COMPACT QUESTIONS (X)

SIMULTANEOUS EQUATIONS

1) a(x+ y)+ b(x - y)= a²- ab + b²; a(x+ y)- b(x - y)= a²+ ab + b².     b²/2a, (2a²+ b²)/2a

2) ax + by = c; bx + ay = 1+ c.        

3) x/a + y/b = 2; ax - by= a²- b².     a, b

4) 2/x + 3/y= 13; 5/x - 4/y= -2.      1/2,1/3

5) ax+ by= (a+ b)/2; 3x + 5y=4.      1/2,1/2

6) x{a - b + ab/(a- b)}= y{a + b - ab/(a + b)}; x + y= 2a².     (a³- b³)/a,  (a³ +b³)/a

7) 57/(x + y) + 6/(x - y) =5; 38/(x + y) + 21/(x - y) =9.      11,8

8) 6(ax + by)= 3a + 2b; 6(bx - ay)= 3b - 2a.       1/2,1/3

9) x+ y= 7, xy= 12.            (4,3),(3,4)

10) x + 4/y = 1, y+ 4/x =25.            (1/5,5),(4/5,20)

11) For what value of k will the equation x+ 2y +7=0, 2x + ky+14=0 represent coincident lines.        4

12) Determine the values of a, b for which the following system of linear equations has infinite solutions: 
2x -(a -4)y = 2b +1; 4x -(a -1)y= 5b -1.          7,3

13) Find the values of p and q for which the following system of equations has infinite solutions: 2x + 3y =7; (p+ q)x + (2p - q)y = 21.         5,1

14) For what value of k, will the system of equations x+ 2y = 5; 3x + ky+15=0 has
a) unique solution.         k≠ 6
b) no solution.           k= 6 and k≠ -6, which is not possible.

15) Determine the value of k so that the following linear equations have no solution:
(3k +1)x + 3y -2=0; (k²+1)x + (k -2)y -5=0.                   -1



Continue.......



MENSURATION

Cube/Cuboid
1) How many 3 metres cubes can be cut from a cuboid measuring 18mx12 mx 9m ?      72

2) A cube of 9cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15m and 12cm, find the rise in water level in the vessel .        4.05cm

3) The length of a cold storage is doubled its breadth. Its height is 3m. The area of its four walls (including doors) is 108m². Find its volume .       216m³

4) Two cube each of 10 cm edge are joined end to end. Find the surface area of the resulting cuboid.        1000 cm²

5) The sum of the length, breath and depth of a cuboid is 19cm and the length of its diagonal is 11cm. Find the surface area of the cuboid.        240cm²

6) A plot of land in the form of a rectangle has a dimension 240m x180m. A drainlet 10m wide is dug all around it (on the outside) and the earth dug out is evenly spread over the plot p, increasing its surface level by 25cm. Find the depth of the drainlet .   1.227m

7) How many planks each of which is 2 m long, 2.5cm broad and 4 cm thick can be cut off from a wooden block 6m long, 15cm broad and 40cm thick ?   180

8) An agricultural field is in the form of a rectangle of length 20m and a width 14m.  A pit 6 m long, 3m wide and 2.5m deep is dug in a corner of the field and the earth taken out of the pit is spreading uniformly over the remaining area of the field. Find the extent to which the level of the field has been raised.       17.18

9) A granary is in the shape of a cuboid of size 8m x 6m x 3m. If a bag of grain occupies a space of 0.65m³, how many bags can be stored in the granary ?    221

10) A long room is 7m long, 6.5m wide and 4 m high. It has one door 3m x 1.4m and three windows, each measuring 2m x 1m. The interior walls are to be colour washed . The contractor charges Rs5.25 per sq.m. Find the cost of the colour washing.    Rs 513.45

11) A room is half as a long again as it broad . The cost of carpeting the room at Rs3.25 per m² is Rs175.50 and the cost of papering the walls at Rs1.40 per m² is Rs 240.80. If 1 door and 2 windows occupy 8m², find the dimensions of the room.    9, 6,6

12)  Water in a canal 30dm wide and 12dm deep, is flowing with a velocity of 20 kmph . How much area will it irrigate in 30 minute if 9cm of outstanding water is desired ?  400000m²

13) A rectangular reservoir is 120m long and 75m wide. At what speed per hour must water flow into it through a square pipe of 20 cm wide so that the water rises by 2.4m in 18 hours.        30 kmph

14) The external length, breadth and height of a closed rectangular wooden box are 18cm, 10cm and 6cm respectively and thickness of the wood is 1/2cm. When the box is empty, it weighs 15kg when filled with sand it weighs 100kg. Find the weight of the cubic cm of wood and cubic cm of sand.       1/9 kg

15) The dimension of a rectangular box are in the ratio 2:3:4 and the difference between the cost of the covering it with sheet of paper at the rate of Rs4 and Rs4.50 per square metre is Rs416. Find the dimension of the box.       8,12,16


RIGHT CIRCULAR CYLINDER




SIMILARITY

1) 

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