The selling price of 20 books is equal to the cost price of 6 books. Find the loss or gain percentage.
70% gain
\( \frac{50}{7} \)% gain
\( \frac{50}{7} \)% loss
70% loss
To find the loss or gain percentage, we need to establish a relationship between the selling price (SP) and the cost price (CP) of a single book. We are given a relationship between the SP of 20 books and the CP of 6 books. We will use this to find the CP and SP of one book, or the total CP and SP for a certain number of books, and then calculate the percentage.
Let the Cost Price (CP) of one book be \(CP\).
Let the Selling Price (SP) of one book be \(SP\).
According to the problem statement, the selling price of 20 books is equal to the cost price of 6 books.
This can be written as:
\[ 20 \times SP = 6 \times CP \]Now, we can find the ratio of SP to CP:
\[ \frac{SP}{CP} = \frac{6}{20} = \frac{3}{10} \]From this ratio, we can infer that if the Cost Price (CP) is 10 units, the Selling Price (SP) is 3 units. Since \(SP < CP\), there is a loss.
Calculate the loss amount:
\[ \text{Loss} = CP - SP = 10 - 3 = 7 \text{ units} \]Calculate the loss percentage. The loss percentage is always calculated on the Cost Price (CP).
\[ \text{Loss Percentage} = \frac{\text{Loss}}{CP} \times 100\% \]\[ \text{Loss Percentage} = \frac{7}{10} \times 100\% \]\[ \text{Loss Percentage} = 7 \times 10\% \]\[ \text{Loss Percentage} = 70\% \]Correct Option: D) 70% loss
The question asks to identify an input device that translates physical, real-world movements into digital signals for navigation and object manipulation in a graphical environment. We need to evaluate each option based on its primary function and how it interacts with a computer system.
Correct Option: C) Mouse
A mouse is specifically designed to translate the user's physical hand movements across a surface into corresponding movements of a cursor or pointer on a computer screen. This allows for intuitive navigation, selection, and manipulation of graphical elements in a digital environment.
First, we need to find the side length of a single cube using its given volume. Then, when five such cubes are joined end to end, they form a cuboid. We need to determine the dimensions (length, breadth, height) of this resulting cuboid. Finally, we will calculate the lateral surface area of this cuboid using the formula \(2h(l+b)\).
Find the side length of one cube:
The volume of a cube is given by \(V = a^3\), where \(a\) is the side length.
Given volume \(V = 1,09,41,048 \text{ cm}^3\).
\[ a^3 = 10941048 \]To find \(a\), we need to calculate the cube root of \(10941048\).
We can estimate the cube root. \(200^3 = 8,000,000\) and \(300^3 = 27,000,000\). So, \(a\) is between 200 and 300. The last digit of \(10941048\) is 8, so the last digit of its cube root must be 2 (since \(2^3 = 8\)). Let's try \(222\).
\[ 222^3 = 222 \times 222 \times 222 = 49284 \times 222 = 10941048 \]So, the side length of one cube is \(a = 222 \text{ cm}\).
Determine the dimensions of the cuboid:
When five cubes are joined end to end, the length of the cuboid will be five times the side length of one cube. The breadth and height will remain the same as the side length of one cube.
Calculate the lateral surface area of the cuboid:
The lateral surface area (LSA) of a cuboid is given by the formula \(2H(L+B)\).
\[ \text{LSA} = 2 \times 222 \times (1110 + 222) \] \[ \text{LSA} = 444 \times (1332) \] \[ \text{LSA} = 591408 \text{ cm}^2 \]Correct Option: A) 5,91,408
Find the roots of \( x^{-4} - 10x^{-2} + 9 = 0 \).
±1, ±\( \frac{1}{4} \)
±1, ±\( \frac{2}{3} \)
±1, ±\( \frac{1}{5} \)
±1, ±\( \frac{1}{3} \)
The given equation is a reciprocal equation involving negative powers of \(x\). We can simplify it by making a substitution to transform it into a standard quadratic equation. Once the quadratic equation is solved, we can find the values of \(x\).
The given equation is:
\[ x^{-4} - 10x^{-2} + 9 = 0 \]We can rewrite \(x^{-4}\) as \((x^{-2})^2\). So the equation becomes:
\[ (x^{-2})^2 - 10x^{-2} + 9 = 0 \]Let \(y = x^{-2}\). Substitute \(y\) into the equation:
\[ y^2 - 10y + 9 = 0 \]This is a quadratic equation in terms of \(y\). We can solve it by factoring. We need two numbers that multiply to 9 and add up to -10. These numbers are -1 and -9.
\[ (y - 1)(y - 9) = 0 \]This gives us two possible values for \(y\):
\[ y - 1 = 0 \implies y = 1 \]\[ y - 9 = 0 \implies y = 9 \]Now, substitute back \(y = x^{-2}\) to find the values of \(x\).
Case 1: \(y = 1\)
\[ x^{-2} = 1 \]\[ \frac{1}{x^2} = 1 \]\[ x^2 = 1 \]\[ x = \pm\sqrt{1} \]\[ x = \pm 1 \]Case 2: \(y = 9\)
\[ x^{-2} = 9 \]\[ \frac{1}{x^2} = 9 \]\[ x^2 = \frac{1}{9} \]\[ x = \pm\sqrt{\frac{1}{9}} \]\[ x = \pm \frac{1}{3} \]Thus, the roots of the equation are \( \pm 1 \) and \( \pm \frac{1}{3} \).
D) ±1, ±\( \frac{1}{3} \)
The question asks about the location where ISRO conducted the hot test of a semi-cryogenic engine in 2025. This requires knowledge of ISRO's various facilities and their specific functions, particularly for engine testing.
Correct Option: A) ISRO Propulsion Complex, Mahendragiri, Tamil Nadu is the correct answer. The ISRO Propulsion Complex (IPRC) at Mahendragiri is ISRO's dedicated center for the testing of liquid, cryogenic, and semi-cryogenic rocket engines and stages. It has the necessary infrastructure and test stands for conducting hot tests of such advanced propulsion systems.
The problem presents an analogy between letter-clusters. We need to identify the pattern or relationship between the first pair of letter-clusters and apply the same logic to the second pair to find the missing clusters.
If \(\sqrt{3}\) tanA = 3 sinA, find the value of (2\(\sqrt{3}\) cosecA × tanA).
The problem requires us to find the value of an expression involving trigonometric ratios, given a relationship between \(\tan A\) and \(\sin A\). We will first use the given equation to find the value of \(\cos A\), and then use this to determine the angle \(A\). Finally, we will substitute the value of \(A\) into the expression to be evaluated.
Simplify the given equation:
We are given the equation \(\sqrt{3} \tan A = 3 \sin A\).
We know that \(\tan A = \frac{\sin A}{\cos A}\). Substitute this into the equation:
\[ \sqrt{3} \frac{\sin A}{\cos A} = 3 \sin A \]Solve for \(\cos A\):
Assuming \(\sin A \neq 0\) (if \(\sin A = 0\), then \(\tan A = 0\), and the expression to evaluate would be undefined or trivial, so we assume a non-zero angle), we can divide both sides by \(\sin A\):
\[ \frac{\sqrt{3}}{\cos A} = 3 \]\[ \cos A = \frac{\sqrt{3}}{3} \]\[ \cos A = \frac{\sqrt{3}}{\sqrt{3} \times \sqrt{3}} \]\[ \cos A = \frac{1}{\sqrt{3}} \]Find the value of \(\sin A\):
We use the identity \(\sin^2 A + \cos^2 A = 1\).
\[ \sin^2 A = 1 - \cos^2 A \]\[ \sin^2 A = 1 - \left(\frac{1}{\sqrt{3}}\right)^2 \]\[ \sin^2 A = 1 - \frac{1}{3} \]\[ \sin^2 A = \frac{3-1}{3} \]\[ \sin^2 A = \frac{2}{3} \]\[ \sin A = \sqrt{\frac{2}{3}} = \frac{\sqrt{2}}{\sqrt{3}} \]Evaluate the expression \((2\sqrt{3} \text{cosec} A \times \tan A)\):
We know that \(\text{cosec} A = \frac{1}{\sin A}\) and \(\tan A = \frac{\sin A}{\cos A}\).
Substitute these into the expression:
\[ 2\sqrt{3} \times \frac{1}{\sin A} \times \frac{\sin A}{\cos A} \]Simplify the expression:
The \(\sin A\) terms cancel out:
\[ 2\sqrt{3} \times \frac{1}{\cos A} \]Substitute the value of \(\cos A\):
We found \(\cos A = \frac{1}{\sqrt{3}}\). So, \(\frac{1}{\cos A} = \sqrt{3}\).
\[ 2\sqrt{3} \times \sqrt{3} \]\[ 2 \times (\sqrt{3})^2 \]\[ 2 \times 3 \]\[ 6 \]A) The calculated value of the expression is 6.
The question asks to identify the title of Sarojini Naidu's first collection of poems, published in 1905. This requires specific knowledge of her literary works and their publication dates.
Sarojini Naidu's first volume of poetry, which brought her significant recognition, was indeed titled The Golden Threshold and was published in 1905.
B) The Golden Threshold is the correct answer. This was Sarojini Naidu's debut collection of poems, published in 1905, and it established her as a prominent poet.
The question asks about the initial focus regions of the Green Revolution in India. To answer this, we need to recall the historical context and geographical implementation of this agricultural strategy.
B) Punjab and Haryana were indeed the primary focus regions for the initial implementation of the Green Revolution due to their conducive agricultural conditions and existing infrastructure, leading to remarkable success in increasing food grain production.
The question asks for the full form of the acronym CPU in the context of computer systems. This is a fundamental concept in computer hardware.
Correct Option: C) Central Processing Unit
The CPU, or Central Processing Unit, is often referred to as the "brain" of the computer. It is responsible for carrying out the instructions of a computer program by performing the basic arithmetic, logic, controlling, and input/output (I/O) operations specified by the instructions.