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X belongs to whole numbers but not natural numbers. So x={0} the number of subsets=2 and number of proper subsets=1.
The cost price of the pen =C= 10 the selling price of the pen =S=15 So Profit=P=S-C=15-10=5
For simplicity Let Anti clock wise as +ve direction so clockwise will be negative direction Anti clock wise= 180 degree clockwise= 135 degree therefore sum= 180-135= 45 degree anti clockwise
Let the number is x As given in the question x*(-1)=(-22) So x=22
When  36516 is divided by 456 we get remainder as 36 So the least number = 456 - 36 = 420 So 420 is the least number which should be added to the 36516 so that the new number is exactly divisible by 456. I.e new number=36516 + 420 = 36936 and this is exactly divisible by 456
Let the 2 digit number be in the form of 10x+y where x and y intergers. so according to question 10x+y= 4(x+y)  10x+y=4x+4y 6x-3y=0 2x-y=0 ......... (i) And If 27 is added to the number the digits are reversed So 10x+y+27=10y+x  9x-9y +27= 0 x-y+3=0  .......................(ii) substracting (ii) from (i) we get 2x-y-x+y-3=0  So x = 3 similarly y=6 So the number is 36
The area of the entire cloth is  80 m2 Area of small cloth = 20 x 0.3=6m2 Number of small cloths he can make= 80/6= 13 cloths approximately  
Real numbers include both rational and irrational numbers
Given the sum, the ratio of angle is 1:3:7:9. That is 20 parts is 360 degree (sum of the interior angles of a quadrilateral is 360 degrees). 1 part = 360/20=18 degrees. So the angles are  18, 3x18, 7x18, 9x18 that is 18, 54, 126 and 162 degrees
Total numeber of corona patients = 3000 Number of people died =  80 Death percentage = 80x100/3000 = 2.666 percentage
 65 litres : 13 litres :: 50 kg : 10 kg​ 5:1 :: 5:1 Each pair in 5:1 hence these pairs are in proportion.
15 x2 - 11x + 2 = 15 x2 - 6x - 5x + 2                          = 3x ( 5x -2 ) -1 (5x -2)                          = (5x -2) ( 3x -1)  
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