The decimal expansion of the rational number will terminate after how many places of decimals?
Answer :
The given expression i.e., can be rewritten as
Now, on dividing 0.043 by 2, we obtain = 0.0215.
Thus, the given expression will terminate after 4 decimal places.
For what value of k, (−4) is a zero of the polynomial x^{2} − x − (2k + 2)?
Answer :
Let p(x) = x^{2} − x − (2k + 2).
If (−4) is a zero of p(x), then p (−4) = 0.
p(−4) = 0
Þ (−4)^{2} − (−4) − 2k − 2 = 0
Þ 16 + 4 − 2k − 2 = 0
Þ 18 − 2k = 0
Þ 2k = 18
Þk = 9
Thus, the required value of k is 9.
For what value of p, are 2p − 1, 7 and 3p three consecutives terms of an A.P.?
Answer :
Let 2p − 1, 7, and 3p 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
⇒ 7 − (2p − 1) = 3p − 7
⇒ 7 − 2p + 1 = 3p − 7
⇒ 8 − 2p = 3p − 7
⇒ 15 = 5p
Thus, if p = 3, then 2p − 1, 7, and 3p are the three consecutive terms of an A.P.
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 :
If, then find the value of (2cot^{2}θ + 2).
Answer :
Find the value of a so that the point (3,
a) lies on the line represented by
2x − 3y = 5.
Answer :
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 :
Find the distance between the points and.
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 :
If the polynomial is divided by another polynomial, the remainder comes out to be, find a and b.
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 :
If S_{n}, the sum of first n terms of an A.P. is given by S_{n} = , then find its nth term.
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 :
Prove that is an irrational number.
Answer :
Solve the following pair of equations:
Answer :
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.
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. 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 :
Find the value of sin 30° geometrically.
OR
Without using trigonometrical tables, evaluate:
Answer :
Find the point on y-axis which is equidistant from the points (5, −2) and (−3, 2)
OR
The line segment joining the points A (2, 1) and B (5, −8)
is trisected at the points P and Q such that P is nearer to A. If
P also lies on the line given by
2x − y + k
= 0, find the value of k.
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 :
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 :
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 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 :
Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
Using the above result, do the following:
In Fig. 7, DE||BC and BD = CE. Prove that ΔABC is an isosceles triangle.
Fig. 7
Answer :
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
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. 8, 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 :
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 :
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.
Fig. 2
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.