Board Paper of Class 10 2019 Maths Abroad(Set 2) - Solutions

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

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

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

How many multiples of 4 lie between 10 and 205 ?
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Determine the A.P. whose third term is 16 and 7^th term exceeds the 5^th by 12. VIEW SOLUTION

Use Euclid's division algorithm to find the HCF of 255 and 867. VIEW SOLUTION

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

Prove that:

(sin θ + 1 + cos θ) (sin θ − 1 + cos θ) . sec θ cosec θ = 2

                                 OR

Prove that :

$\sqrt{\frac{\sec \mathrm{\theta }-1}{\sec \mathrm{\theta }+1}+}\sqrt{\frac{\sec \mathrm{\theta }+1}{\sec \mathrm{\theta }-1}}=2\mathrm{cosec} \mathrm{\theta }$ VIEW SOLUTION

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

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

In Figure 1, BL and CM are medians of a ∆ABC right-angled at A. Prove that 4 (BL² + CM²) = 5 BC².  
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

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

Calculate the mode of the following distribution :
 

Class :	10 − 15	15 − 20	20 − 25	25 − 30	30 − 35
Frequency :	4	7	20	8	1

VIEW SOLUTION

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.
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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

Prove that $2+3\sqrt{3}$ is an irrational number when it is given that $\sqrt{3}$ is an irrational number. VIEW SOLUTION

Sum of the areas of two squares is 157 m². If the sum of their perimeters is 68 m, find the sides of the two squares. VIEW SOLUTION

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

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. Find the dimensions of a rectangular park whose perimeter is 60 m and area 200 m². VIEW SOLUTION

Find the value of x, when in the A.P. given below
2 + 6 + 10 + ... + x = 1800. VIEW SOLUTION

If sec θ + tan θ = m, show that $\frac{m^2-1}{m^2+1}=\sin \theta$. VIEW SOLUTION

In ∆ ABC (Figure 3), AD ⊥ BC. Prove that
AC² = AB² +BC² − 2BC × BD
VIEW SOLUTION

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.

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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

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

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

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