[Download PDF] AP ICET 2014 Paper with Solutions

Instructions

For the following questions answer them individually

Question 121

A pole subtends angles $$30^\circ, 45^\circ, 60^\circ$$ respectively at points A, B and C all lying on a horizontal line through the foot of the pole, Then $$\frac{AB}{BC} = $$

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Question 122

$$x^4 - 4x^3 + 6x^2 - 4x + 1 = 0$$(x ≠ 0) $$\Rightarrow x + \frac{1}{x} =$$

Video Solution

Question 123

If x - 7 is a factor of the polynomial f(x), then a factor of $$f(2x^2 - 1)$$ among the following is

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Question 124

The remainder obtained when $$1! + 2! + 3! + .... + (2014)!$$ is divided by 7 is

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Solution

The remainder will actually depend on the sum from 1!+2!+3!+4!+...........+6! because after that every factorial will be a multiple of 7. This sums up to 873. Hence the sum will be 7m+873. Now 873 when divided by 7, has remainder 5. Hence the remainder will be 5.

Question 125

$$\sqrt{(x + 1)(x + 2)(x + 3)(x + 4) + 1} =$$

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Question 126

The sum of seven consecutive even integers is s. Then, in terms of s, the greatest of these integers is

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Solution

Let the seven even numbers be 2a, 2a+2, 2a+4, 2a+6,2a+8,2a+10,2a+12

There sum is 14a+42=s or 14(a+3)=s or a= s/14-3

Substitute for a in 2a+12 we get s+42/7

hope it helps. Thanks

Question 127

The maximum value of the expression $$2 + 8x - x^2$$ is

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Solution

After differentiating and equating to 0,

8 - 2x = 0

$$\Rightarrow$$ 2x = 8

$$\Rightarrow$$ x = 4

$$\therefore\ $$The maximum value of expression occurs at x = 4.

When x = 4,

$$2+8x-x^2=2+8\left(4\right)-4^2=2+32-16=18$$

Hence, the correct answer is Option C

Question 128

$$\frac{b}{a} = \frac{c}{b} =\frac{d}{c} \Rightarrow (a - c)^2 + (c - b)^2 + (b - d)^2 - (d - a)^2 =$$

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Question 129

The sum of first fifty odd natural numbers is

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Solution

Sum of first 50 odd natural numbers can be taken as an AP with first term a=1, common difference=2 and n=50

$$\frac{50}{2}\left[2\times\ 1+49\times\ 2\right]=25\left[100\right]=2500$$

Question 130

The coefficient of $$x^3$$ in the expansion of $$\left(x^2 - \frac{1}{x^3}\right)^9$$ is

Video Solution

CAT Content

AP ICET 2014

A pole subtends angles $$30^\circ, 45^\circ, 60^\circ$$ respectively at points A, B and C all lying on a horizontal line through the foot of the pole, Then $$\frac{AB}{BC} = $$

$$x^4 - 4x^3 + 6x^2 - 4x + 1 = 0$$(x ≠ 0) $$\Rightarrow x + \frac{1}{x} =$$

If x - 7 is a factor of the polynomial f(x), then a factor of $$f(2x^2 - 1)$$ among the following is

The remainder obtained when $$1! + 2! + 3! + .... + (2014)!$$ is divided by 7 is

$$\sqrt{(x + 1)(x + 2)(x + 3)(x + 4) + 1} =$$

The sum of seven consecutive even integers is s. Then, in terms of s, the greatest of these integers is

The maximum value of the expression $$2 + 8x - x^2$$ is

$$\frac{b}{a} = \frac{c}{b} =\frac{d}{c} \Rightarrow (a - c)^2 + (c - b)^2 + (b - d)^2 - (d - a)^2 =$$

The sum of first fifty odd natural numbers is

The coefficient of $$x^3$$ in the expansion of $$\left(x^2 - \frac{1}{x^3}\right)^9$$ is

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