[Download PDF] AP ICET 2nd May 2018 Shift-1 Paper with Solutions

Instructions

For the following questions answer them individually

Question 121

Two boys who are oneither side of a tower of 100 meters height observe that the angles of elevation of the top of the tower are $$30^\circ$$ and $$45^\circ$$. The distance (in meters) between the boys is

Video Solution

Question 122

For a ≠ b, if the quadratic expression $$x^2 + ax + b$$ and $$x^2 + bx + a$$ have a common factor, then the relation between a and b is

Video Solution

Question 123

If f(x) and g(x) are polynomials of degrees 3 and 2 respectively then f(g(x)) is of degree

Video Solution

Question 124

If two of the factors of the polynomial $$x^3 + x^2 - 10x + 8$$ and x - 1 and x - 2 then the third factors is

Video Solution

Solution

If x+a is factor of a polynomial f(x), then f(-a) should be zero

f(-4) = $$\left(-4\right)^3+\left(-4\right)^2-10\left(-4\right)+8=0$$

Hence x+4 is the third factor.

Question 125

If the remainders when the polynomial f(x) is divided by $$x - 1$$ and $$x + 1$$ are 3 and 4 respectively. then the remainder when f(x) is divided by $$x^2 - 1$$ is

Video Solution

Question 126

If 5 is subtracted from each of the two numbers their ratio becomes 1:2. while 1 is added to each. their ratio becomes 8:13. Then the difference between those numbers is

Video Solution

Solution

Let the numbers be x, y

Given, $$\frac{\left(x-5\right)}{y-5}=\frac{1}{2}$$ => 2x-y =5

Given, $$\frac{\left(x+1\right)}{y+1}=\frac{8}{13}$$ => 13x-8y = -5

Solving we get x=15 and y= 25

Diference = 10

Question 127

The point (x, y) in the plane for which 6x + 6y = 5xy and 6y - 6x = xy is

Video Solution

Solution

Given, equation of planes is

6x + 6y = 5xy .......(1)

6y - 6x = xy .........(2)

Solving equation (1) + equation (2)

12y = 6xy

$$\Rightarrow$$ 12y - 6xy = 0

$$\Rightarrow$$ 6y(2-x) = 0

$$\Rightarrow$$ y = 0 or 2-x = 0

$$\Rightarrow$$ y = 0 or x = 2

From equation (1)

When y = 0, 6x + 0 = 0 $$\Rightarrow$$ x = 0

When x = 2, 6(2) + 6y = 5(2)y $$\Rightarrow$$ y = 3

$$\therefore\ $$Required point is (2,3)

Question 128

In an arithmetic progression the $$8^{th}$$ and $$19^{th}$$ terms are respectively 17 and 39. The $$25^{th}$$ term of it is

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Solution

Given, $$8^{th}$$ and $$19^{th}$$ terms of the arithmetic progression are 17 and 39

$$\Rightarrow$$ a+7d = 17 and a+18d = 39

Solving the above two we get 11d = 22

$$\Rightarrow$$ d= 2 and a = 3

Hence 25th term = a+24d = 3 + 24(2) = 51

Question 129

$$1 + \frac{3}{4} + \frac{5}{16} \frac{7}{64} + ......... \infty =$$

Video Solution

Question 130

The term independent of x in the binomial expansion of $$\left(x - \frac{1}{x^2}\right)^3n$$ is

Video Solution

CAT Content

AP ICET 2nd May 2018 Shift-1

Two boys who are oneither side of a tower of 100 meters height observe that the angles of elevation of the top of the tower are $$30^\circ$$ and $$45^\circ$$. The distance (in meters) between the boys is

For a ≠ b, if the quadratic expression $$x^2 + ax + b$$ and $$x^2 + bx + a$$ have a common factor, then the relation between a and b is

If f(x) and g(x) are polynomials of degrees 3 and 2 respectively then f(g(x)) is of degree

If two of the factors of the polynomial $$x^3 + x^2 - 10x + 8$$ and x - 1 and x - 2 then the third factors is

If the remainders when the polynomial f(x) is divided by $$x - 1$$ and $$x + 1$$ are 3 and 4 respectively. then the remainder when f(x) is divided by $$x^2 - 1$$ is

If 5 is subtracted from each of the two numbers their ratio becomes 1:2. while 1 is added to each. their ratio becomes 8:13. Then the difference between those numbers is

The point (x, y) in the plane for which 6x + 6y = 5xy and 6y - 6x = xy is

In an arithmetic progression the $$8^{th}$$ and $$19^{th}$$ terms are respectively 17 and 39. The $$25^{th}$$ term of it is

$$1 + \frac{3}{4} + \frac{5}{16} \frac{7}{64} + ......... \infty =$$

The term independent of x in the binomial expansion of $$\left(x - \frac{1}{x^2}\right)^3n$$ is

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