[Download PDF] AP ICET 2014 Question Paper 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 $$\frac{AB}{BC} = $$

Video Solution

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

Video Solution

Question 124

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

Video Solution

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

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

Video Solution

Question 126

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

Video Solution

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

Video Solution

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

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

Video Solution

Question 129

The sum of first fifty odd natural numbers is

Video Solution

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 Question Paper

AP ICET 2014 Question Paper

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

Login to your Cracku account

Hello! 👋

Ready to Unlock Your Success?

Please Enter Your OTP

Please enter the following details

Create a free Cracku account

Get Started with 5000+ Free CAT Questions & Mock Tests with Detailed Solutions!