Write whether on simplification gives a rational or an irrational number.
Answer :
The given expression can be simplified as:
Since 6 is a rational number, the expression on simplification gives a rational number.
If α, β are the zeroes of the polynomial 2y^{2} + 7y + 5, write the value of α + β+ αβ.
Answer :
Since α and βare the zeroes of the polynomial 2y^{2} + 7y + 5:
Thus, the value of α + β+ αβ is −1.
If the sum of the first q terms of an A.P. is 2q + 3q^{2}, what is its common difference?
Answer :
Let a and d respectively be the first term and common difference of the A.P.
It is given that S_{q} = 2q + 3q^{2}
∴ S_{1} = 2 × 1 + 3 × 1^{2} = 5
⇒ a_{1} + S_{1} = 5
S_{2} = 2 × 2 + 3 × 2^{2} = 4 + 12 = 16
⇒ a_{1} + a_{2} = 16
⇒ a + (a + d) = 16
⇒ 2 × 5 + d = 16
⇒ d =16 − 10 = 6
Thus, the common difference of the A.P. is 6.
In figure 1, CP and CQ are tangents from an external point C to a circle with O. AB are another tangent which touches the circle at R. If CP =11 cm and BR = 4 cm, find the length of BC.
Answer :
In Figure 2, DE||BC in ΔABC such that BC = 8 cm, AB = 6 cm and DA = 1.5. Find DE.
Answer :
If and , find the value of .
Answer :
What is the distance between the points A(c, 0) and B(0, −c)?
Answer :
In ΔABC, right-angled at C, AC = 6 cm and AB = 12 cm. Find ∠A.
Answer :
The slant height of the frustum of a cone is 5 cm. If the difference the radii of its two circular ends is 4 cm, write the height of the frustum.
Answer :
A die is thrown once. What is the probability of getting a number greater than 4?
Answer :
For what value of k, is 3 a zero of the polynomial 2x^{2} + x + k?
Answer :
Find the value of m for which the pair of linear equations 2x + 3y − 7 = 0 and (m − 1) x + (m + 1) y = (3m − 1) has infinitely many solutions.
Answer :
Find the common differnece of an A.P. whose first term in 4, the lasta term is 49 and the sum of all its terms is265.
Answer :
In figure 3, there are two concentric circles with centre O and of radii 5 cm and 3 cm. From an external point P, Tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.
Answer :
Without using trigonometric tables, evaluate the following:
OR
Find the value of sec60° geometrically.
Answer :
Prove that is an irrational number.
Answer :
Solve the following pair of liner equations for x and y:
x + y = 2ab
OR
The sum of the numerator and the denominator of a fraction is 4 more than twice the numerator. If 3 is added to each of the numerator and denominator, their ratio becomes 2:3 Find the fraction.
Answer :
In an A.P., the sum of its first ten terms is − 80 and the sum of its next ten terms is − 280. Find the A.P.
Answer :
In figure 4, ABC is an isosceles triangle in which AB = AC. E is a point on the side CB produced, Such that FE ⊥ AC. If AD ⊥ CB, prove that AB × EF = AD × EC.
Answer :
Prove the following:
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
OR
Prove the following:
sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A
Answer :
Construct a triangle ABC in which AB = 8 cm, BC = 10 cm and AC = 6 cm. Then construct another triangle whose sides areof the corresponding sides of ABC.
Answer :
Point P divides the line segment joining the points A (−1, 3) and B (9, 8) such that If P lies on the line x − y + 2 = 0, find the value of k.
Answer :
If the points (p, q); (m, n) and (p − m, q − n) are collinear, show that pn = qm.
Answer :
The rain-water collected on the roof of a building, of dimensions 22 m × 20 m, is drained into a cylindrical vessel having base diameter 2 m and height 3.5 m. If the vessel is full up to the brim, find the height of rain-water on the roof
OR
In figure 5, AB and CD are two perpendicular diameters of a circle with centre O. If OA = 7 cm, find the area of the shaded region.
Answer :
A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears
(i) a two digit number,
(ii) a number which is a perfect square.
Answer :
A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.
Answer :
In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite the first side is a right angle.
Using the above, do the following:
In an isosceles triangle PQR, PQ = QR and PR^{2} = 2 PQ^{2}. Prove that ∠Q is a right angle.
Answer :
A man on the deck of a ship, 12 m above water level, observes that the angle of elevation of the top of a cliff is 60° and the angle of depression of the base of the cliff is 30°. Find the distance of the cliff from the ship and the height of the cliff. [Use = 1.732]
OR
The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake.
Answer :
The surface area of a solid metallic sphere is 616 cm^{2}. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed.
OR
The difference between the outer and inner curved surface areas of a hollow right circular cylinder, 14 cm long, is 88 cm^{2}. If the volume of metal used in making the cylinder is 176 cm^{3}, find the outer and inner diameters of the cylinder.
Answer :
Draw ‘less than ogive’ and ‘more than ogive’ for the following distribution and hence find its median.
Class |
20 − 30 |
30 − 40 |
40 − 50 |
50 − 60 |
60 − 70 |
70 − 80 |
80 − 90 |
Frequency |
8 |
12 |
24 |
6 |
10 |
15 |
25 |
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.