To find the side length of a square when its area is given, we use the formula for the area of a square. The area of a square is calculated by squaring the length of its side. Therefore, to find the side, we need to take the square root of the given area.
Correct Option: A) 14 m is the correct answer because \(14 \times 14 = 196\).
This problem can be solved using the Remainder Theorem. The Remainder Theorem states that if a polynomial \(P(x)\) is divided by \(x - c\), the remainder is \(P(c)\). We will apply this theorem to both given conditions to form a system of two linear equations in terms of \(a\) and \(b\), and then solve for \(a\) and \(b\) to find \(a+b\).
Apply the Remainder Theorem to the first condition:
The polynomial is \(P(x) = x^2 + ax + b\). It is divided by \(x + 3\), which can be written as \(x - (-3)\). The remainder is \(-1\).
According to the Remainder Theorem, \(P(-3) = -1\).
Substitute \(x = -3\) into the polynomial:
\[ (-3)^2 + a(-3) + b = -1 \] \[ 9 - 3a + b = -1 \] \[ -3a + b = -1 - 9 \] \[ -3a + b = -10 \quad \text{(Equation 1)} \]Apply the Remainder Theorem to the second condition:
The polynomial is \(Q(x) = x^2 + bx + a\). It is divided by \(x - 3\). The remainder is \(39\).
According to the Remainder Theorem, \(Q(3) = 39\).
Substitute \(x = 3\) into the polynomial:
\[ (3)^2 + b(3) + a = 39 \] \[ 9 + 3b + a = 39 \] \[ a + 3b = 39 - 9 \] \[ a + 3b = 30 \quad \text{(Equation 2)} \]Solve the system of linear equations:
We have two equations:
1) \(-3a + b = -10\)
2) \(a + 3b = 30\)
From Equation 1, we can express \(b\) in terms of \(a\):
\[ b = 3a - 10 \]Substitute this expression for \(b\) into Equation 2:
\[ a + 3(3a - 10) = 30 \] \[ a + 9a - 30 = 30 \] \[ 10a = 30 + 30 \] \[ 10a = 60 \] \[ a = \frac{60}{10} \] \[ a = 6 \]Find the value of \(b\):
Substitute \(a = 6\) back into the expression for \(b\):
\[ b = 3a - 10 \] \[ b = 3(6) - 10 \] \[ b = 18 - 10 \] \[ b = 8 \]Calculate \(a + b\):
\[ a + b = 6 + 8 \] \[ a + b = 14 \]Correct Option: D) 14
The question asks about the winner of a specific sporting event, the 2017 Women's Hockey Asia Cup. To answer this, one needs to recall or know the results of major international sports tournaments, which is a common type of general knowledge question in competitive exams.
B) India — India won the 2017 Women's Hockey Asia Cup by defeating China in the final match.
The question asks about the relationship described by the first equation of motion. We need to recall the standard equations of motion for uniformly accelerated linear motion and identify which quantities are related by the first one.
Correct Option: C) velocity and time
Choose the correct figure to fill in the blank space.
The problem involves identifying the pattern in the given figures and selecting the correct option that completes the sequence.
Correct Option: B) The figure has a circle with a light background and dark shading, matching the pattern.
From a point on the ground, the angle of elevation of a tower was 30°. If the point was 75 m away from the tower, how tall was the tower?
(25\(\sqrt{3}\) + 7) m
25\(\sqrt{3}\) m
50 m
57 m
This problem involves trigonometry, specifically the concept of angles of elevation. We can model the situation as a right-angled triangle where the tower is the perpendicular side, the distance from the point to the tower is the base, and the angle of elevation is given. We need to find the height of the tower using the tangent function.
Correct Option: B) 25\(\sqrt{3}\) m
To find the mean proportional between two numbers, we use the concept of geometric mean. If \(a\), \(x\), and \(b\) are in continued proportion, then \(x\) is the mean proportional between \(a\) and \(b\). This means that the ratio of \(a\) to \(x\) is equal to the ratio of \(x\) to \(b\).
Correct Option: C) 14
The question asks to identify the Chief Secretary of the Delhi Government appointed in December 2017. This is a factual question related to appointments in the Indian bureaucracy.
Correct Option: B) Anshu Prakash was appointed as the Chief Secretary of the Delhi Government in December 2017. He is an IAS officer of the 1986 batch.
The question asks to identify the component that, when combined with kinetic energy, forms mechanical energy. This requires understanding the definition of mechanical energy in physics.
Correct Option: A) Potential energy is the correct answer because mechanical energy is defined as the sum of kinetic energy and potential energy.
This is a blood relation problem. We need to establish the relationships between the individuals mentioned in the statements and then determine U's relationship to V. We can use a family tree or symbolic representation to clarify the connections.
C) Sister — From the first two statements, V is the brother of U, and U is the sister of W. This directly implies that U is V's sister.