For the following questions answer them individually
If $$0 > \alpha, \beta < \frac{\pi}{4}, \cos(\alpha + \beta) = \frac{4}{5}$$ and $$\sin(\alpha - \beta) = \frac{5}{13}$$ then $$\tan 2 \alpha =$$
If $$x = a \cos \theta + b \sin \theta$$ and $$y = a \sin \theta - b \cos \theta$$, then $$x^2 + y^2 =$$
$$\frac{\tan 10^\circ + \tan 50^\circ}{1 - \tan 10^\circ \tan 50^\circ} =$$
A man in a boat rowing away from the cliff 150 meters high, observed that it takes 2 minutes to change the angleofelevation of the top of the cliff from $$60^\circ$$ to $$45^\circ$$, then the speed of the boat in km/hour is
If the polynomial $$-a^2 x^3 - 2ax^2 + b^2 x + 1$$ is divisible by $$x + 1$$, then $$a - 1 =$$
A polynomial in x leaves remainders —1 and 7 when it is divided by x + 1 and x - 3 respectively. If that polynomial is divided by $$x^2 - 2x - 3$$, then the remainder is
If $$73 \times 74 \times 75 \times 76$$ is divided by 14, then the remainder is
The 8th term of the progression 162, 54, 18, .... is
The sum of the first 10 terms of the series 1, 3, 5, 7, ......... is
The coefficient of x in the expansion of $$\left(3x^2 - \frac{1}{2x}\right)^5$$ is
Day-wise Structured & Planned Preparation Guide
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