The sum of the 2nd and the 7th terms of an AP is 30. If its 15th

Subject

Mathematics

Class

CBSE Class 10

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Sample Papers

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 Multiple Choice QuestionsShort Answer Type

11.

If the total surface area of a solid hemisphere is 462 cm2, find its volume.

Take π= 227


12.

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.


13.

Find the values of k for which the quadratic equation

9x2 - 3kx + k = 0 has equal roots.


14.

Solve for x:
   

16x - 1 = 15x+1;     x  0, -1


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 Multiple Choice QuestionsLong Answer Type

15.

The largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the volume of the wood left. Use π =227


16.

Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?


17.

In Figure 2, ABCD is a trapezium of area 24.5 sq. cm. In it, AD|| BC,  DAB = 90°, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region.    Take π= 227                  

                     


18.

Find the ratio in which the line segment joining the points A(3,- 3) and B(- 2, 7) is divided by x-axis. Also find the coordinates of the point of division


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19.

The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.


The sum of the  2nd and the 7th terms of an AP is 30

a + d + a + 6d = 302a + 7d = 3015 th term is 1 less than twice the 8th terma + 14d = 2 (a + 7d ) -1a + 14d = 2a + 14d -1a = 1Now,  2 x 1 + 7d = 30d = 4AP; 1, 5, 9,.................


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20.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.


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