The question asks to identify a spring festival celebrated in Goa from the given options. This requires knowledge of Indian festivals and their regional associations.
Correct Option: C) Shigmotsav is indeed a major spring festival celebrated in Goa. It is a traditional Hindu festival celebrated in the Konkan region, particularly in Goa, during the spring season (usually in March). It involves folk dances, music, and elaborate parades.
When light travels from one medium to another medium then:
Incident ray, normal at the point of incidence and refracted ray all are in the same plane.
Incident ray, normal at the point of incidence and reflected ray are in the same plane.
Incident ray, normal at the point of incidence and emerged ray, all are in the separate plane.
Incident ray, normal at the point of incidence and refracted ray are in different planes.
This question tests the fundamental laws of refraction. When light passes from one medium to another, it changes direction. This phenomenon is governed by specific rules, similar to the laws of reflection.
Correct Option: A) Incident ray, normal at the point of incidence and refracted ray all are in the same plane. This statement correctly describes the first law of refraction. This law ensures that the phenomenon of refraction occurs in a predictable and two-dimensional manner relative to the plane containing these three elements.
To solve this problem, we need to compare the positions of digits in the original number with their positions after arranging the digits in ascending order. We will list the original number and then the sorted number, aligning them to easily identify digits whose positions remain unchanged.
Identify the original number: The given number is 7349842.
List the digits and their original positions:
| Position | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th |
|---|---|---|---|---|---|---|---|
| Digit | 7 | 3 | 4 | 9 | 8 | 4 | 2 |
Arrange the digits in ascending order: The digits in the number 7349842 are 7, 3, 4, 9, 8, 4, 2. Arranging these digits in ascending order gives us 2, 3, 4, 4, 7, 8, 9.
List the digits and their new positions after sorting:
| Position | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th |
|---|---|---|---|---|---|---|---|
| Digit | 2 | 3 | 4 | 4 | 7 | 8 | 9 |
Compare original and new positions: Now, let's compare the digits at each position in the original number and the new number.
| Position | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th |
|---|---|---|---|---|---|---|---|
| Original Digit | 7 | 3 | 4 | 9 | 8 | 4 | 2 |
| Sorted Digit | 2 | 3 | 4 | 4 | 7 | 8 | 9 |
Identify unchanged positions:
The digits at the 2nd and 3rd positions remain unchanged.
Count the unchanged digits: There are 2 digits whose positions remain unchanged.
C) Two. The digits '3' at the second position and '4' at the third position retain their original places after the digits are arranged in ascending order.
To find the number of prime numbers between 400 and 430, we need to list all integers in this range and then eliminate composite numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. We will check divisibility by small prime numbers (2, 3, 5, 7, 11, 13, 17, 19) to identify primes.
D) The prime numbers between 400 and 430 are 401, 409, 419, and 421. There are 4 such numbers.
The question asks to identify the river known as the 'sorrow of Bihar' due to its frequent course changes and destructive nature. This is a direct factual question related to Indian geography and rivers.
D) Kosi — The Kosi River is famously known as the 'Sorrow of Bihar' because of the annual floods it causes, which devastate large areas of Bihar. Its highly unstable nature, characterized by frequent changes in its course and massive silt deposition, leads to immense destruction of life, property, and agricultural land.
This problem involves calculating the profit percentage of a dishonest dealer. The dealer claims to sell goods at cost price but uses a faulty weight. We need to determine the actual profit made due to the reduced weight.
D) 25% is the correct profit percentage. The dealer gains 200g for every 800g he sells, which translates to a 25% profit.
The question asks about the host country for the FIDE World Chess Olympiad 2022. This is a factual question related to current affairs and sports events. Recalling the host country for major international events is key.
Correct Option: D) India
The valency of an element is determined by the number of electrons in its outermost shell (valence electrons) or the number of electrons it needs to gain, lose, or share to achieve a stable electron configuration (usually an octet or duplet). Elements in the same group of the Modern Periodic Table have the same number of valence electrons and thus the same valency.
Correct Option: D) 2
Which of the following statements is true about the nature of roots for the equation x2+x+12=0?
Both roots are positive real
One root is imaginary, and one is real
Both roots are negative real
Both roots are imaginary or non-real
To determine the nature of the roots of a quadratic equation of the form \(ax^2 + bx + c = 0\), we use the discriminant, \(\Delta = b^2 - 4ac\). The value of the discriminant tells us whether the roots are real, imaginary, distinct, or equal.
Identify the coefficients: The given quadratic equation is \(x^2 + x + 12 = 0\). Comparing this with the standard form \(ax^2 + bx + c = 0\), we have:
Calculate the discriminant: Substitute the values of \(a\), \(b\), and \(c\) into the discriminant formula \(\Delta = b^2 - 4ac\):
\[ \Delta = (1)^2 - 4(1)(12) \] \[ \Delta = 1 - 48 \] \[ \Delta = -47 \]Interpret the discriminant: Since \(\Delta = -47\), which is less than 0 (\(\Delta < 0\)), the roots of the equation are imaginary (non-real) and distinct.
D) Both roots are imaginary or non-real. This is correct because the discriminant \(\Delta = -47\), which is less than zero, indicating that the roots are imaginary and distinct.
A) Both roots are positive real. This is incorrect because for roots to be real, the discriminant must be greater than or equal to zero (\(\Delta \ge 0\)). Our discriminant is negative.
B) One root is imaginary, and one is real. This is incorrect. For a quadratic equation with real coefficients, imaginary roots always occur in conjugate pairs. Therefore, if one root is imaginary, the other must also be imaginary.
C) Both roots are negative real. This is incorrect for the same reason as option A. For roots to be real, the discriminant must be non-negative.
The problem can be solved by setting up a linear equation based on the given information. We need to translate the word problem into an algebraic expression and then solve for the unknown number.
Define the unknown: Let the certain number be \(x\).
Translate "6 times a certain number": This can be written as \(6x\).
Translate "39 less than 6 times a certain number": This means we subtract 39 from \(6x\), so it becomes \(6x - 39\).
Formulate the equation: We are told that "39 less than 6 times a certain number is 339". So, we set up the equation:
\[ 6x - 39 = 339 \]Solve for \(x\):
Verify the answer: Substitute \(x = 63\) back into the original statement: "39 less than 6 times 63".
Since this matches the given information, our calculated value for \(x\) is correct.
Correct Option: C) 63