Important Questions Class 10 Maths with solutions pdf

You can download the solutions of this worksheet at the end of this post.

If p and q are natural numbers and p is multiple of q then what is the HCF of p and q ?
What is the ratio of HCF and LCM of the least composite number and least prime number ?
Pove that 2 + 5 is irrational ?
The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7:00 a.m, at what time will they change together next?
If a and b are zeros of the polynomial P(x) = x² -ax-b , then find the value of a² + b².
Find the zeros of the polynomial x² – 3x – m(m+3).
If the sum of the rules of the quadratic equation ky² -11y+(k-23)=0 is 13/21, more than the product of the roots, then find the value of k .
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 the product.
Find the solutions of the pair of equations x+y = a+b and ax – by=a²- b².
Two people are 16 km apart on a straight road. They start working at the same time, if they walk towards each other with different speeds they will meet in 2 hours. Had they walked In the same direction with the same speeds as before, they would have met in 8 hours. Find their working speeds.
A two digit number is 7 times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number.
For what value of m, the quadratic equation mx² -2(m-1)x +(m+2) =0 has two real and equal roots?
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km per hour less, then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.
The sum of two numbers is 34. If 3 is subtracted from one number and 2 is added to another, the product of these two numbers becomes 260.
Find the numbers.In an AP, if the sum of third and seventh term is zero then find its 5th term.
Find the 11th term from the last of the AP 12,8,4,……….,-84.
The 16th term of an AP is one more than twice its 8th term. If the 12th term of the AP is 47, then find its nth term.
If the sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
Solve the equation : 1+5+9+13+……..+x = 1326.
The sum of first 7 terms of an AP is 182. If its fourth term and the 17th term are in the ratio 1:5, find the AP.
The sum of first 7 terms of an AP is 182. If its fourth term and the 17th term are in the ratio 1:5, find the AP.
Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD (produced) in E. Prove that EL= 2BL.
PA, QB and RC are each perpendicular to AC. If AP=x , QB= z, RC =y, AB=a and and BC = b , then prove that 1/x + 1/y = 1/z .
In the given figure, < ADC= <BCA, prove that ACB ADC. Hence find BD if AC=8 cm and AD= 3cm.
Find distance of a point P (x,y) from the origin.
Find the value of x for which the distance between the points P(x,4) and Q(9,10) is 10 units.
Find the ratio in which the y-axis divides the line segment joining the points (6,-4) and(-2,-7). Also find the point of intersection.
A line intersects y axis and x-axis at point P and Q respectively. If R(2,5) is the midpoint of the line segment PQ, then find the coordinates of P and Q.
If SinA -Cos A=0, then find the value of Sin⁴ A + Cos⁴A.
If secM +tanM= p, show that sinM = (p²-1)/p²+1)
The tops of two towers of height X and Y standing on level ground, subtend angles of 30 degree and 60 degree respectively at the centre of the line joining their feet, then find X:Y.
The top of two poles of heights 20 m and 28m are connected with a wire. The wire is inclined to the horizontal at an angle of 30 degree. Find the length of the wire and the distance between the two poles.
From the top of a tower 100m high, a man observes two cars on the opposite side of the tower with angle of depressions 30 degree and 45 degree respectively. Find the distance between the cars.
A man in a Boat rowing away from a Lighthouse 100m high,takes 2 minutes to change the angle of elevation of the top of the Lighthouse from 60 degree to 30 degree. Find the speed of the boat in metre per minute.
From an external point, two tangents are drawn to a circle. Prove that the line joining the external point to the centre of the circle bisect the angle between the two tangents.
A circle touches the side BC of a triangle ABC at a point P and touches AB and AC when produced at Q and R respectively. Show that AQ=1/2 of the perimeter of triangle ABC.
Tangents PA and PB are drawn from an external point P to two concentric circles with Centre O and radii 8 cm and 5 cm respectively, IfAP = 15cm,then find the length of BP.
A chord of a circle of radius 14 cm subtends an angle of 60 degree at the centre. Find the area of the corresponding minor segment of the circle. Also find the area of the major segment of the circle.
A piece of wire 22 cm long is bent into the form of an Arc of a circle subtending and angle of 60 degree at its Centre, find the radius of the circle.
The hour hand of a clock is 6 cm long. What is the angle Swept by it between 7:20 a.m. and 7:55 a.m.
Water in a river which is 3m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in 2 minutes ?
A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 5/6cm³. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of rupees 10 per cm².
A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36cm partly filled with water. If the sphere is completely submerged, then find the height of the water level rises.
From a solid cylinder of height 2.8 cm and diameter 4.2cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.
Find the mean, mode and median of the following frequency.
Find the values of frequencies X and Y in the following frequency distribution table , if N=100 and median is 32.47.
The mean and median of a distribution are 14 ans 15 respectively.What is the value of mode.48.
A bag contains 5 red balls and n green balls. If the probability of drawing a green ball is three times that of a red ball then what is the value of n.49.
A number is selected at random from first 15 natural numbers.Find the probability that it is a multiple of 3 and 4.50.
A bag contains cards number 1 to 49. Occurred is drawn from the bag at random, after mixing the cards thoroughly. Find the polity that the number on the card drawn is a perfect square.