The problem describes a right-angled triangle \(\triangle MNO\) and asks for the length of an altitude \(MP\) from vertex \(M\) to side \(NO\). However, the problem statement seems to have a slight misunderstanding of geometry. If \(MP\) is the perpendicular from \(M\) to \(NO\), and \(\angle N = 90^\circ\), then \(MN\) itself is perpendicular to \(NO\). Therefore, \(P\) must coincide with \(N\), and \(MP\) would be the same as \(MN\). We can find the length of \(MN\) using the Pythagorean theorem.
Since \(\angle N = 90^\circ\), the side \(MN\) is already perpendicular to the side \(NO\). If \(MP\) is the perpendicular from \(M\) to \(NO\), then the point \(P\) must coincide with \(N\). Therefore, the length of \(MP\) is the same as the length of \(MN\).
In the right-angled triangle \(\triangle MNO\), according to the Pythagorean theorem:
\[ MO^2 = MN^2 + NO^2 \]We have \(MO = 10\text{ cm}\) and \(NO = 6\text{ cm}\). We need to find \(MN\).
\[ 10^2 = MN^2 + 6^2 \] \[ 100 = MN^2 + 36 \]Since \(MP = MN\), the length of \(MP\) is \(8\text{ cm}\).
A) 8 cm
The question asks to identify the individual known as the "architect of Indian planning." This requires knowledge of key figures in India's economic planning history and their specific contributions.
Correct Option: D) Prasanta Chandra Mahalanobis is widely regarded as the "architect of Indian planning." He was a renowned statistician who played a pivotal role in formulating India's Second Five-Year Plan, which laid the foundation for industrial development. His contributions include the Mahalanobis model, a statistical model used for planning and development.
This question involves a chemical reaction between a metal (aluminium) and a salt solution (copper sulphate). We need to identify the product responsible for the observed colour change, which implies a displacement reaction.
Correct Option: C) \(\text{Al}_2(\text{SO}_4)_3\) is aluminium sulphate. This compound is formed when aluminium displaces copper from copper sulphate. The formation of colourless aluminium sulphate and the consumption of blue copper sulphate ions lead to the observed colour change (fading of blue colour). This is consistent with the reactivity series where aluminium is more reactive than copper.
This problem can be solved using Ohm's Law, which states the relationship between voltage, current, and resistance in an electrical circuit. Ohm's Law is given by the formula \(V = IR\), where \(V\) is the voltage, \(I\) is the current, and \(R\) is the resistance. We are given the resistance and the voltage, and we need to find the current.
Ohm's Law states:
\[ V = IR \]To find the current, we can rearrange the formula as:
\[ I = \frac{V}{R} \]Substitute \(V = 220 \ \text{V}\) and \(R = 4.2 \ \Omega\) into the rearranged formula:
\[ I = \frac{220 \ \text{V}}{4.2 \ \Omega} \]Perform the division:
\[ I \approx 52.38095 \ \text{A} \]Rounding to two decimal places, the current is approximately \(52.38 \ \text{A}\).
B) \(52.38 \ \text{ampere}\) is the correct current calculated using Ohm's Law.
The question asks to identify the Cabinet Minister for the Ministry of Parliamentary Affairs who took oath in 2019. This requires knowledge of the Union Council of Ministers formed after the 2019 general elections in India.
Correct Option: B) Pralhad Venkatesh Joshi was indeed sworn in as the Cabinet Minister of the Ministry of Parliamentary Affairs (along with Coal and Mines) in 2019.
The quadratic equation with real coefficients which has real roots 4 and −5 is:
x2 − 5x − 24 = 0
x2 + x − 20 = 0
x2 − x − 30 = 0
x2 − 4x − 20 = 0
To find a quadratic equation with given real roots, we can use the relationship between the roots and the coefficients of a quadratic equation. If \(\alpha\) and \(\beta\) are the roots of a quadratic equation, then the equation can be written as \(x^2 - (\alpha + \beta)x + \alpha\beta = 0\).
B) The derived quadratic equation is \(x^2 + x - 20 = 0\), which matches option B.
To solve this problem, we need to perform the division operations first, following the order of operations (BODMAS/PEMDAS), and then perform the addition and subtraction from left to right.
Given expression:
\[ (279 \div 31) + (363 \div 33) - (512 \div 16) \]Step 1: Evaluate the first division term.
\[ 279 \div 31 \]To find the result, we can perform the division:
\[ 31 \times 9 = 279 \]So,
\[ 279 \div 31 = 9 \]Step 2: Evaluate the second division term.
\[ 363 \div 33 \]To find the result, we can perform the division:
\[ 33 \times 11 = 363 \]So,
\[ 363 \div 33 = 11 \]Step 3: Evaluate the third division term.
\[ 512 \div 16 \]To find the result, we can perform the division:
\[ 16 \times 32 = 512 \]So,
\[ 512 \div 16 = 32 \]Step 4: Substitute the results back into the original expression.
The expression becomes:
\[ 9 + 11 - 32 \]Step 5: Perform the addition and subtraction from left to right.
First, perform the addition:
\[ 9 + 11 = 20 \]Now, perform the subtraction:
\[ 20 - 32 = -12 \]Thus, the value of the expression is \(-12\).
D) -12 is the correct answer, as calculated by performing the divisions first and then the addition and subtraction.
The problem requires us to decode a pattern used to transform words into coded forms. We need to identify the rule applied to each letter of the given words 'BLISS' and 'LIGHT' to get their respective codes 'KSNVT' and 'UPLKU'. Once the rule is identified, we apply it to the word 'WHITE' to find its coded form.
Let's find the positional value of each letter in the alphabet (A=1, B=2, ..., Z=26) and the difference between the coded letter and the original letter.
The pattern for the differences is \(+9, +7, +5, +3, +1\).
Let's verify if the same pattern applies.
The pattern \(+9, +7, +5, +3, +1\) is consistent.
Now, we apply the same pattern of adding \(+9, +7, +5, +3, +1\) to the positional values of the letters in 'WHITE'.
So, 'WHITE' is coded as 'FONWF'.
Correct Option: C) FONWF
This problem requires us to substitute the given letter codes with their corresponding mathematical operations and then evaluate the expression using the order of operations (BODMAS/PEMDAS).
Correct Option: C) 39
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. For example, operations on 12, such as adding/subtracting/multiplying, etc. to 12 can be performed. Breaking down 12 into 1 and 2 and then performing mathematical operations on 1 and 2 is not allowed
(11, 154, 7)
(6, 180, 15)
The problem asks us to identify a set of numbers that follows the same relationship as the given sets: (11, 154, 7) and (6, 180, 15). We need to find a mathematical operation or pattern connecting the three numbers in each set.
Let the numbers be \(A\), \(B\), and \(C\). So, \(A = 11\), \(B = 154\), \(C = 7\).
We look for a relationship between these numbers. A common pattern in such problems involves multiplication or division. Let's try multiplying the first and third numbers and see if it relates to the second number.
\[ A \times C = 11 \times 7 = 77 \]This is not equal to \(B = 154\). However, \(154\) is twice \(77\).
\[ 154 = 2 \times 77 \]So, the relationship could be \(B = 2 \times (A \times C)\).
Here, \(A = 6\), \(B = 180\), \(C = 15\).
Using the derived relationship \(B = 2 \times (A \times C)\):
\[ 2 \times (6 \times 15) = 2 \times 90 = 180 \]This matches the second number \(B = 180\). So, the established pattern is \(B = 2 \times A \times C\).