[Download PDF] AP ICET 2012 Paper with Solutions

Instructions

For the following questions answer them individually

Question 121

If $$0 > \alpha, \beta < \frac{\pi}{4}, \cos(\alpha + \beta) = \frac{4}{5}$$ and $$\sin(\alpha - \beta) = \frac{5}{13}$$ then $$\tan 2 \alpha =$$

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Question 122

If $$x = a \cos \theta + b \sin \theta$$ and $$y = a \sin \theta - b \cos \theta$$, then $$x^2 + y^2 =$$

Video Solution

Question 123

$$\frac{\tan 10^\circ + \tan 50^\circ}{1 - \tan 10^\circ \tan 50^\circ} =$$

Video Solution

Question 124

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

Video Solution

Question 125

If the polynomial $$-a^2 x^3 - 2ax^2 + b^2 x + 1$$ is divisible by $$x + 1$$, then $$a - 1 =$$

Video Solution

Question 126

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

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Question 127

If $$73 \times 74 \times 75 \times 76$$ is divided by 14, then the remainder is

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Question 128

The 8th term of the progression 162, 54, 18, .... is

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Question 129

The sum of the first 10 terms of the series 1, 3, 5, 7, ......... is

Video Solution

Question 130

The coefficient of x in the expansion of $$\left(3x^2 - \frac{1}{2x}\right)^5$$ is

Video Solution

CAT Content

AP ICET 2012

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

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