The question asks to identify the Indian company that acquired the British toy retailer Hamleys. This is a factual question related to business acquisitions and general knowledge, often covered in current affairs sections of competitive exams.
In 2019, Reliance Brands Ltd., a subsidiary of Reliance Retail which is part of the Reliance Industries Limited conglomerate, acquired Hamleys Global Holdings Ltd. for approximately £67.96 million (around Rs 620 crore) in an all-cash deal. This acquisition gave Reliance Brands control over the iconic toy brand's global operations.
A) Reliance Brands — Reliance Brands Limited, a subsidiary of Reliance Retail, successfully acquired Hamleys in 2019, making it the correct answer.
Select the option that will replace the question mark (?) in the given equation.
? + \( \frac{18}{24} \) + 3 \( \frac{3}{4} \) = 23 \( \frac{13}{24} \)
0
19 \( \frac{1}{24} \)
1
19 \( \frac{13}{24} \)
To solve this problem, we need to find the value of the question mark (?). This involves isolating the unknown variable by performing arithmetic operations on fractions and mixed numbers. We will convert all mixed numbers to improper fractions or decimal form, then combine the known terms, and finally subtract their sum from the total to find the missing value.
Let the question mark be represented by \(X\). The given equation is:
\[ X + \frac{18}{24} + 3 \frac{3}{4} = 23 \frac{13}{24} \]Simplify the fraction \( \frac{18}{24} \) by dividing both numerator and denominator by their greatest common divisor, which is 6:
\[ \frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \]Convert the mixed numbers to improper fractions:
Substitute the simplified fraction and improper fractions back into the equation:
\[ X + \frac{3}{4} + \frac{15}{4} = \frac{565}{24} \]Combine the fractions on the left side of the equation:
\[ X + \left( \frac{3}{4} + \frac{15}{4} \right) = \frac{565}{24} \] \[ X + \frac{3 + 15}{4} = \frac{565}{24} \] \[ X + \frac{18}{4} = \frac{565}{24} \]Simplify \( \frac{18}{4} \) by dividing both numerator and denominator by 2:
\[ \frac{18}{4} = \frac{9}{2} \]The equation becomes:
\[ X + \frac{9}{2} = \frac{565}{24} \]To find \(X\), subtract \( \frac{9}{2} \) from \( \frac{565}{24} \). First, find a common denominator, which is 24.
\[ \frac{9}{2} = \frac{9 \times 12}{2 \times 12} = \frac{108}{24} \]Now, perform the subtraction:
\[ X = \frac{565}{24} - \frac{108}{24} \] \[ X = \frac{565 - 108}{24} \] \[ X = \frac{457}{24} \]Convert the improper fraction \( \frac{457}{24} \) back to a mixed number. Divide 457 by 24:
So, \( X = 19 \frac{1}{24} \).
Correct Option: B) 19 \( \frac{1}{24} \)
This problem involves trigonometry, specifically the concept of the angle of elevation. We can model the pole, its shadow, and the line of sight from the tip of the shadow to the top of the pole as a right-angled triangle. The angle of elevation of the sun is one of the acute angles in this triangle.
Visualize the scenario: Imagine a pole standing vertically on the ground. The sun casts a shadow of the pole on the ground. The pole, its shadow, and the line connecting the top of the pole to the end of the shadow form a right-angled triangle.
Define variables:
Formulate the relationship: In the right-angled triangle, the height of the pole (\(h\)) is the side opposite to the angle of elevation (\(\theta\)), and the length of the shadow (\(s\)) is the side adjacent to the angle of elevation (\(\theta\)). The trigonometric ratio that relates the opposite and adjacent sides is the tangent function:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{s} \]Apply the given condition: The problem states that the length of the shadow of the pole is equal to its height. So, \(s = h\).
Substitute into the equation: Substitute \(s = h\) into the tangent equation:
\[ \tan(\theta) = \frac{h}{h} \]\[ \tan(\theta) = 1 \]Find the angle: We need to find the angle \(\theta\) whose tangent is 1. We know that \(\tan(45^{\circ}) = 1\).
\[ \theta = \arctan(1) \]\[ \theta = 45^{\circ} \]Therefore, the angle of elevation of the sun is 45°.
D) 45° — As derived, when the height of the pole is equal to the length of its shadow, the tangent of the angle of elevation is 1, which corresponds to an angle of 45°.
Simplify:
(13 + 23 + 33 + ... + 83)-5⁄2
The problem requires simplifying an expression involving the sum of cubes and an exponent. The key is to recognize the formula for the sum of the first 'n' cubes and then apply the rules of exponents.
Correct Option: B) \( 6^{-10} \)
This is a coding-decoding question. We need to identify the pattern used to assign numerical values to letters and then apply that pattern to find the value for "CARE". The pattern usually involves the alphabetical position of the letters.
Correct Option: B) 359
The question asks to identify the government program among the given options that specifically aims at creating self-employment opportunities. To answer this, we need to know the full forms and primary objectives of each program listed.
D) PMRY — The Pradhan Mantri Rozgar Yojana (PMRY) was specifically designed to create self-employment opportunities for educated unemployed youth and women by providing financial assistance for setting up micro-enterprises.
This problem involves trigonometric identities, specifically the complementary angle relationship between sine and cosine. We will use the identity \(\cos \theta = \sin (90^\circ - \theta)\) or \(\sin \theta = \cos (90^\circ - \theta)\) to convert one of the trigonometric functions so that both sides of the equation have the same function. Then, we can equate the angles and solve for the required expression.
Given the equation:
\[ \sin(3A - 20^\circ) = \cos(20^\circ - 3B) \]We know the complementary angle identity: \(\cos \theta = \sin (90^\circ - \theta)\). Let \(\theta = 20^\circ - 3B\).
Apply the identity to the right side of the equation:
\[ \cos(20^\circ - 3B) = \sin(90^\circ - (20^\circ - 3B)) \] \[ \cos(20^\circ - 3B) = \sin(90^\circ - 20^\circ + 3B) \] \[ \cos(20^\circ - 3B) = \sin(70^\circ + 3B) \]Substitute this back into the original equation:
\[ \sin(3A - 20^\circ) = \sin(70^\circ + 3B) \]Since the sine function is equal on both sides, their arguments (angles) must be equal (within the typical range for such problems, assuming acute angles or general solutions that lead to this specific relationship):
\[ 3A - 20^\circ = 70^\circ + 3B \]Rearrange the equation to find the value of \(A - B\):
\[ 3A - 3B = 70^\circ + 20^\circ \] \[ 3(A - B) = 90^\circ \] \[ A - B = \frac{90^\circ}{3} \] \[ A - B = 30^\circ \]Correct Option: A) 30°
The question asks to identify the state where the Pachmarhi Biosphere Reserve is located. This requires knowledge of the geographical distribution of India's biosphere reserves.
Correct Option: B) Madhya Pradesh
The Pachmarhi Biosphere Reserve is indeed located in the Hoshangabad, Betul, and Chhindwara districts of Madhya Pradesh. It was established in 1999 and includes the Bori Sanctuary, Pachmarhi Wildlife Sanctuary, and Satpura National Park.
To find the area of the greatest circle that can be inscribed inside a square, we first need to determine the relationship between the side of the square and the diameter of the inscribed circle. The diameter of the largest inscribed circle will be equal to the side length of the square. Once the diameter is known, we can find the radius and then calculate the area of the circle using the formula \(A = \pi r^2\).
Given, the side of the square is \(21 \text{ cm}\).
For the greatest circle that can be inscribed inside a square, its diameter will be equal to the side length of the square.
\[ \text{Diameter} (D) = \text{Side of the square} = 21 \text{ cm} \]The radius \(r\) is half of the diameter.
\[ r = \frac{D}{2} = \frac{21}{2} \text{ cm} = 10.5 \text{ cm} \]The area of a circle is given by the formula \(A = \pi r^2\). We will use the approximation \(\pi = \frac{22}{7}\).
\[ A = \pi r^2 = \frac{22}{7} \times \left(\frac{21}{2}\right)^2 \] \[ A = \frac{22}{7} \times \frac{21 \times 21}{2 \times 2} \] \[ A = \frac{22}{7} \times \frac{441}{4} \]Now, simplify the expression:
\[ A = \frac{22 \times 441}{7 \times 4} \] \[ A = \frac{11 \times 441}{7 \times 2} \quad (\text{dividing 22 by 2 and 4 by 2}) \] \[ A = \frac{11 \times 63}{2} \quad (\text{dividing 441 by 7, since } 441 = 7 \times 63) \] \[ A = \frac{693}{2} \] \[ A = 346.5 \text{ cm}^2 \]Correct Option: C) 346.5 cm²
To express one number as a percentage of another, we first form a fraction with the first number as the numerator and the second number as the denominator. Then, we multiply this fraction by 100 to convert it into a percentage.
Correct Option: B) 420%