We need to find a two-digit number that satisfies the given condition: the number itself is exactly three times the product of its digits. We can solve this by either setting up an algebraic equation or by checking each option provided.
Let the two-digit number be represented as \(10t + u\), where \(t\) is the tens digit and \(u\) is the units digit. The product of its digits is \(t \times u\). According to the problem statement, the number is three times the product of its digits.
So, we can write the equation:
\[ 10t + u = 3 \times (t \times u) \]Correct Option: C) 24
The question asks about the ownership of the IPL team 'Kolkata Knight Riders' as of February 2018. This is a general knowledge question related to sports and entertainment, specifically the Indian Premier League (IPL).
Correct Option: D) Shah Rukh Khan is the principal owner of the Kolkata Knight Riders through his company Red Chillies Entertainment, in partnership with Juhi Chawla and Jay Mehta. This ownership structure was in place in February 2018 and continues to be so.
Consider the given question and decide which of the following statements is/are sufficient to answer the question.
Is X – 5 even? X is a real number.
Statements:
1. X – 15 belongs to integer
2. X – 10 is an odd integer
Statement 1 alone is sufficient while statement 2 alone is insufficient
Neither statement 1 nor 2 is sufficient
Statement 2 alone is sufficient while statement 1 alone is insufficient
Both statements 1 and 2 are sufficient
The question asks whether \(X - 5\) is an even number, where \(X\) is a real number. We need to evaluate if each statement alone or both statements together are sufficient to answer this question. We will analyze each statement independently.
Let \(X - 15 = K\), where \(K\) is an integer.
Then \(X = K + 15\).
We need to find if \(X - 5\) is even. Substitute the value of \(X\):
\[ X - 5 = (K + 15) - 5 = K + 10 \]Since \(K\) is an integer, \(K + 10\) is also an integer. However, we don't know if \(K + 10\) is even or odd. For example:
Since \(X - 5\) can be either even or odd, Statement 1 alone is not sufficient to answer the question.
Let \(X - 10 = M\), where \(M\) is an odd integer.
An odd integer can be represented as \(2n + 1\) for some integer \(n\).
So, \(X - 10 = 2n + 1\).
We need to find if \(X - 5\) is even. We can rewrite \(X - 5\) in terms of \(X - 10\):
\[ X - 5 = (X - 10) + 5 \]Substitute \(X - 10 = 2n + 1\):
\[ X - 5 = (2n + 1) + 5 = 2n + 6 \]We can factor out 2 from \(2n + 6\):
\[ 2n + 6 = 2(n + 3) \]Since \(n\) is an integer, \(n + 3\) is also an integer. Therefore, \(2(n + 3)\) is always an even integer.
Thus, \(X - 5\) is always an even integer. Statement 2 alone is sufficient to answer the question.
C) Statement 2 alone is sufficient while statement 1 alone is insufficient.
The question asks about the specific legislation that led to the partition of British India into two independent nations: India and Pakistan. This is a direct historical fact related to the end of British rule in India.
Correct Option: D) Indian Independence Act 1947
This is a statement and conclusion type of question. We need to assume the given statement to be true and then determine which of the conclusions logically follow from the information provided in the statement. The conclusions must be directly inferable from the statement, without introducing outside information or making assumptions.
B) Only conclusion 1 follows.
To find the square root of a number, we can use a few methods: prime factorization, long division, or by estimating and checking the last digit. Given the options, estimation and checking the last digit is an efficient method.
A) \(124\) is the square root of \(15376\) because \(124 \times 124 = 15376\).
Select the option that depicts the correct mirror image of the given word when the mirror is placed horizontally below the word.
HEALTHY
To find the mirror image of a word when the mirror is placed horizontally below it, each letter in the word needs to be flipped vertically. This means the top part of each letter will become the bottom part in the mirror image.
Correct Option: D) HE∀β⊥HΚ
To determine which assumption is implicit, we need to identify what must be true for the statement to make sense or be a logical directive. An implicit assumption is something taken for granted or presupposed by the statement.
Correct Option: D) Only assumption (I) is implicit.
The statement implies that there is a positive outcome or benefit from attending workshops. Assumption (I) provides this positive outcome (updating teachers), making it a necessary underlying belief for the statement to be made. Assumption (II) suggests a negative outcome, which would contradict the purpose of mandating attendance.
This question tests the understanding of current behavior in a series circuit. In a series circuit, components are connected end-to-end, forming a single path for the current. According to Kirchhoff's Current Law, the current is the same at every point in a series circuit.
Correct Option: B) remains the same. In a series circuit, the current has only one path to flow, so the current is identical through every component connected in series.
A convex mirror of focal length f (in air) is immersed in a liquid (μ = \( \frac{4}{3} \)). The focal length of the mirror in liquid will be:
\( \frac{7}{3} \)f
f
\( \frac{4}{3} \)f
\( \frac{3}{4} \)f
The focal length of a mirror depends only on its radius of curvature, which is a physical property of the mirror itself. It does not depend on the medium in which it is placed. This is different from lenses, whose focal length changes with the surrounding medium's refractive index.
B) f β The focal length of a mirror depends only on its radius of curvature, which is an intrinsic property of the mirror and does not change when the mirror is immersed in a different medium. The refractive index of the surrounding medium does not affect the reflection of light from a mirror surface.
