To solve this problem, we need to compare the original position of each letter in the given word with its position after arranging all the letters in alphabetical order. We will count how many letters retain their original position.
The given word is 'BOARD'.
The letters and their original positions are:
The letters in the word 'BOARD' are B, O, A, R, D.
Arranging these letters alphabetically, we get: A, B, D, O, R.
Now, let's list the letters in their new, alphabetically ordered positions:
By comparing the original positions with the new positions, we can see if any letter remains in its original place:
None of the letters remain in their original positions.
Correct Option: C) None
This problem involves tracking a person's direction after a series of turns. We will start with the initial direction and apply each 90-degree turn sequentially to determine the final facing direction.
Correct Option: C) West
The question asks to identify a heterotrophic organism from the given options. To answer this, it's essential to understand the definition of heterotrophs and autotrophs.
Correct Option: D) A tiger is a heterotrophic organism because it obtains its nutrition by consuming other organisms.
The problem describes the formation of an image by a converging lens. We are given the object distance and the characteristics of the image (real, inverted, and equal in size to the object). These characteristics are key to determining the position of the object relative to the lens, specifically that the object is placed at \(2F\) (twice the focal length). Once the focal length is found, the power of the lens can be calculated.
Correct Option: C) +10 D
To find the missing number in the series, we need to identify the pattern or rule governing the sequence of numbers. We will examine the differences between consecutive terms to determine if there's an arithmetic progression, a pattern in the differences, or another type of sequence.
C) 23 is the correct answer because the pattern of differences between consecutive terms is decreasing by one each time (5, 4, 3, 2, 1).
Factorise
(64x6−y6).
(2x−y)(2x+y)(4x2−2xy+y2)(4x2−2xy−y2)
(2x−y)(2x+y)(4x2+2xy+y2)(4x2−2xy+y2)
(2x−y)(2x+y)(4x2+2xy+y2)(4x2−2xy−y2)
(2x−y)(2x+y)(4x2+2xy-y2)(4x2−2xy+y2)
To factorize the given expression \( (64x^6 - y^6) \), we will use the algebraic identities for the difference of squares and the difference/sum of cubes. The expression can be written as a difference of squares first, and then the resulting terms can be factorized further using the sum and difference of cubes identities.
Recognize as difference of squares:
The given expression is \( 64x^6 - y^6 \). This can be written as \( (8x^3)^2 - (y^3)^2 \).
Apply the difference of squares identity:
The identity is \( a^2 - b^2 = (a-b)(a+b) \). Here, \( a = 8x^3 \) and \( b = y^3 \).
\[ 64x^6 - y^6 = (8x^3 - y^3)(8x^3 + y^3) \]Factorize \( (8x^3 - y^3) \) using the difference of cubes identity:
The identity is \( a^3 - b^3 = (a-b)(a^2+ab+b^2) \). Here, \( a = 2x \) and \( b = y \).
\[ 8x^3 - y^3 = (2x)^3 - (y)^3 = (2x-y)((2x)^2 + (2x)(y) + y^2) = (2x-y)(4x^2+2xy+y^2) \]Factorize \( (8x^3 + y^3) \) using the sum of cubes identity:
The identity is \( a^3 + b^3 = (a+b)(a^2-ab+b^2) \). Here, \( a = 2x \) and \( b = y \).
\[ 8x^3 + y^3 = (2x)^3 + (y)^3 = (2x+y)((2x)^2 - (2x)(y) + y^2) = (2x+y)(4x^2-2xy+y^2) \]Combine the factorized terms:
Substitute the factorized forms back into the expression from step 2:
\[ (8x^3 - y^3)(8x^3 + y^3) = (2x-y)(4x^2+2xy+y^2)(2x+y)(4x^2-2xy+y^2) \]Rearrange the terms (optional, for matching options):
Rearranging the terms to match the options:
\[ (2x-y)(2x+y)(4x^2+2xy+y^2)(4x^2-2xy+y^2) \]B) \( (2x-y)(2x+y)(4x^2+2xy+y^2)(4x^2-2xy+y^2) \)
This question involves a double displacement reaction, specifically a precipitation reaction. When two soluble ionic compounds are mixed, their ions can exchange partners. If one of the new combinations forms an insoluble compound, it will precipitate out of the solution.
Correct Option: D) Lead iodide
When lead nitrate solution is mixed with sodium iodide solution, a double displacement reaction occurs. The products formed are lead iodide (\(\text{PbI}_2\)) and sodium nitrate (\(\text{NaNO}_3\)). According to solubility rules, lead iodide is insoluble in water and thus precipitates as a bright yellow solid. Sodium nitrate, being soluble, remains in the solution.
The question asks for the budgetary outlay approved by the Government of India for the Production Linked Incentive (PLI) Scheme National Programme on Advanced Chemistry Cell (ACC) Battery Storage in May 2021. This is a factual question requiring knowledge of specific government scheme details.
D) Rs 18,100 crore — The Government of India approved the PLI Scheme National Programme on Advanced Chemistry Cell (ACC) Battery Storage with a budgetary outlay of Rs 18,100 crore in May 2021.
In this question, a group of letters is coded using symbols as per the table given below and the conditions which follow. The correct combination of codes following the conditions will be your answer.
| Letters | D | T | V | O | I | A | P | E |
| Codes | @ | > | ^ | % | = | # | $ | + |
Conditions:
i. If both the first and last letters of the word are vowels, then both these letters will be coded as ‘&’.
ii. If both the first and last letters of the word are consonants, then both these letters will be coded as ‘*’.
What will be the code for the word “ADOPTIVE”?
& @ % $ > = ^ &
# @ % $ > = ^ +
# @ % $ > = ^ &
& @ % $ > = ^ +
The problem requires us to code the word "ADOPTIVE" based on a given table of letter-to-symbol mappings and two conditions. We need to first identify the individual codes for each letter, then check if any of the conditions apply to the first and last letters of the word, and finally apply the conditions if necessary.
A) & @ % \) > = ^ &
This option matches the code derived by correctly applying the conditions and the given table.
To determine which pair of numbers is co-prime, we need to find the greatest common divisor (GCD) for each pair. Two numbers are co-prime (or relatively prime) if their GCD is 1. We will use prime factorization or the Euclidean algorithm to find the GCD for each option.
D) 59, 97. The greatest common divisor of 59 and 97 is 1, which means they are co-prime.