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

Instructions

For the following questions answer them individually

Question 131

The coefficient of $$x^8$$ in $$\left(x - \frac{2}{x}\right)^{20}$$ is

Video Solution

Question 132

If the system of equations $$3x - 2y + z = 0, \lambda x - 14y + 15z = 0, x + 2y + 3z = 0$$ has non-trivial solution, then $$\lambda$$ is a root of the equation

Video Solution

Question 133

$$A = \begin{bmatrix}4 & 0 & 0 \\0 & 5 & 0 \\0 & 0 & 6 \end{bmatrix} \Rightarrow A^{-1} =$$

Video Solution

Question 134

$$\lim_{x \rightarrow 0}\frac{1 - \cos 4x}{1 - \cos 5x} =$$

Video Solution

Question 135

If $$y = \sqrt{x + y}$$ then $$\frac{dx}{dy} =$$

Video Solution

Solution

Given, $$y = \sqrt{x + y}$$

Squaring on both sides, we get

$$y^2=x+y$$

$$\Rightarrow$$ $$x=y^2-y$$

$$\Rightarrow$$ $$\frac{dx}{dy} = 2y^{2-1}-y^{1-1}$$

$$\Rightarrow$$ $$\frac{dx}{dy} = 2y-1$$

Hence, the correct answer is Option D

Question 136

If each interior angle of a regular polygon is $$135^\circ$$, then the number of sides of the polygon is

Video Solution

Solution

Each interior angle of the regular polygon = $$\frac{\left(n-2\right)180^{\circ\ }}{n}$$

Given, each interior angle of the regular polygon is $$135^\circ$$

$$\Rightarrow$$ $$\frac{\left(n-2\right)180^{\circ\ }}{n}=135^{\circ\ }$$

$$\Rightarrow$$ $$4\left(n-2\right)\ =3n$$

$$\Rightarrow$$ $$\ 4n-8=3n$$

$$\Rightarrow$$ $$n=8$$

$$\therefore\ $$Number of sides of the polygon = 8

Question 137

ABCD is a quadrilateral and P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. Then PQORS is a

Video Solution

Question 138

A parallelogram and a triangle have same base and the third vertex of the triangle lies on the side parallel to base. If the area of the triangle is 36 sq.cms then the area (in square cms) ofthe parallelogram is

Video Solution

Question 139

The area (in sq. units) of the triangle formed by points (2, 3), (3, 4) and (4, 2) is

Video Solution

Solution

Area of triangle formed by points (2, 3), (3, 4) and (4, 2) = $$\frac{1}{2}\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|$$

$$=\frac{1}{2}\left|2\left(4-2\right)+3\left(2-3\right)+4\left(3-4\right)\right|$$

$$=\frac{1}{2}\left|2\left(2\right)+3\left(-1\right)+4\left(-1\right)\right|$$

$$=\frac{1}{2}\left|4-3-4\right|$$

$$=\frac{1}{2}\left|-3\right|$$

$$=\frac{3}{2}$$

Question 140

PQR is a right angled triangle where P and R are the points (2, 4) and (6, 10) respectively and $$\angle Q = 90^\circ$$. Then the circumcentre of the triangle is

Video Solution

Solution

In a right-angled triangle, circumcentre is the centre of the hypotenuse.

Hence circumcentre = $$\frac{\left(6+2\right)}{2},\ \frac{\left(10+4\right)}{2}=\left(4,7\right)$$

CAT Content

AP ICET 2nd May 2018 Shift-1

The coefficient of $$x^8$$ in $$\left(x - \frac{2}{x}\right)^{20}$$ is

If the system of equations $$3x - 2y + z = 0, \lambda x - 14y + 15z = 0, x + 2y + 3z = 0$$ has non-trivial solution, then $$\lambda$$ is a root of the equation

$$A = \begin{bmatrix}4 & 0 & 0 \\0 & 5 & 0 \\0 & 0 & 6 \end{bmatrix} \Rightarrow A^{-1} =$$

$$\lim_{x \rightarrow 0}\frac{1 - \cos 4x}{1 - \cos 5x} =$$

If $$y = \sqrt{x + y}$$ then $$\frac{dx}{dy} =$$

If each interior angle of a regular polygon is $$135^\circ$$, then the number of sides of the polygon is

ABCD is a quadrilateral and P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. Then PQORS is a

A parallelogram and a triangle have same base and the third vertex of the triangle lies on the side parallel to base. If the area of the triangle is 36 sq.cms then the area (in square cms) ofthe parallelogram is

The area (in sq. units) of the triangle formed by points (2, 3), (3, 4) and (4, 2) is

PQR is a right angled triangle where P and R are the points (2, 4) and (6, 10) respectively and $$\angle Q = 90^\circ$$. Then the circumcentre of the triangle is

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