CBSE[All India]_X_Mathematics_2017_Set III
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The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. what is the number of rotten apples in the heap?Marks:1
Number of apples in heap = 900
P(a rotten apple) = 0.18
Let number of rotten apple = x
If a tower 30 m high, casts a shadow m long on the ground, then what is the angle of elevation of the sun?Marks:1
Let the tower AB has height of 30 m and length of its shadow
be 10√3 m. Let the angle of elevation of sun be θ .
Therefore, the angle of elevation of the sun is 60°.
If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP.Marks:1
Since, OP is the bisector of angle APB and radius of circle is a.
So, angle APO = 30°.
What is the common difference of an A.P. in which a21–a7= 84?Marks:1
Let first term and common difference of A.P. are a and d respectively.
Given; A21 – A7 = 84
(a + 20d) – (a + 6d) = 84
20d – 6d = 84
14d = 84
d = 84/14
Therefore, the common difference is 6.
A circle touches all the four sides of a quadrilateral ABCD, Prove that AB + CD = BC + DAMarks:2
Since, the tangents drawn on a circle from same external point are equal.
AP = AS
BP = BQ
CQ = CR
DR = DS
LHS: AB + CD = (AP + BP) + (CR + RD)
= AS + BQ + CQ + DS
= (AS + DS) + (BQ + CQ)
= AD + BC = RHS
Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.Marks:2
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2,-5) is the mid-point of PQ, then find the coordinates of P and Q.Marks:2
If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.Marks:2
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.Marks:2
For what value of n, are the nth terms of two A.P.s 63, 65, 67,… and 3, 10, 13,… equal?Marks:2