials CANNOT be used to make a spherical lens?
To make a spherical lens, the material must be transparent and allow light to pass through it, enabling refraction. We need to identify which of the given options does not possess these properties.
C) Wood — Wood is an opaque material. It does not transmit light, which is a fundamental requirement for a material to function as a lens. Lenses rely on the refraction of light, which necessitates transparency.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some bracelets are rings.
Some bangles are bracelets.
All watches are bracelets.
Conclusions:
I. Some rings are bracelets.
II. Some bracelets are watches.
Only conclusion II follows.
Neither conclusion I nor II follows.
Only conclusion I follows.
Both conclusions I and II follow.
This is a syllogism problem. We need to evaluate the given conclusions based on the provided statements. We can use Venn diagrams or direct logical deduction to determine which conclusions logically follow.
Since both Conclusion I and Conclusion II logically follow from the given statements, the correct option is D.
Correct Option: D) Both conclusions I and II follow.
Which state had fielded a 396-member contingent, the largest at Khelo India Youth Games 2021 and competed in every sport?
The question asks to identify the state that sent the largest contingent (396 members) to the Khelo India Youth Games 2021 and participated in every sport. This requires knowledge of specific details about the Khelo India Youth Games 2021.
Correct Option: B) Haryana
The question asks for the full form of the SAMRIDH initiative, which was announced in partnership with Atal Innovation Mission (AIM), NITI Aayog, and USAID in February 2022. This requires knowledge of current affairs and specific government initiatives.
C) Sustainable Access to Markets and Resources for Innovative Delivery of Healthcare
The SAMRIDH (Sustainable Access to Markets and Resources for Innovative Delivery of Healthcare) initiative is a blended finance facility supported by USAID and implemented by IPE Global. It aims to improve access to affordable and quality healthcare for vulnerable populations in India by leveraging private sector investment and market-based solutions. The partnership with AIM and NITI Aayog focuses on strengthening healthcare innovation and entrepreneurship.
The area (in cm²) of an equilateral triangle of side 3 cm is:
\(\frac{\sqrt{243}}{6}\)
\(\frac{\sqrt{243}}{3}\)
\(\frac{\sqrt{243}}{4}\)
\(\frac{\sqrt{243}}{2}\)
To find the area of an equilateral triangle, we use the standard formula involving its side length. We are given the side length, so we will substitute this value into the formula and simplify the expression to match one of the given options.
The formula for the area of an equilateral triangle with side length \(a\) is given by:
\[ \text{Area} = \frac{\sqrt{3}}{4} a^2 \]In this problem, the side length \(a = 3 \text{ cm}\). Substitute this value into the formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} (3)^2 \]Calculate \(3^2\):
\[ 3^2 = 9 \]Substitute this back into the area formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} \times 9 \]\[ \text{Area} = \frac{9\sqrt{3}}{4} \]Now, we need to express this in a form similar to the options provided. The options have \(\sqrt{243}\) in the numerator. Let's see if we can convert \(9\sqrt{3}\) into a form involving \(\sqrt{243}\).
We know that \(9 = \sqrt{81}\). So, we can write:
\[ 9\sqrt{3} = \sqrt{81} \times \sqrt{3} \]\[ 9\sqrt{3} = \sqrt{81 \times 3} \]\[ 9\sqrt{3} = \sqrt{243} \]Substitute this back into the area expression:
\[ \text{Area} = \frac{\sqrt{243}}{4} \]The unit of area will be \(\text{cm}^2\).
C) \(\frac{\sqrt{243}}{4}\) is the correct expression for the area of the equilateral triangle.