The question asks to identify the part of the nervous system that includes cranial nerves arising from the brain and spinal nerves arising from the spinal cord. This requires understanding the basic divisions of the human nervous system.
Correct Option: A) peripheral nervous system. This option correctly identifies the division of the nervous system that includes cranial and spinal nerves, as these nerves extend from the CNS to the rest of the body.
This problem can be solved by applying a fundamental property relating the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers. The property states that the product of two numbers is equal to the product of their HCF and LCM.
We are given the HCF of two numbers as 7 and their LCM as 245.
For any two positive integers, say \(a\) and \(b\), the following relationship holds:
\[ a \times b = \text{HCF}(a, b) \times \text{LCM}(a, b) \]Let the two numbers be \(N_1\) and \(N_2\). We need to find their product, \(N_1 \times N_2\).
\[ N_1 \times N_2 = \text{HCF} \times \text{LCM} \]\[ N_1 \times N_2 = 7 \times 245 \]Multiply the HCF and LCM values:
\[ 7 \times 245 = 1715 \]The product of the two numbers is 1715.
D) 1715 — The product of the two numbers is found by multiplying their HCF (7) and LCM (245), which results in 1715.
This question tests fundamental knowledge about atomic structure, specifically the definition of atomic number. We need to recall what atomic number represents in terms of subatomic particles.
Correct Option: A) total number of protons present in the nucleus of an atom
This problem involves decoding a blood relation expression using given symbolic representations. We need to break down the expression 'P – Q ÷ R × S + T' step by step, determining the relationship between each pair of individuals, and then combine these relationships to find how Q is related to S.
Correct Option: B) Wife's father
Q is the father of R, and R is the wife of S. Thus, Q is the father of S's wife.
To evaluate the given expression, we need to apply the rules of exponents. Specifically, we will calculate the value of each term separately and then multiply them. Remember that any non-zero number raised to the power of zero is 1.
Thus, the value of the expression \(2^3 \times (-9)^0 \times 3^3\) is 216.
B) 216 is the correct answer, as calculated by evaluating each exponential term and then multiplying them together.
The problem requires us to perform a series of transformations on the letters of a given word: first, change each vowel and consonant to the letter following it in the English alphabet. Then, arrange the newly formed letters in reverse alphabetical order. Finally, identify the fourth letter from the left in this new arrangement.
Identify vowels and consonants in the word REALISM:
Apply the transformation rule: Change each vowel to the letter following it and each consonant to the letter following it.
The new set of letters is S, F, B, M, J, T, N.
Arrange the new letters in reverse alphabetical order:
First, list them in alphabetical order: B, F, J, M, N, S, T.
Now, arrange them in reverse alphabetical order: T, S, N, M, J, F, B.
Identify the fourth letter from the left:
In the arrangement T, S, N, M, J, F, B, the fourth letter from the left is M.
D) M is the fourth letter from the left in the final arrangement.
The problem presents a coding scheme where letters are represented by digits. We are given two coded words and need to find the code for a specific letter. This type of problem is solved by comparing the given coded words to identify the unique code for each common letter and then deducing the codes for other letters.
The letters common to 'NUMB' and 'BUNT' are N, U, B.
The digits common to '4618' and '6438' are 4, 6, 8.
Let's match them:
Now let's try to find a consistent mapping:
From 'NUMB' \(\rightarrow\) '4618'
From 'BUNT' \(\rightarrow\) '6438'
The common letters are N, U, B. The common digits are 4, 6, 8.
Let's assume a one-to-one mapping:
Let's re-evaluate by finding the unique codes:
From 'NUMB' \(\rightarrow\) '4618'
From 'BUNT' \(\rightarrow\) '6438'
Common letters: N, U, B
Common digits: 4, 6, 8
Let's try to assign the codes:
Let's verify this mapping with the given codes:
For 'NUMB' \(\rightarrow\) '4618':
N = 4
U = 6
M = 1 (remaining letter and digit)
B = 8
This mapping works for 'NUMB'.
For 'BUNT' \(\rightarrow\) '6438':
B = 8 (verified)
U = 6 (verified)
N = 4 (verified)
T = 3 (remaining letter and digit)
This mapping works for 'BUNT'.
B) 3 is the correct code for 'T'.
This problem involves work and time, and the distribution of wages based on the work done. We need to calculate the individual work rates, then determine the work done by each person, including C, and finally distribute the total amount proportional to their work contributions.
A alone can do the work in 6 days. So, A's one day's work is:
\[ \text{A's 1 day's work} = \frac{1}{6} \]B alone can do the work in 8 days. So, B's one day's work is:
\[ \text{B's 1 day's work} = \frac{1}{8} \]With the help of C, A and B completed the work in 3 days. So, (A + B + C)'s one day's work is:
\[ \text{(A + B + C)'s 1 day's work} = \frac{1}{3} \]C's one day's work can be found by subtracting A's and B's one day's work from the combined one day's work of A, B, and C:
\[ \text{C's 1 day's work} = \text{(A + B + C)'s 1 day's work} - (\text{A's 1 day's work} + \text{B's 1 day's work}) \]\[ \text{C's 1 day's work} = \frac{1}{3} - \left(\frac{1}{6} + \frac{1}{8}\right) \]\[ \text{C's 1 day's work} = \frac{1}{3} - \left(\frac{4+3}{24}\right) \]\[ \text{C's 1 day's work} = \frac{1}{3} - \frac{7}{24} \]\[ \text{C's 1 day's work} = \frac{8-7}{24} = \frac{1}{24} \]Since they worked for 3 days to complete the job, the amount of work done by each is their one day's work multiplied by 3 days.
Work done by A in 3 days \[= 3 \times \frac{1}{6} = \frac{1}{2}\]
Work done by B in 3 days \[= 3 \times \frac{1}{8} = \frac{3}{8}\]
Work done by C in 3 days \[= 3 \times \frac{1}{24} = \frac{1}{8}\]
The ratio of work done by A : B : C is:
\[ \frac{1}{2} : \frac{3}{8} : \frac{1}{8} \]\[ \text{Multiply by 8 to clear denominators:} \]\[ 4 : 3 : 1 \]The total amount to be paid is ₹3,200. The payment is distributed in the ratio of work done.
Sum of the ratio parts \( = 4 + 3 + 1 = 8 \)
C's share \[= \frac{\text{C's ratio part}}{\text{Total ratio parts}} \times \text{Total amount}\]
\[ \text{C's share} = \frac{1}{8} \times 3200 \]\[ \text{C's share} = 400 \]So, C is to be paid ₹400.
B) ₹400 is the correct amount to be paid to C, based on the proportion of work C contributed.
To find the single equivalent discount for successive discounts, we can assume an initial price (e.g., Rs. 100) and apply each discount one after another. Alternatively, we can use the formula for equivalent discount.
Method 1: Assuming an initial price
Method 2: Using the equivalent discount formula
Both methods yield the same result.
D) 8.8% is the correct equivalent single discount.
A triangle has sides of length 5 cm, 7 cm and 10 cm. Find the area of the triangle (in cm²).
To find the area of a triangle given its three side lengths, we can use Heron's formula. This formula requires calculating the semi-perimeter first.
A) \(2\sqrt{66}\) is the correct area calculated using Heron's formula.