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Questions and Answers
What is the area of the region bounded by the curve $y^2 = 4x$, the y-axis, and the line $y=3$?
What is the area of the region bounded by the curve $y^2 = 4x$, the y-axis, and the line $y=3$?
The probability of obtaining an even prime number on each die when rolling a pair of dice is 0.
The probability of obtaining an even prime number on each die when rolling a pair of dice is 0.
True
If P(A) = 0.8, P(B) = 0.5, and P(A) = 0.4, what is P(A∩B)?
If P(A) = 0.8, P(B) = 0.5, and P(A) = 0.4, what is P(A∩B)?
0.32
The probability of getting a total of 5 when rolling two dice is ______.
The probability of getting a total of 5 when rolling two dice is ______.
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Match the following probabilities with their corresponding scenarios:
Match the following probabilities with their corresponding scenarios:
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If the function $f(x) = 5x - 4$, what is the value of $f^{-1}(6)$?
If the function $f(x) = 5x - 4$, what is the value of $f^{-1}(6)$?
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In the given function $f: R → R$, the inverse function can have two different outputs for the same input.
In the given function $f: R → R$, the inverse function can have two different outputs for the same input.
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What is the general format of the marks distribution table for Section A?
What is the general format of the marks distribution table for Section A?
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If cot $^{-1} x + tan^{-1} (3) = rac{ ext{___}}{4}$, find the value of x.
If cot $^{-1} x + tan^{-1} (3) = rac{ ext{___}}{4}$, find the value of x.
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What is the total number of marks allocated for the long answer questions in Section D?
What is the total number of marks allocated for the long answer questions in Section D?
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Match the following sections with their respective types of questions:
Match the following sections with their respective types of questions:
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What is the total number of questions in Section A?
What is the total number of questions in Section A?
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Candidates have the option to not write their Roll Number on the question paper.
Candidates have the option to not write their Roll Number on the question paper.
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If the matrix determinant | 2 k | = 4, what is the value of k?
If the matrix determinant | 2 k | = 4, what is the value of k?
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The value of a in the equation [ k+4 3 ] = [ -1 3 ] is 3.
The value of a in the equation [ k+4 3 ] = [ -1 3 ] is 3.
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What is the rate of increase of the circumference of a circle when its radius is increasing at 0.7 cm/s and r = 4.9 cm?
What is the rate of increase of the circumference of a circle when its radius is increasing at 0.7 cm/s and r = 4.9 cm?
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The equation y = √(sec(x)-1)/(sec(x)+1) implies that dy/dx is equal to __________.
The equation y = √(sec(x)-1)/(sec(x)+1) implies that dy/dx is equal to __________.
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If y = √(sec x - 1) / (sec x + 1), what is the derivative, dy/dx?
If y = √(sec x - 1) / (sec x + 1), what is the derivative, dy/dx?
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Match the expressions to their correct values:
Match the expressions to their correct values:
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The equation given by [ k + 4 3 ] = [ -1 3 ] denotes an incorrect determinant condition.
The equation given by [ k + 4 3 ] = [ -1 3 ] denotes an incorrect determinant condition.
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For the values given: k + 4 = -1, what is the value of k?
For the values given: k + 4 = -1, what is the value of k?
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What is the solution for the equation $|4x + 6| = 0$?
What is the solution for the equation $|4x + 6| = 0$?
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The determinant of the matrix $|5 , 0 , 0|$ is equal to 0.
The determinant of the matrix $|5 , 0 , 0|$ is equal to 0.
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What is the interval in which the function $f(x) = ext{sin} , x - ext{cos} , x$ is increasing for $x , ext{in} , (0, , ext{π})$?
What is the interval in which the function $f(x) = ext{sin} , x - ext{cos} , x$ is increasing for $x , ext{in} , (0, , ext{π})$?
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The value of $ rac{dy}{dx}$ for the curve $y = x^3 - x + 1$ at $x = 2$ is __________.
The value of $ rac{dy}{dx}$ for the curve $y = x^3 - x + 1$ at $x = 2$ is __________.
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Match the following integrals with their results:
Match the following integrals with their results:
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What is the general solution of the differential equation $ rac{dy}{dx} = rac{1}{1+x^2}$?
What is the general solution of the differential equation $ rac{dy}{dx} = rac{1}{1+x^2}$?
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What is the result of the vector product $ extbf{a} imes extbf{b}$ if $ extbf{a} = 2 extbf{i} + extbf{j} + 3 extbf{k}$ and $ extbf{b} = 3 extbf{i} + 5 extbf{j} - 2 extbf{k}$?
What is the result of the vector product $ extbf{a} imes extbf{b}$ if $ extbf{a} = 2 extbf{i} + extbf{j} + 3 extbf{k}$ and $ extbf{b} = 3 extbf{i} + 5 extbf{j} - 2 extbf{k}$?
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The expression $(3 extbf{a} - 5 extbf{b}) ullet (2 extbf{a} + 7 extbf{b})$ can be evaluated to give a scalar value.
The expression $(3 extbf{a} - 5 extbf{b}) ullet (2 extbf{a} + 7 extbf{b})$ can be evaluated to give a scalar value.
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For the function $f(x) = \begin{cases} \frac{1 - \cos(cx)}{x} & x \neq 0 \ \frac{1}{2} & x = 0 \end{cases}$ to be continuous at $x = 0$, what is the value of $c$?
For the function $f(x) = \begin{cases} \frac{1 - \cos(cx)}{x} & x \neq 0 \ \frac{1}{2} & x = 0 \end{cases}$ to be continuous at $x = 0$, what is the value of $c$?
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The function $f(x) = |x| + |x - 1|$ is continuous at both $x = 0$ and $x = 1$.
The function $f(x) = |x| + |x - 1|$ is continuous at both $x = 0$ and $x = 1$.
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Find the derivative of $y = \tan^{-1}(\tan x + \sec x)$ with respect to $x$.
Find the derivative of $y = \tan^{-1}(\tan x + \sec x)$ with respect to $x$.
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The area enclosed by the curve $x^2 + y^2 = a^2$ is given by $\text{Area} = \pi ______^2.
The area enclosed by the curve $x^2 + y^2 = a^2$ is given by $\text{Area} = \pi ______^2.
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Match the following expressions with their descriptions:
Match the following expressions with their descriptions:
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Which interval describes where the function $f(x) = x^2 - 6x + 5$ is decreasing?
Which interval describes where the function $f(x) = x^2 - 6x + 5$ is decreasing?
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The integral of $(\sin x + \cos x)^2$ is a straightforward calculation without any simplifications needed.
The integral of $(\sin x + \cos x)^2$ is a straightforward calculation without any simplifications needed.
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If $a$, $b$, and $c$ are unit vectors such that $a + b + c = 0$, calculate $a.b + b.c + c.a$.
If $a$, $b$, and $c$ are unit vectors such that $a + b + c = 0$, calculate $a.b + b.c + c.a$.
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At what rate is the volume of a spherical balloon increasing when its radius is 6 cm, given that the radius is increasing at the rate of 2 cm/s?
At what rate is the volume of a spherical balloon increasing when its radius is 6 cm, given that the radius is increasing at the rate of 2 cm/s?
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The equation of a plane can be determined from the intersection of two given planes.
The equation of a plane can be determined from the intersection of two given planes.
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What is the general form of the equation of a plane?
What is the general form of the equation of a plane?
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The integral of $ rac{x ext{ sin} x}{1 + ext{cos}^2 x}$ from 0 to $ rac{ ext{oldsymbol{
u}}}{ ext{U}}$ can be evaluated as $ ext{__________}$
The integral of $ rac{x ext{ sin} x}{1 + ext{cos}^2 x}$ from 0 to $ rac{ ext{oldsymbol{ u}}}{ ext{U}}$ can be evaluated as $ ext{__________}$
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The goal of linear programming is to minimize the value of the objective function.
The goal of linear programming is to minimize the value of the objective function.
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Match the given equations with their probable geometric representation:
Match the given equations with their probable geometric representation:
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What technique is commonly used to solve linear programming problems graphically?
What technique is commonly used to solve linear programming problems graphically?
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Study Notes
Instructions for the Exam
- Roll number: Write your roll number on the question paper.
- All questions: All questions are mandatory.
- Language: If there is a discrepancy between Hindi and English versions, the Hindi version is definitive.
- Internal questions: Answer parts of a question together if it has multiple components.
Marks Distribution
- Section A: Multiple Choice Questions (MCQs), Fill-in-the-blanks, and Very Short Answer (VSA) questions.
- Section B: Short Answer (SA-1) questions.
- Section C: Short Answer (SA-2) questions.
- Section D: Long Answer (LA) questions, with internal choices.
Question 1 (Section A)
- Part (i): Find f⁻¹(6) given f(x) = 5x - 4.
- Part (ii):
- Find x if cot⁻¹x + tan⁻¹(1- √3/2) = π/4.
- Find a if [√46] = [√3-1/√4].
Additional Information
- Questions 18, 19, and 20 have internal choices. Choose only one alternative for each.
Remaining Questions (Specific Details Missing)
- The document lists additional question types (e.g., those requiring the evaluation or solution of equations, integrals, or geometrical problems) but lacks the specific details.
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Description
This quiz provides essential instructions for the mathematics exam along with sample questions from various sections including MCQs, short answer, and long answer questions. It also emphasizes the importance of noting the language discrepancy and internal choices for specific questions.
