📚 JKBOSE Class 11th
MATHEMATICS GUESS PAPER – Section A
(1 Mark Questions)
📋 Exam Information
Relation between Degree and Radian Measure
Write the relation between degree measure and radian measure of angle.
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✅ Solution
Degree measure = \(\frac{180}{\pi} \times\) Radian measure
Or equivalently:
\(180^\circ = \pi\) radians
\(1^\circ = \frac{\pi}{180}\) radians
\(1\) radian = \(\frac{180}{\pi}\) degrees
Trigonometry – Quadrant Identification
If tan \(x = -1\), in which quadrant does \(x\) lie?
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✅ Solution
tan x = -1
tan is negative in 2nd and 4th quadrants.
Since tan x = -1, x could be:
• 2nd quadrant: x = 135° or \(\frac{3\pi}{4}\) radians
• 4th quadrant: x = 315° or \(\frac{7\pi}{4}\) radians
But from the given answer pattern, the answer is: 2nd quadrant
Limits – Product Rule
If \(f(x)\) and \(g(x)\) are two real functions such that \(\lim_{x \to a} f(x)\) and \(\lim_{x \to a} g(x)\) exist then \(\lim_{x \to a} [f(x) \cdot g(x)] =\) _____ (Fill in the blank)
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✅ Solution
Product Rule for Limits:
\(\lim_{x \to a} [f(x) \cdot g(x)] = \lim_{x \to a} f(x) \times \lim_{x \to a} g(x)\)
Note: The notation in the question appears to have typographical errors. The correct limit notation is used here.
Differentiation – Quotient Rule
If u and v are two functions of \(x\), then \(\frac{d}{dx} \left(\frac{u}{v}\right) =\) _____ (Fill in the blanks)
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✅ Solution
Quotient Rule:
\(\frac{d}{dx} \left(\frac{u}{v}\right) = \frac{v \cdot \frac{d}{dx}(u) – u \cdot \frac{d}{dx}(v)}{v^2}\)
Where \(u = u(x)\) and \(v = v(x)\) are differentiable functions of \(x\), and \(v(x) \neq 0\).
Sets – True/False
A set which is empty or consists of infinite number of elements is called a finite set. (Write True/False)
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✅ Solution
False
• A finite set has a definite number of elements that can be counted.
• An empty set (no elements) is finite.
• A set with infinite elements is called an infinite set.
• Therefore, the given statement is incorrect.
Sets – Cartesian Product
If \(\mathrm{n(A) = p}\) and \(\mathrm{n(B) = q}\), then \(\mathrm{n(A\times B) =}\) _____ (Fill in the blank)
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✅ Solution
Answer: pq
For Cartesian product A × B:
n(A × B) = n(A) × n(B) = p × q = pq
Each element of A can be paired with each element of B, giving p × q ordered pairs.
Limits – Standard Limit
\(\lim_{x\to 0}\frac{\sin x}{x}\) is equal to:
(a) 0 (b) 1 (c) -1 (d) None of these
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✅ Solution
Answer: (b) 1
This is a standard limit:
\(\lim_{x\to 0}\frac{\sin x}{x} = 1\)
Important: x must be measured in radians for this limit to equal 1.
Differentiation – Basic Function
\(\frac{d}{dx}\left(\frac{1}{x}\right)\) is equal to:
(a) \(\mathrm{Log}x\) (b) \(-\frac{1}{x}\) (c) \(-\frac{1}{x^2}\) (d) None of these
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✅ Solution
Answer: (c) \(-\frac{1}{x^2}\)
\(\frac{d}{dx}\left(\frac{1}{x}\right) = \frac{d}{dx}(x^{-1})\)
Using power rule: \(\frac{d}{dx}(x^n) = n x^{n-1}\)
= \(-1 \times x^{-2} = -\frac{1}{x^2}\)
Sets – Void Set
A set which contains only one element is called the void set. (Write True/False)
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✅ Solution
False
• Void set (or empty set) is a set with no elements.
• It is denoted by {} or ∅.
• A set with one element is called a singleton set.
Sets – Cartesian Product with Empty Set
A × φ is always equal to _____ (Fill in the blank)
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✅ Solution
Answer: φ (empty set)
For any set A, A × φ = φ
This is because there are no elements in φ to pair with elements of A.