Mathematics Delhi Set 2 2018-2019 English Medium Class 10 Question Paper Solution

Find the coordinates of point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4).

Find a rational number between `sqrt2` and `sqrt3`

How many two digits numbers are divisible by 3?

Find If A If tan 2A = cot (A-24°)

Find the value of (sin² 33 + sin² 57°)

For what value of k, the roots of the equation x² + 4x + k = 0 are real?

Find the value of k for which the roots of the equation 3x² - 10x + k = 0 are reciprocal of each other.

In Fig. 1, DE || BC, AD = 1 cm and BD = 2 cm. What is the ratio of the ar (Δ ABC) to the ar (Δ ADE)?

Find the value of k for which the following pair of linear equations has infinitely many solutions. 
2x + 3y = 7, (k +1) x+ (2k -1) y = 4k + 1

A die is thrown once. Find the probability of getting a number which is a prime number

A die is thrown once. Find the probability of getting a number which
lies between 2 and 6.

Find the ratio in which the segment joining the points (1, –3) and (4, 5) is divided by the x-axis? Also, find the coordinates of this point on the x-axis.

A game consists of tossing a coin 3 times and noting the outcome each time. If getting the same result in all the tosses is a success, find the probability of losing the game.

Which term of the AP 3, 15, 27, 39, .... will be 120 more than its 21st term?

If S_n, the sum of first n terms of an AP is given by Sn = 3n² - 4n, find the nth term.

Find the HCF of 1260 and 7344 using Euclid's algorithm.

Show that every positive odd integer is of the form (4q + 1) or (4q + 3), where q is some integer.

The arithmetic mean of the following frequency distribution is 53. Find the value of k.

Find the area of the segment shown in Fig. 2, if the radius of the circle is 21 cm and ∠AOB = 120° `( "Use"  π = (22)/(7))`

In Fig. 3, ∠ACB = 90° and CD ⊥ AB, prove that CD² = BD x AD.

If P and Q are the points on side CA and CB respectively of ΔABC, right angled at C, prove that (AQ² + BP² ) = (AB² + PQ²)

In Fig. 4, a circle is inscribed in a ΔABC having sides BC = 8 cm, AB = 10 cm and AC = 12 cm. Find the lengths BL, CM and AN.

Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/hour. How much area will it irrigate in 30 minutes; if 8 cm standing water is needed?

Prove that is `sqrt2` irrational number.

Find the value of k such that the polynomial x2 − (k + 6)x + 2(2k −1) has sum of its zeros equal to half of their product.

Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).

The line segment joining the points A(2, 1) and B(5, −8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x − y + k = 0, find the value of k.

A father's age is three times the sum of the ages of his two children. After 5 years his age will be two times the sum of their ages. Find the present age of the father.

A fraction becomes `(1)/(3)` when 2 is subtracted from the numerator and it becomes `(1)/(2)` when 1 is subtracted from the denominator. Find the fraction.

Prove that `(sin θ + cosec θ)^2 + (cos θ + sec θ)^2 = 7 + tan^2 θ + cot^2 θ`.

Prove that (1 + cot A - cosec A ) (1 + tan A + sec A) = 2

Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`

The first term of an AP is 3, the last term is 83 and the sum of all its terms is 903. Find the number of terms and the common difference of the AP.

Construct a triangle ABC with side BC = 6 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are `(3)/(4)` times the corresponding sides of the ΔABC.

If the median of the following frequency distribution is 32.5. Find the values of f₁ and f2.

The marks obtained by 100 students of a class in an examination are given below.

Draw 'a less than' type cumulative frequency curves (ogive). Hence find the median.

Prove that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm³. The radii of the top and bottom of the circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of the metal sheet used in making it. (Use π = 3.14)

Two water taps together can fill a tank in `1(7)/(8)`  hours. The tap with longer diameter takes 2 hours less than the tap with a smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.

A man in a boat rowing away from a lighthouse 100 m high takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60° to 30°.
Find the speed of the boat in metres per minute. [Use `sqrt(3` = 1.732]Use 3=1.732">

Two poles of equal heights are standing opposite each other an either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30º, respectively. Find the height of poles and the distance of the point from the poles.