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Mathematics
List of top Mathematics Questions
In triangle $ ABC $, if: $$ r_1 = 36,\quad r_2 = 18,\quad r_3 = 12 $$ then find the semi-perimeter $ s $.
AP EAPCET - 2022
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Mathematics
Trigonometry
Given: $$ \frac{2x^2 + 1}{x^3 - 1} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + x + 1} $$ Find the value of $ 7A + 2B + C $
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Mathematics
Algebra
Which of the following trigonometric values are negative?
I) $ \sin(-292^\circ) $
II) $ \tan(-193^\circ) $
III) $ \cos(-207^\circ) $
IV) $ \cot(-222^\circ) $
AP EAPCET - 2022
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Mathematics
Trigonometry
In an exam:
- Three subjects have maximum marks = $ n $ each
- Fourth subject has max marks = $ 2n $
- Find the number of ways to score total $ 3n $ marks.
AP EAPCET - 2022
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Mathematics
Combinatorics
Evaluate: $$ \frac{1}{\sin 1^\circ \sin 2^\circ} + \frac{1}{\sin 2^\circ \sin 3^\circ} + \cdots + \frac{1}{\sin 89^\circ \sin 90^\circ} $$
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Mathematics
Trigonometry
If $ \sin \theta = -\frac{3}{4} $, then compute $ \sin 2\theta $
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Mathematics
Trigonometry
Out of 205 students:
- 105 pass in English
- 70 pass in Mathematics
- 30 pass in both
How many students fail in both subjects?
AP EAPCET - 2022
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Mathematics
Set Theory
The sum of the real roots of the equation: $$ x^4 - 2x^3 + x - 380 = 0 $$ is:
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Mathematics
Polynomials
Solve: $$ 4^x - 3^{x - \frac{1}{2}} = 3^{x + \frac{1}{2}} - 2^{2x - 1} $$
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Mathematics
Exponents
There are 10 points in a plane, out of which 6 are collinear. If $ N $ is the number of triangles that can be formed, then $ N = $ ?
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Mathematics
Combinatorics
If $$ \sin^4 \theta \cos^2 \theta = \sum_{n=0}^{\infty} a_{2n} \cos 2n\theta $$ then the least value of $ n $ for which $ a_{2n} = 0 $ is:
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Mathematics
Trigonometry
If $$ ^{10}C_2 = ^{3^{n+1}}C_3 $$ then the value of $ n $ is:
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Mathematics
Combinatorics
If one root of the cubic equation: $$ x^3 + 36 = 7x^2 $$ is double of another, then the number of negative roots is:
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Mathematics
Polynomials
If $$ S = \left\{ m \in \mathbb{R} : x^2 - 2(1 + 3m)x + 7(3 + 2m) = 0 \text{ has distinct roots} \right\} $$ then the number of elements in $ S $ is:
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Mathematics
Quadratic Equations
By simplifying the expression: $$ i^{18} - 3i^7 + i^2(1 + i^4)(i^{22}) $$ we get:
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Mathematics
Complex numbers
Find the values of $ x $ for which the expressions $$ \sin x + i\cos 2x \quad \text{and} \quad \cos x - i\sin 2x $$ are conjugate to each other.
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Mathematics
Complex numbers
The locus of a point $ z $ satisfying: $$ |z|^2 = \text{Re}(z) $$ is a circle with centre:
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Mathematics
Complex numbers
Let $$ G(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix} $$ If $ x + y = 0 $, then evaluate $ G(x)G(y) $
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Mathematics
Matrices
If $f(x) = \begin{cases} \dfrac{x^2 \log(\cos x)}{\log(1+x)}, & x \neq 0 \\ 0, & x = 0 \end{cases}$, then at $x=0$, $f(x)$ is
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Mathematics
Calculus
Let $f(x) = \begin{cases} \dfrac{1}{|x|}, & |x|>1 \\ ax^2 + b, & |x| \leq 1 \end{cases}$. If $\lim_{x \to 1} f(x)$ and $\lim_{x \to -1} f(x)$ exist, then the possible values for $a$ and $b$ are
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Mathematics
Limits
Evaluate: \[ \int_{0}^{\pi/4} e^{\tan^2 \theta} \sin^2 \theta \tan \theta \, d\theta = \]
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Mathematics
Calculus
Evaluate: \( \int \frac{1 + \tan x \tan(x + \alpha)}{\tan x \tan(x + \alpha)} dx \):
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Mathematics
Calculus
If \( I_a = \int_0^{\pi/4} \tan^n x \, dx \), then \[ \frac{1}{I_2 + I_4} + \frac{1}{I_3 + I_5} + \frac{1}{I_4 + I_6} = \]
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Mathematics
Calculus
Evaluate: \[ \int_{\pi/4}^{5\pi/4} \left(\cos t |\sin t| + \sin t |\cos t|\right) dt = \]
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Mathematics
Calculus
If \( l \) and \( m \) are the order and degree of the differential equation of all the straight lines at constant distance \( P \) units from the origin, then \[ lm^2 + l^2 m = \]
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Mathematics
Differential Equations
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