Mathematics 30/1/1 2018-2019 English Medium Class 10 Question Paper Solution

Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, -3) and B is (1, 4).

For what values 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.

Find A if tan 2A = cot (A-24°).

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

How many two digits numbers are divisible by 3?

In fig.DE || BC ,AD = 1 cm and BD = 2 cm. what is the ratio of the ar(ΔABC) to the  ar (ΔADE)?

Find a rational number between `sqrt(2) " and sqrt(3) `.

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.

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 S_n =3n²- 4n, find the nth term.  

Find the ratio In which is the segment joining the points (1, - 3} and (4, 5) ls divided by 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 result in the tosses is a success, find the probability of losing the game. 

A die is thrown once. Find the probability of getting a number which (i) is a prime number (ii) lies between 2 and 6.

Find c if the system of equations cx+3y+(3 - c ) = 0, 12x + cy - c = 0 has infinitely many solutions?

Prove that is `sqrt2` irrational number.

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

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.

Find the point on the y-axis which is equidistant from the points (S, - 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.

Prove that :(sinθ+cosecθ)²+(cosθ+ secθ)² = 7 + tan² θ+cot² θ.

Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2. 

ln Figure, PQ is a chord of length 8 cm of a circle of radius 5 cm and centre O. The tangents at P and Q intersect at point T. find the length of TP.

In the following Figure ∠ACB= 90° and CD ⊥ AB, prove that  CD²  = BD × 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)

Find the area of the shaded region in the figure If ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. (Take π= 3.14)

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

Find the mode of the following frequency distribution.

Two water taps together can fill a tank in `1 7/8` hours. The tap with a 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.

If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.

Prove that `(sin "A" - cos "A" + 1)/(sin "A" + cos "A" - 1) = 1/(sec "A" - tan "A")`

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 `sqrt3` = 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.

Construct a ΔABC in which CA = 6 cm, AB = 5 cm and ∠BAC = 45°. Then construct a triangle whose sides are `3/5` of the corresponding sides of ΔABC.

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. 

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

If the median of the following frequency distribution is 32.5, find the values of `f_1 and f_2`.

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

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