List of top Mathematics Questions asked in TS EAMCET

Evaluate the integral: \[ \int 4\cos^2 x - 5\sin^2 x \cos x \, dx. \]
Evaluate the integral: \[ \int \frac{4\tan^4 x + 3 \tan^2 x - 1}{\tan^2 x + 4} \, dx. \]
Evaluate the integral: \[ \int \frac{(\sin^4x + 2\cos^2x - 1) \cos x}{(1 + \sin x)^6} \, dx \]
Evaluate the integral: \[ \int (\log x)^3 \, dx \]
Evaluate the integral: \[ \int \left( \sin^3 x + \cos^2 x \right)^2 \, dx \]
Evaluate the integral: \[ I = \int_{-\frac{\pi}{8}}^{\frac{\pi}{8}} \frac{\sin^4(4x)}{1 + e^{4x}} \, dx \]
The area of the region enclosed by the curves \( y^2 = 4(x+1) \) and \( y^2 = 5(x-4) \) is:
If \(\theta\) is the angle between the vectors \(4\mathbf{i} - \mathbf{j} + 2\mathbf{k}\) and \( \mathbf{i} + 3\mathbf{j} - 2\mathbf{k}\), then \(\sin 2\theta\) is:
The slope of a common tangent to the circles \( x^2 + y^2 - 4x - 8y + 16 = 0 \) and \( x^2 + y^2 - 6x - 16y + 64 = 0 \) is:
If \( (h, k) \) is the internal center of similitude of the circles \( x^2 + y^2 + 2x - 6y + 1 = 0 \) and \( x^2 + y^2 - 4x + 2y + 4 = 0 \), then find \( 4h \).
If the probability that a randomly selected student from a college is good at mathematics is 0.6, then the probability of having exactly two students who are good at mathematics in a group of 8 students standing in front of the college is:
If on average 4 customers visit a shop in an hour, then the probability that more than 2 customers visit the shop in a specific hour is:
When 2 dice are thrown, it is observed that the sum of the numbers appeared on the top faces of both the dice is a prime number. Then the probability of having a multiple of 3 among the pair of numbers thus obtained is:
A dealer gets refrigerators from 3 different manufacturing companies \(C_1, C_2, C_3\). 25\% of his stock is from \(C_1\), 35\% from \(C_2\), and 40\% from \(C_3\). The percentages of receiving defective refrigerators from \(C_1, C_2, C_3\) are 3\%, 2\%, and 1\%, respectively. If a refrigerator sold at random is found to be defective, then the probability that it is from \(C_2\) is:
The circles \(x^2 + y^2 + 2x - 6y - 6 = 0\) and \(x^2 + y^2 - 6x - 2y + k = 0\) are two intersecting circles and \(k\) is not an integer. If \( \theta \) is the angle between the two circles and \( \cos \theta = -\frac{5}{24} \), then find \( k \).
If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of getting a card having a composite number and a card having a number which is a multiple of 3 is:
The centroid of a variable triangle ABC is at the distance of 5 units from the origin. If A = (2,3) and B = (3,2), then the locus of C is:
If the normal drawn at the point \( P(9, 9) \) on the parabola \( y^2 = 9x \) meets the parabola again at \( Q(a, b) \), then \( 2a + b = \text{?} \)
If the tangents \( x + y + k = 0 \) and \( x + ay + b = 0 \) drawn to the circle \( S : x^2 + y^2 + 2x - 2y + 1 = 0 \) are perpendicular to each other and \( k, b \) are both greater than 1, then find \( b - k \).
If \( (1,1), (-2,2), (2,-2) \) are 3 points on a circle \( S \), then the perpendicular distance from the center of the circle \( S \) to the line \( 3x - 4y + 1 = 0 \) is:
The length of the latus rectum of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) \( (a>b) \) is \( \frac{8}{3} \). If the distance from the center of the ellipse to its focus is \( \sqrt{5} \), then \( \sqrt{a^2 + 6ab + b^2} = \text{?} \)
If the line \( 4x - 3y + p = 0 \) (where \( p + 3>0 \)) touches the circle \( x^2 + y^2 - 4x + 6y + 4 = 0 \) at the point \( (h,k) \), then the value of \( h - 2k \) is:
Area of the triangle bounded by the lines given by the equations: \[ 12x^2 - 20xy + 7y^2 = 0 \quad \text{and} \quad x + y - 1 = 0 \]
S' is the focus of the ellipse \( \frac{x^2}{25} + \frac{y^2}{b^2} = 1, (b<5) \) lying on the negative X-axis and \( P(\theta) \) is a point on this ellipse. If the distance between the foci of this ellipse is 8 and \( S'P = 7 \), then \( \theta \) is:
(a,b) is the point of concurrency of the lines \(x-3y+3=0\), \(Kx+y+k=0\) and \(2x+y-8=0\). If the perpendicular distance from the origin to the line \(L: ax-by+2k=0\) is \(p\), then the perpendicular distance from the point \((2,3)\) to \(L=0\) is: