Cbse Class 10 Maths Important 4 Marks Questions

Maths requires skills and understanding rather than just memorizing. As every other subject just requires knowledge where memorization technique works fine, but for the subject of mathematics, it requires deep conceptual knowledge.

We at BYJU’S provide students of class 10th with important 4 marks question which students can practice them. Students can get a replica of these question, provided here, in their board examination.

Students preparing for CBSE Class 10 Maths Board Examination are advised to practice question provided below:

Important 4 Marks Questions for Class 10 Maths Board are as follows-

Question 1- Solve for x:

\(\frac{1}{x-2} + \frac{2}{x – 1} = \frac{6}{x},\)

\(x \neq 0, 1, 2\)

Question 2- Find the sum of first 24 terms of an A.P. whose nth term is given by \(a_{n} = 3 + 2n\).

Question 3- A bucket, is in the form of frustum of a cone whose height is 42 cm and the radii of its circular ends are 30 cm and 10 cm. Find the amount of milk (in litres) which this bucket can hold. If the milkman sells the milk at the rate of Rs. 40 per litre, what amount he will get from the sale?

If the milkman sells half the milk at less rate to the economically weaker section of society, what value he exhibits by doing this?

Question 4- If the coordinates of two points are A(3,4), B (5,-2) and a point P (x,5) is such that PA = PB, then find the area of \(\Delta PAB\).

Question 5- A solid metallic cylinder of diameter 12 cm and height 15 cm is melted and recast into toys in the shape of a cone of radius 3 cm and height 9 cm. Find the number of toys so formed.

Question 6- From a pack of 52 playing cards, Jacks and Kings of red colour and Queens and Aces of black colour are removed. The remaining cards are mixed and a card is drawn at random. Find the probability that the drawn card is

(i) a black Queen

(ii) a card of red colour

(iii) a Jack of black colour

(iv) a face card

Question 7- From a point P on the ground, the angles of elevation of the top of a 10 m tall building and a helicopter, hovering at some vertically over the top the building are \(30^{\circ}\) and \(60^{\circ}\) respectively. Find the height of the helicopter above the ground.

Question 8- Draw an isosceles triangle ABC in which the base BC is 8 cm long and its altitude AD through A is 4 cm long. Then draw another triangle whose side is \(\frac{2}{3}\) of the corresponding sides of \(\Delta ABC\).

Question 9- A and B working together can do a work in 6 days. If A takes 5 days less than B to finish the work, in how many days B alone can do the work.

Question 10- A hollow metallic sphere of external and internal diameters 8 cm and 4 cm respectively is melted to form a solid cone of base diameter 8 cm. Find the height of the cone.

Question 11- Find the area of the triangle formed by joining the mid-points of sides of triangle vertices (2,1), (4,3) and (2,5).

Question 12- Prove that the parallelogram circumscribing a circle is a rhombus.

Question 13- A sum of Rs. 4000 is to be used to give 10 cash prizes to students of a school, for their overall academic performance. If each prize is Rs. 50 less than its preceding prize, find the value of each prize.

Question 14- Find the sum of all such multiples of 7 which are less than 500.

Question 15- In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and \(\angle BOD = 90^{\circ}\). Find the area of the shaded region.

Important 4 Marks Questions

Question 16 – Prove that the lengths of two tangents drawn from an external point to a circle are equal.

Question 17- In a rain-water harvesting system, the rain-water from a roof of 22m \(\times\) 20 m drains into a cylindrical tank having diameter of base 2 m and height 3.5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.


Practise This Question

Consider the following figure. If AB = 2BD, PD = AC and 2AP = AD. 

What is the ratio BC:BD?