Board Paper of Class 10 2019 Maths Abroad(Set 3)  Solutions
General Instructions:
(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
Evaluate:$\frac{\mathrm{tan}65\xb0}{\mathrm{cot}25\xb0}$OR
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 $\sqrt{2}$ and $\sqrt{7}$.
OR
Write the number of zeroes in the end of a number whose prime factorization is 2^{2 }× 5^{3} × 3^{2} × 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 cm^{2} and 121 cm^{2}. If EF = 15⋅4 cm, find BC. VIEW SOLUTION
 Question 7
Find the solution of the pair of equation :
$\frac{3}{x}+\frac{8}{y}=1;$ $\frac{1}{x}\frac{2}{y}=2,x,y\ne 0$
OR
Find the value(s) of k for which the pair of equations $\left\{\begin{array}{l}kx+2y=3\\ 3x+6y=10\end{array}\right.$ 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 $AR=\frac{3}{4}AB.$ Find the coordinates of R. VIEW SOLUTION
 Question 10
How many multiples of 4 lie between 10 and 205 ?
OR
Determine the A.P. whose third term is 16 and 7^{th} term exceeds the 5^{th} 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 rightangled at A. Prove that 4 (BL^{2} + CM^{2}) = 5 BC^{2}.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.
VIEW SOLUTION
 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.
OR
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 $\frac{2+3\sqrt{2}}{7}$ is not a rational number, given that $\sqrt{2}$ is an irrational number. VIEW SOLUTION
 Question 18
Obtain all the zeroes of the polynomial 2x^{4} − 5x^{3} − 11x^{2 }+ 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
Prove that:
(sin θ + 1 + cos θ) (sin θ − 1 + cos θ) . sec θ cosec θ = 2
OR
Prove that :
$\sqrt{\frac{\mathrm{sec}\mathrm{\theta}1}{\mathrm{sec}\mathrm{\theta}+1}+}\sqrt{\frac{\mathrm{sec}\mathrm{\theta}+1}{\mathrm{sec}\mathrm{\theta}1}}=2\mathrm{cosec}\mathrm{\theta}$ VIEW SOLUTION
 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.
OR
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
 Question 26
Solve for x :$\frac{1}{2a+b+2x}=\frac{1}{2a}+\frac{1}{b}+\frac{1}{2x};x\ne 0,x\ne \frac{2ab}{2},a,b\ne 0$
OR
The sum of the areas of two squares is 640 m^{2}. If the difference of their perimeters is 64 m, find the sides of the square. VIEW SOLUTION
 Question 27
 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.
OR
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
OR
The following table gives production yield in kg per hectare of wheat of 100 farms of a village :Production yield
(kg/hectare) :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 cm^{2}. (Take π = 3⋅14) VIEW SOLUTION

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