Mathematics 30/4/3 2018-2019 English Medium Class 10 Question Paper Solution

Which term of the A.P. −4, −1, 2, ... is 101?

Evaluate:
`(tan 65°)/(cot 25°)`

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

Find the value of k for which the quadratic equation kx (x − 2) + 6 = 0 has two equal roots.

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.

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

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

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
kx +  2y = 3
3x + 6y = 10 has a unique solution.

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.

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.

Three different coins are tossed simultaneously. Find the probability of getting exactly one head.

A die is thrown once. Find the probability of getting.
(a) a prime number.
(b) an odd number

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 , two concentric circles with centre O, have radii 21cm and 42 cm. If ∠ AOB = 60°, find the area of the shaded region. [use π=22/7]

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?

Calculate the mode of the following distribution:

Show that `(2+3√2)/7` is not a rational number, given that √2 is an irrational number.

Obtain all the zeroes of the polynomial 2x⁴ − 5x³ − 11x² + 20x + 12 when 2 and − 2 are two zeroes of the above polynomial.

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

Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2cosecθ`

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 an AP, the first term is -4, the last term is 29 and the sum of all its terms is 150. Find its common difference.

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.

Prove that :
2(sin⁶ θ + cos⁶ θ) − 3 (sin⁴ θ + cos⁴ θ) + 1 = 0

Solve for x : `1/(2a + b + 2x) =1/(2a) + 1/b + 1/(2x); x ≠ 0, x ≠ (−2a −b)/2`, a, b ≠ 0

The sum of the areas of two squares is `640m^2` . If the difference in their perimeter be 64m, find the sides of the two square 

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.

Find the mean of each of the following frequency distributions

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)