[Download PDF] AP ICET 2017 Paper with Solutions

Instructions

For the following questions answer them individually

Question 131

If the coefficients of $$x^7$$ and $$x^8$$ are equal in the binomial expansion of $$(3 + \frac{x}{2})^n$$ then $$n =$$

Video Solution

Question 132

If $$\alpha$$ is an integer, $$A = \begin{bmatrix}\alpha^2 & 5 \\5 & -\alpha \end{bmatrix}$$ and $$\mid A \mid^{10} = 1024$$ then $$\alpha =$$

Video Solution

Question 133

$$A_x = \begin{bmatrix}\sin x & -\cos x \\\cos x & \sin x \end{bmatrix} \Rightarrow \sin x.A_x + \cos x.A_{\left(\frac{\pi}{2} + x\right)} =$$

Video Solution

Question 134

$$\lim_{x \rightarrow a}\frac{(\sqrt{3x - a} - \sqrt{(x + a)})}{(x - a)} =$$

Video Solution

Question 135

$$y = \cot^{-1}\left(\frac{1 - 3x^2}{3x - x^3}\right) \Rightarrow \frac{dy}{dx} =$$

Video Solution

Question 136

The hypotenuse (in cms) of a right angle triangle whosesides are in the ratio 3:4 and having area 24 sq.cmsis

Video Solution

Solution

Let the two sides be 3x and 4x. By Pythagoras' theorem, we get hypotenuse as 5x.
Now, Area of triangle = 0.5*3x*4x = 6x*x = 24 sq cm
Hence, x = 2 and thus, hypotenuse = 10 cm

Question 137

If the two diagonals of a parallelogram are equal and perpendicular bisectors of each other then it is a

Video Solution

Solution

The diagonals of a parallelogram can be equal only if it is a square or rectangle.
The diagonals of a parallelogram can be perpendicular bisectors of each only if it is a square or a rhombus.
The only common feature in both the conditions is a squre.
Hence, the answer.

Question 138

If O is the center of a circle on which A, B and C are three points; and if $$\angle BOC = 100^\circ$$ then $$\angle ABC + \angle ACB =$$

Video Solution

Solution

For ease of determination, make A and B ends of a diameter of a circle. This makes triangle ACB a right angled triangle and hence angle ACB becomes = 90 degrees.

Now, in isosceles triangle BOC, OB = OC (radii of same circle) and angle BOC = 100 degrees.
Hence, angles OBC and OCB = 40 degrees each. Hence, this also makes angle ABC = 40 degrees.

Hence, sum of the two required angles = 90+40 = 130 degrees.

Question 139

The triangle with vertices at (0, 0), (2, 2) and (0, 4) is

Video Solution

Solution

If you plot the points roughly on a graph and drop a perpendicular from (2,2) on the side joining (0,0) and (0,4), it can be seen that the point (2,2) lies equidistant from the other two vertices.

Also, Pythagoras' theorem gets satisfied for the given triangles.
Hence, the triangle is an isosceles right angled triangle.

Question 140

If $$(\alpha, \beta)$$ and $$(\gamma, \delta)$$ are respectively the points which divide the line joining(7, -5) and (-2, 6) in the ratios 1 : 2 and 2 : 1 then $$\alpha + \gamma - \beta - \delta =$$

Video Solution

CAT Content

AP ICET 2017

If the coefficients of $$x^7$$ and $$x^8$$ are equal in the binomial expansion of $$(3 + \frac{x}{2})^n$$ then $$n =$$

If $$\alpha$$ is an integer, $$A = \begin{bmatrix}\alpha^2 & 5 \\5 & -\alpha \end{bmatrix}$$ and $$\mid A \mid^{10} = 1024$$ then $$\alpha =$$

$$A_x = \begin{bmatrix}\sin x & -\cos x \\\cos x & \sin x \end{bmatrix} \Rightarrow \sin x.A_x + \cos x.A_{\left(\frac{\pi}{2} + x\right)} =$$

$$\lim_{x \rightarrow a}\frac{(\sqrt{3x - a} - \sqrt{(x + a)})}{(x - a)} =$$

$$y = \cot^{-1}\left(\frac{1 - 3x^2}{3x - x^3}\right) \Rightarrow \frac{dy}{dx} =$$

The hypotenuse (in cms) of a right angle triangle whosesides are in the ratio 3:4 and having area 24 sq.cmsis

If the two diagonals of a parallelogram are equal and perpendicular bisectors of each other then it is a

If O is the center of a circle on which A, B and C are three points; and if $$\angle BOC = 100^\circ$$ then $$\angle ABC + \angle ACB =$$

The triangle with vertices at (0, 0), (2, 2) and (0, 4) is

If $$(\alpha, \beta)$$ and $$(\gamma, \delta)$$ are respectively the points which divide the line joining(7, -5) and (-2, 6) in the ratios 1 : 2 and 2 : 1 then $$\alpha + \gamma - \beta - \delta =$$

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