The problem involves finding a pattern in letter coding based on the English alphabetical order. We need to identify the relationship between the letters in the given pairs (SKIB to OGNG and CUCV to YQHA) and then apply the same logic to find the code for QIRK.
D) MEWP — This matches our derived code for QIRK based on the established pattern.
The question asks about the nature of the magnetic field inside a long, straight solenoid carrying current. We need to recall the properties of the magnetic field produced by a solenoid.
Correct Option: A) uniform and parallel to the axis of the solenoid
This option accurately describes the magnetic field inside a long, straight solenoid. The field lines are parallel to the axis, indicating a uniform direction, and their density is constant, indicating a uniform strength (magnitude) throughout the interior, away from the ends.
The question asks to identify a non-biodegradable material from the given options. Biodegradable materials are those that can be decomposed by natural processes and microorganisms, returning to the environment. Non-biodegradable materials, on the other hand, cannot be broken down by these natural processes and persist in the environment for a very long time.
Correct Option: B) Plastic is a synthetic material that is not easily broken down by natural processes or microorganisms. It can persist in the environment for hundreds to thousands of years, making it non-biodegradable and a significant environmental pollutant.
The question asks to identify the article of the Indian Constitution that deals with the Finance Commission and its role in distributing taxes between the Centre and States. We need to recall the constitutional provisions related to the Finance Commission.
Correct Option: D) Article 280 deals with the Finance Commission, which is responsible for recommending the distribution of taxes between the Centre and the States. It mandates the President to constitute a Finance Commission every five years or at such earlier time as he considers necessary.
The problem asks us to find the fourth angle of a quadrilateral given its three other angles. The key property to use here is that the sum of the interior angles of any quadrilateral is always 360 degrees.
Identify the given angles of the quadrilateral:
\[ \text{Angle}_1 = 70^\circ \]\[ \text{Angle}_2 = 85^\circ \]\[ \text{Angle}_3 = 95^\circ \]Let the fourth angle be \(\text{Angle}_4\).
Recall the property of quadrilaterals: The sum of the interior angles of a quadrilateral is \(360^\circ\).
Set up the equation:
\[ \text{Angle}_1 + \text{Angle}_2 + \text{Angle}_3 + \text{Angle}_4 = 360^\circ \]Substitute the given values into the equation:
\[ 70^\circ + 85^\circ + 95^\circ + \text{Angle}_4 = 360^\circ \]Sum the known angles:
\[ 70^\circ + 85^\circ + 95^\circ = 250^\circ \]Substitute this sum back into the equation:
\[ 250^\circ + \text{Angle}_4 = 360^\circ \]Solve for \(\text{Angle}_4\):
\[ \text{Angle}_4 = 360^\circ - 250^\circ \]\[ \text{Angle}_4 = 110^\circ \]Thus, the fourth angle of the quadrilateral is \(110^\circ\).
C) 110° — As calculated, the sum of the three given angles is \(250^\circ\). Subtracting this from \(360^\circ\) (the total sum of angles in a quadrilateral) gives \(110^\circ\).
The problem presents a series of letter groups, and we need to find the next group in the sequence. This type of problem usually involves identifying a pattern in the alphabetical positions of the letters or a transformation rule applied to each letter in the group.
C) KJH is the correct option because by analyzing the alternate terms in the series, we find a consistent pattern of subtracting 2 from the alphabetical position for each corresponding letter (first, second, and third).
To find the missing number in the series, we need to identify the pattern or relationship between consecutive terms. This can often be done by looking at the differences between adjacent numbers, or the differences of these differences (second-order differences).
Write down the given series: \(1, 13, 28, 46, 67, ?\)
Calculate the differences between consecutive terms:
Difference between the 1st and 2nd term: \(13 - 1 = 12\)
Difference between the 2nd and 3rd term: \(28 - 13 = 15\)
Difference between the 3rd and 4th term: \(46 - 28 = 18\)
Difference between the 4th and 5th term: \(67 - 46 = 21\)
The first-order differences are: \(12, 15, 18, 21\).
Observe the pattern in the first-order differences. We can see that these differences are increasing by a constant value. Let's calculate the second-order differences:
Difference between \(15\) and \(12\): \(15 - 12 = 3\)
Difference between \(18\) and \(15\): \(18 - 15 = 3\)
Difference between \(21\) and \(18\): \(21 - 18 = 3\)
The second-order differences are constant, which is \(3\). This indicates that the first-order differences form an arithmetic progression.
To find the next term in the series, we need to find the next first-order difference. Since the second-order difference is \(3\), the next first-order difference will be \(21 + 3 = 24\).
Now, add this new difference to the last term of the given series to find the missing number:
\(67 + 24 = 91\)
Thus, the missing number in the series is \(91\).
D) 91 is the correct answer because it follows the established pattern of increasing differences by 3.
A) 90 — This would imply the next difference was 23, which does not fit the pattern of increasing by 3 (i.e., \(21+2 = 23\), not \(21+3\)).
B) 92 — This would imply the next difference was 25, which does not fit the pattern of increasing by 3 (i.e., \(21+4 = 25\), not \(21+3\)).
C) 93 — This would imply the next difference was 26, which does not fit the pattern of increasing by 3 (i.e., \(21+5 = 26\), not \(21+3\)).
The question asks to identify which option is NOT an agent of seed dispersal. Seed dispersal is the movement or transport of seeds away from the parent plant. This process is crucial for plant survival and colonization of new areas. Various natural agents facilitate this movement.
Correct Option: B) Sunlight is not an agent of dispersal of seeds. While crucial for plant life, it does not physically transport seeds.
To expand the given expression \((9a + 4b + 5c)^2\), we will use the algebraic identity for the square of a trinomial: \((x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx\).
In our expression \((9a + 4b + 5c)^2\), we have:
Substitute these values into the identity \((x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx\):
\[ (9a + 4b + 5c)^2 = (9a)^2 + (4b)^2 + (5c)^2 + 2(9a)(4b) + 2(4b)(5c) + 2(5c)(9a) \]Add all the calculated terms together:
\[ (9a + 4b + 5c)^2 = 81a^2 + 16b^2 + 25c^2 + 72ab + 40bc + 90ac \]C) \(81a^2 + 16b^2 + 25c^2 + 72ab + 40bc + 90ac\)
To evaluate the given expression, we must follow the order of operations, commonly remembered by the acronym BODMAS/PEMDAS. This stands for Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
The given expression is:
\[ 16 + 16 \div 4 - 3 \times 3 \]According to BODMAS, we first perform Division and Multiplication from left to right.
First, perform the division:
\[ 16 \div 4 = 4 \]Next, perform the multiplication:
\[ 3 \times 3 = 9 \]Substitute these results back into the expression:
\[ 16 + 4 - 9 \]Now, perform Addition and Subtraction from left to right.
First, perform the addition:
\[ 16 + 4 = 20 \]Finally, perform the subtraction:
\[ 20 - 9 = 11 \]Thus, the value of the expression is 11.
C) 11 is the correct answer, as derived by following the BODMAS/PEMDAS rule.
A) 14 — This result might be obtained if operations are performed incorrectly, for example, if subtraction is done before multiplication or division, or if the order of addition and subtraction is not strictly left to right after multiplication/division.
B) 13 — This could result from an error in calculation or an incorrect order of operations, such as \(16 + 4 - 3 \times 3 = 20 - 3 \times 3 = 17 \times 3 = 51\) (incorrect) or \(16 + 4 - 9 = 11\), so 13 is not possible with correct BODMAS.
D) 10 — This result would occur if there was a calculation error, for instance, if \(16 + 4 - 9\) was incorrectly calculated as 10 instead of 11.