Mathematics Abroad Set(2) 2018-2019 English Medium Class 10 Question Paper Solution

For what values of k does the quadratic equation 4x2 − 12x − k = 0 has no real roots?

Find the distance between the points (a, b) and (−a, −b).

Find a rational number between `sqrt(2)  "and" sqrt(7)`.

Write the number of zeroes in the end of a number whose prime factorization is 2² × 5³ × 3² × 17.

Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm² and 121 cm². If EF = 15⋅4 cm, find BC.

Evaluate:

`(tan 65^circ)/(cot 25^circ)`

Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.

Find the number of terms in the A.P.: 18, `15 1/2, 13, ...., -47.`

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 `2/3`, then find how many white balls are there in the bag.

A card is drawn at random from a pack of 52 playing cards. Find the probability of drawing a card that is neither a spade nor a king.

Find the solution of the pair of the equation :
`3/x + 8/y = - 1; 1/x - 2/y = 2`, x, y ≠ 0

Find the value (s) of k for which the pair of equations

How many multiples of 4 lie between 10 and 205?

Determine the A.P. whose 3^rd term is 16 and the 7^th term exceeds the 5^th term by 12.

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

The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.

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

Prove that:

`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`

In what ratio does the point P(−4, y) divides 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.

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.

In the given figure, 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

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.

Calculate the mode of the following distribution:

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 form 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/h, in how much time will the tank be filled?

Prove that `2 + 3sqrt(3)` is an irrational number when it is given that `sqrt(3)` is an irrational number.

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.

Find the quadratic polynomial, sum, and product of whose zeroes are −1 and −20 respectively. Also, find the zeroes of the polynomial so obtained.

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.

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

If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`

In ∆ ABC, AD ⊥ BC.
Prove that  AC² = AB² +BC² − 2BC x BD

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.

Construct a triangle with sides 5 cm, 6 cm, and 7 cm and then another triangle whose sides are `3/5` of the corresponding sides of the first triangle.

Calculate the mean of the following frequency distribution :

The following table gives production yield in kg per hectare of wheat of 100 farms of a village :

Change the distribution to a 'more than type' distribution, and draw its ogive.

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)