Board Paper of Class 10 2019 Maths Abroad(Set 3) - Solutions
(i) All questions are compulsory.
(ii) The question paper consists of 30 questions divided into four sections – A, B, C and D.
(iii) Section A comprises 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each.
(iv) There is no overall choice. However, an internal choice has been provided in two questions of 1 mark, two questions of 2 marks, four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternative in all such questions.
(v) Use of calculators is not permitted.
- Question 1
Which term of the A.P. −4, −1, 2, ... is 101? VIEW SOLUTION
- Question 2
Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°. VIEW SOLUTION
- Question 3
Find the value of k for which the quadratic equation kx (x − 2) + 6 = 0 has two equal roots. VIEW SOLUTION
- Question 4
Find a rational number between and .
Write the number of zeroes in the end of a number whose prime factorization is 22 × 53 × 32 × 17. VIEW SOLUTION
- Question 5
Find the distance between the points (a, b) and (−a, −b). VIEW SOLUTION
- Question 6
Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm2 and 121 cm2. If EF = 15⋅4 cm, find BC. VIEW SOLUTION
- Question 7
Find the solution of the pair of equation :
Find the value(s) of k for which the pair of equations has a unique solution. VIEW SOLUTION
- Question 8
Use Euclid's division algorithm to find the HCF of 255 and 867. VIEW SOLUTION
- Question 9
The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that Find the coordinates of R. VIEW SOLUTION
- Question 10
How many multiples of 4 lie between 10 and 205 ?
Determine the A.P. whose third term is 16 and 7th term exceeds the 5th by 12. VIEW SOLUTION
- Question 11
Three different coins are tossed simultaneously. Find the probability of getting exactly one head. VIEW SOLUTION
- Question 12
A die is thrown once. Find the probability of getting.
(a) a prime number.
(b) an odd number VIEW SOLUTION
- Question 13
In Figure 1, BL and CM are medians of a ∆ABC right-angled at A. Prove that 4 (BL2 + CM2) = 5 BC2.OR
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. VIEW SOLUTION
- Question 14
In Figure 2, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region.
- Question 15
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, how much time will the tank be filled ? VIEW SOLUTION
- Question 16
Calculate the mode of the following distribution :
Class : 10 − 15 15 − 20 20 − 25 25 − 30 30 − 35 Frequency : 4 7 20 8 1
- Question 17
Show that is not a rational number, given that is an irrational number. VIEW SOLUTION
- Question 18
Obtain all the zeroes of the polynomial 2x4 − 5x3 − 11x2 + 20x + 12 when 2 and − 2 are two zeroes of the above polynomial VIEW SOLUTION
- Question 19
A motorboat whose speed is 18 km/hr in still water takes on hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. VIEW SOLUTION
- Question 20
(sin θ + 1 + cos θ) (sin θ − 1 + cos θ) . sec θ cosec θ = 2
Prove that :
- Question 21
In what ratio does the point P(−4, y) divide the line segment joining the points A(−6, 10) and B(3, −8) ? Hence find the value of y.
Find the value of p for which the points (−5, 1), (1, p) and (4, −2) are collinear. VIEW SOLUTION
- Question 22
ABC is a right triangle in which ∠B = 90°. If AB = 8 cm and BC = 6 cm, find the diameter of the circle inscribed in the triangle. VIEW SOLUTION
- Question 23
In an A.P., the first term is −4, the last term is 29 and the sum of all its terms is 150. Find its common difference VIEW SOLUTION
- Question 24
Draw a circle of radius 4 cm. From a point 6 cm away from its centre, construct a pair of tangents to the circle and measure their lengths VIEW SOLUTION
- Question 25
Prove that :
2(sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) + 1 = 0 VIEW SOLUTION
- Question 26
Solve for x :
The sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m, find the sides of the square. VIEW SOLUTION
- Question 27
In ∆ ABC (Figure 3), AD ⊥ BC. Prove that
AC2 = AB2 +BC2 − 2BC × BD
- Question 28
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole. VIEW SOLUTION
- Question 29
Calculate the mean of the following frequency distribution :
Class : 10−30 30−50 50−70 70−90 90−110 110−130 Frequency : 5 8 12 20 3 2
The following table gives production yield in kg per hectare of wheat of 100 farms of a village :
40−45 45−50 50−55 55−60 60−65 65−70 Number of farms 4 6 16 20 30 24
Change the distribution to a 'more than type' distribution, and draw its ogive. VIEW SOLUTION
- Question 30
A container opened at the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container, at the rate of ₹ 50 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 10 per 100 cm2. (Take π = 3⋅14) VIEW SOLUTION