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AP EAPCET
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Mathematics
List of top Mathematics Questions asked in AP EAPCET
In a committee of 25 members, each member is proficient either in Mathematics or in Statistics or in both. If 19 of them are proficient in Mathematics and 16 of them are proficient in Statistics, then the probability that a person selected at random from the committee is proficient in both is
AP EAPCET - 2023
AP EAPCET
Mathematics
Probability
If \( \cos A + \cos(A + B) + \cos(A + 2B) + \cdots \) upto \( n \) terms \( = \cos \left( \frac{2A + (n-1)B}{2} \right) \frac{\sin \frac{nB}{2}}{\sin \frac{B}{2}} \), then \( \cos \frac{3\pi}{19} + \cos \frac{5\pi}{19} + \cos \frac{7\pi}{19} + \cdots + \cos \frac{17\pi}{19} = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Trigonometric Identities
If two angles \( \alpha, \beta \) are such that \( 0<\alpha, \beta<\frac{\pi}{4} \), \( \sqrt{1 + \cos 2\alpha} = \frac{3}{\sqrt{5}} \) and \( \frac{\sqrt{1 - \cos 2\beta}}{\sqrt{1 + \cos 2\beta}} = \frac{1}{7} \), then \( (2\alpha + \beta) = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Trigonometric Identities
If \( \cosh \alpha + \sinh \alpha = e^x \) and \( \sinh x = \frac{\alpha}{\alpha + 1} \), then \( \tanh x = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Trigonometric Identities
In \( \triangle ABC \), if \( \tan \frac{A}{2} + \tan \frac{C}{2} = \frac{b}{s} \), then \( \sin \left( \frac{A + C}{3} \right) = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Trigonometric Identities
If \( \frac{x^4 - 6x^3 + 9x^2 + 5x - 20}{x^2 - x - 2} = f(x) + \frac{a}{x + p} + \frac{b}{x + q} \), then \( 2(a + b) = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Algebra
In \( \triangle ABC \), if \( r_1 = 2r_2 = 3r_3 \), then
AP EAPCET - 2023
AP EAPCET
Mathematics
Triangles
In \( \triangle ABC \), \( \angle B = 60^\circ \) and \( \angle A = 75^\circ \). If a point \( D \) divides \( BC \) in the ratio \( 2:3 \), then \( \sin \angle BAD : \sin \angle CAD = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Triangles
\( \sin^4 \frac{\pi}{8} + \sin^4 \frac{3\pi}{8} + \sin^4 \frac{5\pi}{8} + \sin^4 \frac{7\pi}{8} = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Trigonometric Identities
In \( \triangle ABC \), if \( \cos A \cos B \cos C = \frac{1}{5} \), then \( \tan A \tan B + \tan B \tan C + \tan C \tan A = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Trigonometric Identities
If \( \cos(\theta - \alpha), \cos \theta \) and \( \cos(\theta + \alpha) \) are in harmonic progression, then \( 2 \tan^2 \theta = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Trigonometric Identities
If \( 3 \cdot {}^5C_0 + 8 \cdot {}^5C_1 + 13 \cdot {}^5C_2 + 18 \cdot {}^5C_3 + 23 \cdot {}^5C_4 + 28 \cdot {}^5C_5 = k \cdot 2^5 \), then \( k = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Binomial theorem
The least value of \( n \) such that \( {}^{n-1}C_6 + {}^{n-1}C_7<{}^nC_8 \) is
AP EAPCET - 2023
AP EAPCET
Mathematics
Combinatorics
If a seven digit number formed with distinct digits 4, 6, 9, 5, 3, \( x \) and \( y \) is divisible by 3, then the number of such ordered pairs \( (x, y) \) is
AP EAPCET - 2023
AP EAPCET
Mathematics
Number System
The coefficient of \( x^r \) in the expansion of \( \frac{1}{\sqrt{(1 - 2x)^3}} \) is
AP EAPCET - 2023
AP EAPCET
Mathematics
Binomial Expansion
If the roots of the equation \( 16x^3 - 44x^2 + 36x - 9 = 0 \) are in harmonic progression, then its greatest root is
AP EAPCET - 2023
AP EAPCET
Mathematics
Algebra
If \( \omega \) is a complex cube root of unity, then \( \cos \left( \sum_{k=1}^{2} (k - \omega)(k - \omega^2) \frac{\pi}{175} \right) = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Complex numbers
Let the two values of \( z = \frac{1 - i}{\sqrt{1 + i}} \) be \( z_1 \) and \( z_2 \). If \( -\frac{\pi}{2}<\text{Arg}(z_1)<\text{Arg}(z_2)<\pi \), then \( \text{Arg}(z_1) + \text{Arg}(z_2) = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Complex numbers
If \( \alpha \) and \( \beta \) are the roots of the equation \( x^2 + x + 1 = 0 \), then the quadratic equation whose roots are \( \alpha^{2023} \) and \( \beta^{2012} \) is
AP EAPCET - 2023
AP EAPCET
Mathematics
Complex numbers
If \( 2^n \) divides \( 16! \) and \( 2^{n+1} \) does not divide \( 16! \), then \( n = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Number System
If \( \alpha \) and \( \beta \) are the roots of the equation \( 2x^2 - 4x + 3 = 0 \), then \( \frac{2(\alpha^4 + \beta^4) + 3(\alpha^2 + \beta^2)}{\alpha + \beta} = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Algebra
If \( \alpha \) and \( \beta \) are the roots of the equation \( ax^2 + bx + c = 0 \), then the equation whose roots are \( \alpha + \beta \) and \( \frac{1}{\alpha} + \frac{1}{\beta} \) is
AP EAPCET - 2023
AP EAPCET
Mathematics
Algebra
If \( \sqrt{-3 - 4i} = re^{i\theta} \), then \( r^2 \tan \theta = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Complex numbers
If \( z_1 = 2 - 3i \) and the roots of the equation \( z^3 + bz^2 + cz + d = 0 \) are \( i, z_1 \) and \( \overline{z_1} \), then \( b + c + d = \)
AP EAPCET - 2023
AP EAPCET
Mathematics
Complex numbers
Let \( f(x) = |x| \) and \( g(x) = |x| + a \), \( (a>0) \). For \( 0 \le x \le b \), \( \{(x, y) / g(x) \le y \le f(x)\} \) represents all the points in the interior of
AP EAPCET - 2023
AP EAPCET
Mathematics
Functions
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