List of top Mathematics Questions

If \(\cos x + \cos y = \tfrac{2}{3}\) and \(\sin x - \sin y = \tfrac{3}{4}\), then \[ \sin(x - y) \;+\; \cos(x - y) \;=\;? \]
The solution set of the equation \(\cos^2(2x) + \sin^2(3x) = 1\) is \;?

Match the functions in List--I with their corresponding properties in List--II:

If \( \cos^2 84^\circ + \sin^2 126^\circ - \sin 84^\circ \cos 126^\circ = K \) and \( \cot A + \tan A = 2K \), then the possible values of \( \tan A \) are:
The equation that is satisfied by the general solution of the equation \( 4 - 3 \cos \theta = 5 \sin \theta \cos \theta \) is:
If \( \sin^{-1}(4x) - \cos^{-1}(3x) = \frac{\pi}{6} \), then \( x = \):
If \(2\,\tan^{-1}x = 3\,\sin^{-1}x\) and \(x \neq 0\), then \(8x^2 +1 =\;?\)
In a triangle \(ABC\), if \(\tan\tfrac{A}{2} : \tan\tfrac{B}{2} : \tan\tfrac{C}{2} = 15 : 10 : 6\), then \(\frac{a}{b - c} = \,?\)
If \( \tan A = -\frac{60}{11} \) and A does not lie in the 4th quadrant. \( \sec B = \frac{41}{9} \) and B does not lie in the 1st quadrant. If \( \csc A + \cot B = K \), then \( 24K = \):
If \( \tan A + \tan B + \cot A + \cot B = \tan A \tan B - \cot A \cot B \) and \( 0^\circ<A + B<270^\circ \), then \( A + B = \):
If \( \sinh^{-1}(-\sqrt{3}) + \cosh^{-1}(2) = K \), then \( \cosh K = \):
In triangle ABC, if \( a = 4, b = 3, c = 2 \), then \( 2(a - b \cos C)(a - c \sec B) = \):
If \( y = \cos^{-1}\left( \frac{6x^2 - 2x^2 - 4}{2x^2 - 6x + 5} \right) \), then find \( \frac{dy}{dx} \).
The approximate value of \( \sec 59^\circ \) obtained by taking \( 1^\circ = 0.0174 \) and \( \sqrt{3} = 1.732 \) is:
If \( y = \frac{\tan x \cos^{-1}x}{\sqrt{1 - x^2}} \), then the value of \( \frac{dy}{dx} \) when \( x = 0 \) is:
If \( y (\cos x)^{\sin x} = (\sin x)^{\sin x} \), then the value of \( \frac{dy}{dx} \) at \( x = \frac{\pi}{4} \) is:
If \( x = \cos 2t + \log (\tan t) \) and \( y = 2t + \cot 2t \), then \( \frac{dy}{dx} \) is:
The general solution of the differential equation $$ \frac{dy}{dx} = \frac{2y^2 + 1}{2y^3 - 4xy + y}. $$ 
If A and B are arbitrary constants, then the differential equation having \[ y = Ae^{-x} + B \cos x \] as its general solution is:
If \( y = 44x^{45} + 45x^{44} \), then \( y'' \) is:
The approximate value of \( \sqrt[3]{730} \) obtained by the application of derivatives is:
The general solution of the differential equation \[ (9x - 3y + 5) dy = (3x - y + 1) dx. \]
If \( \log y = y^{\log x} \), then \( \frac{dy}{dx} \) is:
The general solution of the differential equation \[ \frac{dy}{dx} + \frac{\sin(2x + y)}{\cos x} + 2 = 0 \] is:
If \( m \) is the slope and \( P(\beta, \beta) \) is the midpoint of a chord of contact of the circle \[ x^2 + y^2 = 125, \] then the number of values of \( \beta \) such that \( \beta \) and \( m \) are integers is: \