CBSE[All India]_X_Mathematics_2017_Set I
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Q1
What is the common difference of an A.P. in which a_{21}–a_{7}= 84?
Marks:1Answer:
Let first term and common difference of A.P. are a and d respectively.
Given; A_{21} – A_{7} = 84
(a + 20d) – (a + 6d) = 84
20d – 6d = 84
14d = 84
d = 84/14
= 6Therefore, the common difference is 6.

Q2
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:1Answer:
Since, OP is the bisector of angle APB and radius of circle is a.
So, angle APO = 30°.

Q3
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:1Answer:
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°. 
Q4
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:1Answer:
Number of apples in heap = 900
P(a rotten apple) = 0.18
Let number of rotten apple = x 
Q5
Find the value of p, for which one root of the quadratic equation px^{2} – 14x + 8 = 0 is 6 times the other.
Marks:2Answer:

Q6Marks:2
Answer:

Q7
Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.
Marks:2Answer:

Q8
A circle touches all the four sides of a quadrilateral ABCD, Prove that AB + CD = BC + DA
Marks:2Answer:
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

Q9
A line intersects the yaxis and xaxis at the points P and Q respectively. If (2,5) is the midpoint of PQ, then find the coordinates of P and Q.
Marks:2Answer:

Q10
If the distances of P(x, y) from A(5, 1) and B(1, 5) are equal, then prove that 3x = 2y.
Marks:2Answer: