Board Paper of Class 10 2019 Maths Abroad(Set 2)  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
For what values of k does the quadratic equation 4x^{2} − 12x − k = 0 have no real roots? VIEW SOLUTION
 Question 2
Find the distance between the points (a, b) and (−a, −b). VIEW SOLUTION
 Question 3
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 4
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 5
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 6
Find the number of terms in the A.P. : $18,15\frac{1}{2},13,...,47.$ VIEW SOLUTION
 Question 7
A bag contains 15 balls, out of which some are white and the others are black. If the probability of drawing a black ball at random from the bag is $\frac{2}{3}$, then find how many white balls are there in the bag. VIEW SOLUTION
 Question 8
A card is drawn at random from a pack of 52 playing cards. Find the probability of drawing a card which is neither a spade nor a king. VIEW SOLUTION
 Question 9
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 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
Use Euclid's division algorithm to find the HCF of 255 and 867. VIEW SOLUTION
 Question 12
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 13
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 14
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 15
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 16
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 17
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 18
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 19
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 20
Prove that $2+3\sqrt{3}$ is an irrational number when it is given that $\sqrt{3}$ is an irrational number. VIEW SOLUTION
 Question 21
Sum of the areas of two squares is 157 m^{2}. If the sum of their perimeters is 68 m, find the sides of the two squares. VIEW SOLUTION
 Question 22
Find the quadratic polynomial, sum and product of whose zeroes are −1 and −20 respectively. Also find the zeroes of the polynomial so obtained. VIEW SOLUTION
 Question 23
A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away on time, it has to increase its speed by 250 km/hr from its usual speed. Find the usual speed of the plane.ORFind the dimensions of a rectangular park whose perimeter is 60 m and area 200 m^{2}. VIEW SOLUTION
 Question 24
Find the value of x, when in the A.P. given below
2 + 6 + 10 + ... + x = 1800. VIEW SOLUTION
 Question 25
If sec θ + tan θ = m, show that $\frac{{m}^{2}1}{{m}^{2}+1}=\mathrm{sin}\theta $. VIEW SOLUTION
 Question 26
 Question 27
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 28
Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are $\frac{3}{5}$ of the corresponding sides of the first triangle. 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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