CAT 2020 Question Paper Slot 3 with Solutions, Download PDF

Instructions

For the following questions answer them individually

Question 71

Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

Video Solution

Solution

Anil and Sunil will meet at a first point after LCM ( $$\frac{3}{15},\frac{3}{10}$$) = 3/5 hr

In the mean time, distance travelled by ravi = 8 * 3/5 = 4.8 km

Question 72

In a trapezium $$ABCD$$, $$AB$$ is parallel to $$DC$$, $$BC$$ is perpendicular to $$DC$$ and $$\angle BAD=45^{0}$$. If $$DC$$ = 5cm, $$BC$$ = 4 cm,the area of the trapezium in sq cm is

Backspace
789
456
123
0.-
Clear All

Video Solution

Solution

Given, BC = DE = 4

CD = BE = 5

In triangle ADE, EAD=45^{0}$$

$$\tan\ 45\ =\ \frac{DE}{AE}$$ => AE = 4

Area of trapezium = Area of rectangle BCDE + Area of triangle AED

= 20 + 8 = 28

Question 73

The area, in sq. units, enclosed by the lines $$x=2,y=\mid x-2\mid+4$$, the X-axis and the Y-axis is equal to

Video Solution

Solution

The required figure is a trapezium with vertices A(0,0), B(2,0), C(2,4) and D(0,6)

AB = 2 BC = 4 and AD = 6

Area of trapezium = $$\frac{1}{2}\left(sum\ of\ the\ opposite\ sides\right)\cdot height$$ = $$\frac{1}{2}\left(4+6\right)\cdot2\ =\ 10$$

Question 74

If $$f(x+y)=f(x)f(y)$$ and $$f(5)=4$$, then $$f(10)-f(-10)$$ is equal to

Video Solution

Solution

The given function is equivalent to f(x) = $$a^x$$

Given, f(5) = 4

=> $$a^5=4=>\ a=4^{\frac{1}{5}}$$

=> f(x) = $$4^{\frac{x}{5}}$$

f(10) - f(-10) = 16 - 1/16 = 15.9375

Question 75

$$\frac{2\times4\times8\times16}{(\log_{2}{4})^{2}(\log_{4}{8})^{3}(\log_{8}{16})^{4}}$$ equals

Backspace
789
456
123
0.-
Clear All

Video Solution

Solution

$$\frac{\left(2\cdot4\cdot8\cdot16\right)}{\left(\log_22^2\right)^2\cdot\left(\log_{2^2}2^3\right)^3\cdot\left(\log_{2^3}2^4\right)^4}\cdot$$

= $$\frac{2^{10}}{4\cdot\left(\frac{3}{2}\right)^3\cdot\left(\frac{4}{3}\right)^4}=24$$

Question 76

The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

Video Solution

Solution

Equation of circle $$x^2+y^2+2gx+2fy+c=0$$

It passes through (0,0), (4,0) and (3,9). Substitute each point in the above equation:

=> On substituting the value (0,0) in the above equation, we obtain: $$c=0$$

=> On substituting the value (4,0) in the above equation, we obtain: $$16+0+8g+0 = 0$$ ; $$g=-2$$

=> On substituting the value (3,9) in the above equation, we obtain: $$9+81-12+18f = 0$$ ; $$f= -13/3$$

Radius of the circle r = $$\sqrt{\ g^2+f^2-c}$$ => $$r^2=\frac{205}{9}$$

Therefore, Area = $$\pi\ r^2=\frac{205\pi\ }{9}$$

CAT Content

CAT 2020 Question Paper Slot 3

In a trapezium $$ABCD$$, $$AB$$ is parallel to $$DC$$, $$BC$$ is perpendicular to $$DC$$ and $$\angle BAD=45^{0}$$. If $$DC$$ = 5cm, $$BC$$ = 4 cm,the area of the trapezium in sq cm is

The area, in sq. units, enclosed by the lines $$x=2,y=\mid x-2\mid+4$$, the X-axis and the Y-axis is equal to

If $$f(x+y)=f(x)f(y)$$ and $$f(5)=4$$, then $$f(10)-f(-10)$$ is equal to

$$\frac{2\times4\times8\times16}{(\log_{2}{4})^{2}(\log_{4}{8})^{3}(\log_{8}{16})^{4}}$$ equals

The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

Related Formulas With Tests

CAT Quant Questions | CAT Quantitative Ability

CAT DILR Questions | LRDI Questions For CAT

CAT Verbal Ability Questions | VARC Questions For CAT

Also Read

CAT Content

CAT 2020 Question Paper Slot 3

In a trapezium $$ABCD$$, $$AB$$ is parallel to $$DC$$, $$BC$$ is perpendicular to $$DC$$ and $$\angle BAD=45^{0}$$. If $$DC$$ = 5cm, $$BC$$ = 4 cm,the area of the trapezium in sq cm is

The area, in sq. units, enclosed by the lines $$x=2,y=\mid x-2\mid+4$$, the X-axis and the Y-axis is equal to

If $$f(x+y)=f(x)f(y)$$ and $$f(5)=4$$, then $$f(10)-f(-10)$$ is equal to

$$\frac{2\times4\times8\times16}{(\log_{2}{4})^{2}(\log_{4}{8})^{3}(\log_{8}{16})^{4}}$$ equals

The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points 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

Related Formulas With Tests

CAT Quant Questions | CAT Quantitative Ability

CAT DILR Questions | LRDI Questions For CAT

CAT Verbal Ability Questions | VARC Questions For CAT

Also Read

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