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Mathematics - Questions

CBSE 10th Grade Standard Questions

**find the value(s) of k for which the pair of linear equation kx - 3y = k - 2 and 12x + ky = k has no solution.**

(class:
10th std
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mathematics

**The sum of 4th and 8th terms of an A.P. is 24 and sum of 6th and 10th terms. is 44. Find A.P.**

(class:
10th std
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mathematics

**Find the point on y-axis which is equidistant from the points (5, -2) and (-3, 2).**

(class:
10th std
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mathematics

**From the top of a building 60 m high, the angles of depression of the top and the bottom of a tower are observed to be 30° and 60°. Find the height of the tower. **

(class:
10th std
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mathematics

**A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.**

(class:
10th std
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mathematics

**A two digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.**

(class:
10th std
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mathematics

**Prove that three times the square of any side of an equilateral-triangle is equal to four times the square of the altitude.**

(class:
10th std
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mathematics

**A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle.**

(class:
10th std
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mathematics

**Find the area of the segment of a circle, given that the angle of the sector is 120° and the radius of the circle is 21cm.**

(class:
10th std
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mathematics

**Divide a line segment of length 8 cm internally in the ratio 3 : 4.**

(class:
10th std
)
mathematics

**Show that four points (0, -1), (8, 3) (6, 7) and (-2, 3), taken in order, are the vertices of rectangle Also, find its area.**

(class:
10th std
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mathematics

**If the point C (-1, 2) divides internally the line segment joining A (2, 5) and B in ratio 3:4, find the coordinates of B.**

(class:
10th std
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mathematics

**Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3.**

(class:
10th std
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mathematics

**Find the sum of first 20 terms of an A.P., in which 3rd term is 7 and 7th term is two more than thrice of its 3trd term.**

(class:
10th std
)
mathematics

**Find the value of x, if the distance between the points (x, -1) and (3, 2) is 5.**

(class:
10th std
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mathematics

**It is known that a box of 600 electric bulbs contains 12 defective bulbs. One bulb is taken out at random from this box. What is the probability that it is a non-defective bulb?**

(class:
10th std
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mathematics

**An unbiased die is thrown. What is the probability of getting a multiple of 3?**

(class:
10th std
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mathematics

**Which type of triangles are similar?**

(class:
10th std
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mathematics

**Three cubes whose edges measure 3 cm, 4 cm and 5 cm respectively to form a single cube. Find its edge.**

(class:
10th std
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mathematics

**Find the mode of the following data:120, 110, 130, 110, 120, 140, 130, 120, 140, 120**

(class:
10th std
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mathematics

**Show that x = 2, y = 1 is a solution of the system of simultaneous linear equations 3x-2y=4, 2x+y=5**

(class:
10th std
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mathematics

**In a ?ABC, right angled at A, if AB = 12, AC = 5 and BC = 13, find sinB.**

(class:
10th std
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mathematics

**What is the common point of a tangent and the circle called?**

(class:
10th std
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mathematics

**Show that any positive integer is of the form 3q, or, 3q + 1 or, 3q + 2 for some integer q.**

(class:
10th std
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mathematics

**ABC is a right-angled triangle right angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 6 cm and 8 cm. Find the radius of the circle.**

(class:
10th std
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mathematics

**Water is flowing at the rate of 5 km / hr through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Determine the time in which the level of the water in the tank will rise by 7 cm.**

(class:
10th std
)
mathematics

**Determine the height of a mountain if the elevation of its top at an unknown distance from the base is 30° and at a distance 10 km further off from the mountain, along the same line, the angle of elevation is 15°**

(class:
10th std
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mathematics

**A plane left 30 minutes later then the scheduled time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km / hr from its usual speed. Find its usual speed.**

(class:
10th std
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mathematics

**The perimeter of a sector of a circle of radius 5.4 cm is 17.4 cm. Find the area of the sector.**

(class:
10th std
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mathematics

**Take a point O on the plane of the paper. With O as centre draw a circle of radius 3 cm. Take a point P on this circle and draw a tangent at P**

(class:
10th std
)
mathematics

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