Instructions

For the following questions answer them individually

Question 121

The angles of elevation of a tower fromthe top and bottomofa building of height 30 meters are $$30^\circ$$ and $$60^\circ$$ respectively. Then the height of the tower(in meters) is:

Video Solution

Question 122

$$x + \frac{1}{x} = 5 \Rightarrow x^3 + \frac{1}{x^3} =$$

Video Solution

Question 123

$$3x - 4y = 7; xy = 5 \Rightarrow 9x^2 + 16y^2 =$$

Video Solution

Question 124

The remainder when the polynomial $$7x^3 + 13x^2 - 19x - 20$$ is divided by x + 2 is:

Video Solution

Question 125

If a polynomial in x leaves remainders -19, 17 respectively when divided by x + 4 and x - 5, then the remainder it leaves when divided by $$x^2 - x - 20$$ is

Video Solution

Question 126

The value of k for which the system ky + 3y = k - 3 and 12x + ky = k of equations has infinitely many solutions is:

Video Solution

Solution

KX + 3Y = K -3

KX + 3Y - ( K -3) = 0 ------------(1)

And,

12X + KY = K

12X + KY - K = 0

These equations are of the form of A1X + B1Y + C1 = 0 and A2X + B2Y + C2 = 0

Where,

A1 = K , B1 = 3 and C1 = -K +3

And,

A2 = 12 , B2 = K and C2 = -K

For no solution we must have,

A1/A2 = B1/B2 =C1/C2 [ Where # stand for not equal]

K / 12 = 3/K

$$K^2 = 12 × 3$$

$$K^2 = 36$$

$$K = \sqrt{36} = 6$$

Question 127

A fraction becomes $$\frac{4}{5}$$ if 1 is added to both its numerator and denominator while it becomes $$\frac{1}{2}$$ if 5 is subtracted from its numerator and denominator. The fraction is

Video Solution

Solution

$$\frac{x+1}{y+1}$$=$$\frac{4}{5}$---------equation 1

$$\frac{x-5}{y-5}$$=$$\frac{1}{2}$$---------equation 2

from equation 1 and 2,

5x-4y=-1------ multiply with 2

2x-y=5----------multiply with 5

therefore

10x-8y=-2-----(1)

10-5y=25------(2)

by subtracting we get Y=9

subsitute y value in any equation we get X=7

Question 128

If the sum of first 21 terms of an arithmetic progression is 609, then the $$11^{th}$$ term of progression is

Video Solution

Solution

Sn=n/2[2a+(n-1)d]

609=21/2[2a+(21-1)d]

by taking 2 common and eliminate 2

609/21=a+10d i.e a11

a11=29

Question 129

The harmonic mean of $$\frac{1}{x}$$ and $$\frac{1}{y}$$ is

Video Solution

Solution

If X1,X2,X3 are in harmonic mean

harmonic mean=$$\frac{n}{x1}±\frac{n}{x2}±\frac{n}{x3}$$

Therefore harmonic mean of $$\frac{1}{x}$$ and $$\frac{1}{y}$$

is $$\frac{x+y}2$

Question 130

The coefficient of $$x^{12}$$ in the expansion of (x - 1)(x - 2)(x - 3)......(x - 13) is

Video Solution

Solution

CAT Content

TS ICET 24th May 2019 Shift-1

The angles of elevation of a tower fromthe top and bottomofa building of height 30 meters are $$30^\circ$$ and $$60^\circ$$ respectively. Then the height of the tower(in meters) is:

$$x + \frac{1}{x} = 5 \Rightarrow x^3 + \frac{1}{x^3} =$$

$$3x - 4y = 7; xy = 5 \Rightarrow 9x^2 + 16y^2 =$$

The remainder when the polynomial $$7x^3 + 13x^2 - 19x - 20$$ is divided by x + 2 is:

If a polynomial in x leaves remainders -19, 17 respectively when divided by x + 4 and x - 5, then the remainder it leaves when divided by $$x^2 - x - 20$$ is

The value of k for which the system ky + 3y = k - 3 and 12x + ky = k of equations has infinitely many solutions is:

A fraction becomes $$\frac{4}{5}$$ if 1 is added to both its numerator and denominator while it becomes $$\frac{1}{2}$$ if 5 is subtracted from its numerator and denominator. The fraction is

If the sum of first 21 terms of an arithmetic progression is 609, then the $$11^{th}$$ term of progression is

Sn=n/2[2a+(n-1)d]

The harmonic mean of $$\frac{1}{x}$$ and $$\frac{1}{y}$$ is

The coefficient of $$x^{12}$$ in the expansion of (x - 1)(x - 2)(x - 3)......(x - 13) is

CAT Content

TS ICET 24th May 2019 Shift-1

The angles of elevation of a tower fromthe top and bottomofa building of height 30 meters are $$30^\circ$$ and $$60^\circ$$ respectively. Then the height of the tower(in meters) is:

$$x + \frac{1}{x} = 5 \Rightarrow x^3 + \frac{1}{x^3} =$$

$$3x - 4y = 7; xy = 5 \Rightarrow 9x^2 + 16y^2 =$$

The remainder when the polynomial $$7x^3 + 13x^2 - 19x - 20$$ is divided by x + 2 is:

If a polynomial in x leaves remainders -19, 17 respectively when divided by x + 4 and x - 5, then the remainder it leaves when divided by $$x^2 - x - 20$$ is

The value of k for which the system ky + 3y = k - 3 and 12x + ky = k of equations has infinitely many solutions is:

A fraction becomes $$\frac{4}{5}$$ if 1 is added to both its numerator and denominator while it becomes $$\frac{1}{2}$$ if 5 is subtracted from its numerator and denominator. The fraction is

If the sum of first 21 terms of an arithmetic progression is 609, then the $$11^{th}$$ term of progression is

Sn=n/2[2a+(n-1)d]

The harmonic mean of $$\frac{1}{x}$$ and $$\frac{1}{y}$$ is

The coefficient of $$x^{12}$$ in the expansion of (x - 1)(x - 2)(x - 3)......(x - 13) 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