In Fig. 1, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm, and BC = 7 cm, then find the length of BR.
Fig. 1
Answer :
It is given that CP and CQ are the tangents from the same point C.
We know that the lengths of tangents drawn from an external point to a circle are equal.
CP = CQ = 11 cm [CP = 11 cm]
∴CQ = 11 cm
⇒ CB + BQ = 11 cm
⇒ 7 cm + BQ = 11 cm [BC = 7 cm]
⇒ BQ = 11 cm − 7 cm = 4 cm
According to the given figure, BQ and BR are the tangents from the same point B.
∴BR = BQ = 4 cm.
Thus, the length of BR is 4 cm.
If, then find the value of (2cot^{2}θ + 2).
Answer :
It is given that.
For what value of p are 2p + 1, 13 and 5p − 3, three consecutives terms of an A.P.?
Answer :
Let 2p + 1, 13, and 5p − 3 be the three consecutive terms of an A.P.
The difference between any two consecutive terms of an A.P. is equal.
∴2^{nd} term − 1^{st} term = 3^{rd} term − 2^{nd} term
⇒ 13 − (2p + 1) = 5p − 3 − 13
⇒ 13 − 2p − 1 = 5p − 16
⇒ 12 − 2p = 5p − 16
⇒ 28 = 7p
Thus, if p = 4, then 9, 13, and 17 are the three consecutive terms of an A.P.
A cylinder and a cone are of same base radius and of same height. Find the ratio of the volume of cylinder to that of the cone.
Answer :
Write the median class of the following distribution:
Classes Frequency
0−10 4
10−20 4
20−30 8
30−40 10
40−50 12
50−60 8
60−70 4
Answer :
In Fig, 2, ∠M = ∠N = 46°. Express x in terms of a, b and c where a, b and c are lengths, of LM, MN and NK respectively.
Answer :
For what value of k, (−4) is a zero of the polynomial x^{2} − x − (2k + 2)?
Answer :
Find the distance between the points and.
Answer :
Find the value of a so that the point (3,
a) lies on the line represented by
2x − 3y = 5.
Answer :
The decimal expansion of the rational number will terminate after how many places of decimals.
Answer :
Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that ∠APB = 2 ∠OAB.
Fig. 3
OR
Prove that the parallelogram circumscribing a circle is a rhombus.
Answer :
If the polynomial is divided by another polynomial, the remainder comes out to be, find a and b.
Answer :
If S_{n}, the sum of first n terms of an A.P. is given by S_{n} = , then find its nth term.
Answer :
Find the value(s) of k for which the pair of linear equations kx + 3y = k − 2 and 12x + ky = k has no solution.
Answer :
Prove that is an irrational number.
Answer :
The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs.
Answer :
The sum of 5th and 9th terms of an A.P. is 72 and sum of 7th and 12th terms is 97. Find the A.P.
Answer :
In Fig. 4, ΔABC is right angled at C and DE ⊥ AB. Prove that ΔABC ∼ ΔADE and hence find the lengths of AE and DE.
Fig. 4
OR
In Fig, 5, DEFG is a square and ∠BAC = 90°. Show that DE^{2} = BD × EC.
Fig. 5
Answer :
If P (x, y) is any point on the line joining the points A (a, 0) and B (0, b), then show that .
Answer :
Solve the following pair of equations:
Answer :
Find the point on x-axis which is equidistant from the points (2, − 5) and (− 2, 9)
OR
The line segment joining the points P (3, 3) and Q (6, − 6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
Answer :
Find the value of sin 30° geometrically.
OR
Without using trigonometrical tables, evaluate:
Answer :
Construct a ΔABC in which BC = 6.5 cm, AB = 4.5 cm and ∠ABC = 60°. Construct a triangle similar to this triangle whose sides are of the corresponding sides of the triangle ABC.
Answer :
In Fig. 6, PQ = 24 cm, PR = 7 cm and O is the centre of the circle. Find the area of shaded region (take π = 3.14)
Fig. 6
Answer :
From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and of base radius 6 cm, is hollowed out. Find the volume of the remaining solid correct to two places of decimals. Also find the total surface area of the remaining solid. (take π = 3.1416)
OR
In Fig. 7, ABC is a right triangle right angled at A. Find the area of shaded region if AB = 6 cm, BC = 10 cm and O is the centre of the incircle of ΔABC.
(take π = 3.14)
Answer :
Prove that, in a right triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
Using the above, prove the following:
Prove that, in a ΔABC, if AD is perpendicular to BC, then AB^{2} + CD^{2} = AC^{2} + BD^{2}.
Answer :
The angles of depression of the top and bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings.
Answer :
The following table gives the daily income of 50 workers of a factory:
Daily income (in Rs.) |
100−120 |
120−140 |
140−160 |
160−180 |
180−200 |
Number of workers |
12 |
14 |
8 |
6 |
10 |
Find the Mean, Mode and Median of the above data.
Answer :
The sum of the squares of two consecutive odd numbers is 394. Find the numbers.
OR
Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Answer :
10th Maths Paper Solutions Set 3 : CBSE Delhi Previous Year 2013 will be available online in PDF book soon. The solutions are absolutely Free. Soon you will be able to download the solutions.