A card is drawn at random from a well -shuffled fled pack of 52

Subject

Mathematics

Class

CBSE Class 10

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Sample Papers

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 Multiple Choice QuestionsShort Answer Type

1.

In Fig. , PQ is tangent at point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°, find ∠PCA.

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2.

For what value of k will k+9, 2k-1 and 2k+7 are the consecutive terms of an A.P?

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3.

A ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

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4.

A card is drawn at random from a well -shuffled fled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.


There space are space 26 space red space cards space including space 2 space red space queens.
Two space more space queens space with space 26 space red space cards space will space be space space 26 plus 2 space equals space 28
therefore space Probability space of space getting space straight a space red space card space or space straight a space queen space equals space 28 over 52
therefore Probability space of space getting space neither space straight a space red space card space nor space space queen space equals
1 minus 28 over 52 space equals space 24 over 52 equals 6 over 13

1.

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5.

If -5 is a root of the quadratic equation 2x2  + px – 15 = 0 and the quadratic equation p(x2 + x)k = 0 has equal roots, find the value of k.

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6.

Let P and Q be the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4) such that P is nearer to A. Find the coordinates of P and Q.

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7.

In Fig.2, a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that AB + CD = BC + DA.

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8.

Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.

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9.

The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.

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10.

In Fig, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP=2r, show that  ∠ OTS = ∠ OST = 30°.

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