New Exam Prep
Full explanation, worked examples & memory tricks in the app
New Exam Prep
English 17 leveled MCQs Free
Shared by a Veda learner · Generated with Veda AI
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What you'll study, topic by topic
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Sample questions with model answers
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10 marks Long answer
Solve the following linear programming problem graphically : Maximize $Z = 10500x + 9000y$ Subject to constraints $x+y \le 50$, $2x+y \le 80$, $x, y \ge 0$
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Graph the constraints and find the optimal solution.
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10 marks Long answer
A rectangle of perimeter 36 cm is revolved around one of its sides to sweep out a cylinder of maximum volume.
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Use optimization to find dimensions for maximum volume.
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7 marks Long answer
If the volume of a solid hemisphere increases at a uniform rate, prove that its surface area varies inversely as its radius.
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Surface area $A = 2\pi r^2$ varies inversely with volume $V = \frac{2}{3}\pi r^3$.
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7 marks Long answer
Find : $\int \frac{x+2}{\sqrt{9x-x^2}} dx$
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Use substitution to solve the integral.
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7 marks Long answer
Evaluate : $\int_{\frac{\pi}{12}}^{\frac{5\pi}{12}} \frac{dx}{1+\sqrt{\cot x}}$
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Evaluate using trigonometric identities.
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7 marks Long answer
Evaluate : $\int_{-\frac{\pi}{6}}^{\frac{\pi}{2}} (\sin |x| + \cos |x|) dx$
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Calculate the integral considering the absolute values.
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7 marks Long answer
Find the sub intervals in which $f(x) = \cot^{-1} (\sin x + \cos x), x \in (0, \pi)$ is increasing and decreasing.
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Analyze the derivative of the function.
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4 marks Medium answer
Check whether $f: R - \{3\} \to R$ defined as $f(x) = \frac{x-2}{x-3}$ is onto or not.
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The function is not onto.
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4 marks Medium answer
Check whether $f: Z \times Z \to Z \times Z$ (where Z is the set of integers) defined as $f(x, y) = (2y, 3x)$ is injective or not.
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The function is injective.
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4 marks Medium answer
If $x = a \sin^3 t, y = b \cos^3 t$, then find $\frac{dy}{dx}$ at $t = \frac{\pi}{4}$.
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$\frac{dy}{dx} = -\frac{3b}{3a} = -\frac{b}{a}$.
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4 marks Medium answer
Find the absolute maximum value of $f(x) = \cos x + \sin^2 x, x \in [0, \pi]$.
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The absolute maximum value is 1.
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1 marks Short answer
A relation R on set $A = \{1, 2, 3\}$ defined as $R = \{(1, 1), (2, 2), (1, 2)\}$ is
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Reflexive only
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1 marks Short answer
If $e^{-x} + e^{-y} = 2$, then $\frac{dy}{dx}$ is
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$-e^{y-x}$
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1 marks Short answer
For $f(x) = x + \frac{1}{x}$ ($x \neq 0$)
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local maximum value is 2
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1 marks Short answer
If $\int_{0}^{2a} \frac{1}{1+4x^2} dx = \frac{\pi}{6}$, then the value of a is
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$\frac{\sqrt{3}}{4}$
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1 marks Short answer
In a linear programming problem, the linear function which has to be maximized or minimized is called
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an objective function
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1 marks Short answer
For the feasible region shown below, the non-trivial constraints of the linear programming problem are
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$x+y \le 5, x+3y \le 9$
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