Find the [HCF × LCM] for the numbers 100 and 190.
Answer :
For two numbers a and b, HCF × LCM = a × b
∴ For the given numbers 100 and 190:
HCF × LCM = 100 × 190
HCF × LCM = 19000
If 1 is a zero of the polynomial p(x) = ax^{2} − 3(a − 1) x − 1, then find the value of a.
Answer :
If 1 is a zero of polynomial p(x), then p(1) = 0.
∴ p(1) = a(1)^{2} − 3(a − 1) (1) − 1 = 0
⇒ a − 3a + 3 − 1 = 0
⇒ −2a = −2
⇒ a = 1
Thus, the value of a is 1.
In ΔLMN, ∠L = 50° and ∠N = 60°. If ΔLMN ∼ ΔPQR, then find ∠Q.
Answer :
∠L + ∠M + ∠N = 180° (Angle sum property)
Substituting ∠L = 50° and ∠N = 60° in this equation:
50° + ∠M + 60° = 180°
∠M = 70°
It is given that ΔLMN ∼ ΔPQR.
We know that corresponding angles in similar triangles are of equal measures.
∴ ∠M = ∠Q = 70°
Thus, the measure of ∠Q is 70°.
If sec^{2}θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
Answer :
If the diameter of a semicircular protractor is 14 cm, then find its perimeter.
Answer :
Find the number of solutions of the following pair of linear equations:
x + 2y − 8 = 0
2x + 4y = 16
Answer :
Find the discriminant of the quadratic equation
Answer :
If, a, and 2 are three consecutive terms of an A.P., then find the value of a.
Answer :
In figure 1, ΔABC is circumscribing a circle. Find the length of BC.
Answer :
Two coins are tossed simultaneously. Find the probability of getting exactly one head.
Answer :
Find all the zeroes of the polynomial x^{3} + 3x^{2} − 2x − 6, if two of its zeroes are and.
Answer :
Which term of the A.P. 3, 15, 27, 39… will be 120 more than its 21^{st} term?
Answer :
In Figure 2, ΔABD is a right triangle, right-angled at A and AC ⊥BD. Prove that AB^{2}= BC . BD.
Answer :
If , then evaluate
OR
Find the value of tan 60°, geometrically.
Answer :
If the points A (4, 3) and B (x, 5) are on the circle with the centre O (2, 3), find the value of x.
Answer :
Prove that is an irrational number.
Answer :
Solve for x and y:
ax− by= 2ab
OR
The sum of two numbers is 8. Determine the numbers if the sum of their reciprocals is
Answer :
The sum of first six terms of an arithmetic progression is 42. The ratio of its 10^{th}term to its 30^{th}term is 1 : 3. Calculate the first and the thirteenth term of the A.P.
Answer :
Draw a right triangle in which sides (other than hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are times the corresponding sides of the first triangle.
Answer :
In Figure, 3, AD ⊥ BC and BD CD. Prove that 2CA^{2} = 2AB^{2} + BC^{2}.
OR
In Figure 4, M is mid-point of side CD of a parallelogram ABCD. The line BM is drawn intersecting AC at L and AD produced at E. Prove that EL = 2 BL.
Answer :
Find the ratio in which the point (2, y) divides the line segment joining the points A (−2, 2) and B (3, 7). Also find the value of y.
Answer :
Find the area of the quadrilateral ABCD whose vertices are A(−4, −2), B(−3, −5), C (3, −2) and D (2, 3).
Answer :
The area of an equilateral triangle is cm^{2}. Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of triangle not included in the circles. [Take= 1.73]
OR
Figure 5 shows a decorative block which is made of two solids − a cube and a hemisphere. The base of the block is a cube with edge 5 cm and the hemisphere, fixed on the top, has a diameter of 4.2 cm. Find the total surface area of the block. [Take π=]
Answer :
Two dice are thrown simultaneously. What is the probability that
(i) 5 will not come up on either of them?
(ii) 5 will come up on at least one?
(iii) 5 will come up at both dice?
Answer :
Solve the following equation for x:
9x^{2}− 9(a+ b)x+ (2a^{2}+ 5ab + 2b^{2}) = 0
OR
If (−5) is a root of the quadratic equation 2x^{2}+ px − 15 = 0 and the quadratic equation p(x^{2}+ x) + k= 0 has equal roots, then find the values of pand k.
Answer :
Prove that the lengths of the tangents drawn from an external point to a circle are equal.
Using the above theorem prove that:
If quadrilateral ABCD is circumscribing a circle, then AB + CD = AD + BC
Answer :
An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the distance between the two planes at that instant.
Answer :
A juice seller serves his customers using a glass as shown in Figure 6. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass. If the height of the glass is 10 cm, find the apparent capacity of the glass and its actual capacity. (Use π= 3.14)
OR
A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of
(i) water displaced out of the cylindrical vessel.
(ii) water left in the cylindrical vessel.
[Take π]
Answer :
During the medical check-up of 35 students of a class their weights were recorded as follows:
Weight (in kg) |
Number of students |
38 − 40 |
3 |
40 − 42 |
2 |
42 − 44 |
4 |
44 − 46 |
5 |
46 − 48 |
14 |
48 − 50 |
4 |
50 − 52 |
3 |
Draw a less than type and a more than type ogive from the given data. Hence obtain the median weight from the graph.
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.