 # CBSE Class 10 Maths Board Exam 2018: Important 3 marks questions

CBSE examination is already nearby, and most of the students are still not confident in the subject of Mathematics. As the subject requires proper understanding to excel an examination. Students who are planning to choose their future carrier in the field of Engineering, it is quite essential to do extensively great on the subject.

Class 10 maths paper comprises of 1, 2, 3 & 4 marks questions, where one-third of the paper comprises of 3 marks questions. Thus if one wishes to excel in the examination, a good practice of 3 marks question is essential. Thus we at BYJU’S provide students of class 10 with important 3 marks question, that are crucial from exam perspective.

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

Important 4 Marks Questions for Class 12 Maths Board are as follows-

Question 1- If mth term of an A.P. is $\frac{1}{n}$ and nth term is $\frac{1}{m}$, then find the sum of its first mn terms.

Question 2- 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 form 60$60^{\circ}$ to $45^{\circ}$ in 2 minutes. Find the speed of the boat in m/h.

Question 3- Two different dice are thrown together. Find the probability that the numbers obtained

(i) have a sum less than 7

(ii) have a product less than 16

(iii) is a doublet of odd numbers.

Question 4- The area of a triangle is 5 sq units. Two of its vertices are (2,1) and (3,-2). If the third vertex is $\left ( \frac{7}{2},y \right )$, then find the value of y.

Question 5- Show that $\Delta ABC$, where A(-2,0), B(2,0), C(0,2) and $\Delta PQR$ where P(-4,0), Q(4,0), R(0,4) are similar triangles.

Question 6- The $\frac{3}{4}$th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.

Question 7- In the given figure, OACB is quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region. Question 8- Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that $\angle PTQ = 2 \angle OPQ$

Question 9- If the equation $(1+m^{2})x^{2} + 2mcx + c^{2} – a^{2} = 0$ has equal roots then show that $c^{2} = a^{2}(1+m^{2})$.

Question 10- Find the sum of n terms of the series $\left ( 4-\frac{1}{n} \right ) + \left ( 4-\frac{2}{n} \right ) + \left ( 4-\frac{3}{n} \right ) + ……..$

Question 11- In a game, a one-rupee coin is tossed three times and the result is recorded every time. Haneef will win, if he gets at least two heads. Calculate Haneef’s probability of losing the game.

Question 12- From a point of a ground, the angle of elevation of the bottom and top of a communication tower fixed on the top of a 20 m high building are $45^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower. (Take $\sqrt{3} = 1.732$).

Question 13- The mid-points of the side BC, CA, and AB of a $\Delta ABC$ are D(3,4), E(8,9) and F(6,7) respectively. Find the coordinates of the vertices of the triangle.

Question 14- Water is flowing into a canal, 6 m wide and 1.5 m deep, at the rate of 10km/hr. How much area will it irrigate in 30 minutes, if 8 cm of standing water is required for irrigation.

Question 15- A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cons, each of radius 4.5 cm and height 3 cm. Find the number of cones so formed.

Question 16- A hemisphere of maximum possible diameter is placed over a cuboidal block of side 7 cm. Find the surface area of the solid so formed.

Question 17- The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/hr?

Question 18- If the sixth term of an A.P. is zero, then show that its 33rd term is three times its 15th term.

Question 19- Show that $x = -\frac{bc}{ad}$ is a solution of the quadratic equation $ad^{2}\left ( \frac{ax}{b} + \frac{2c}{d}\right )x + bc^{2} = 0$

Question 20- In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If $\angle AOB = 60^{\circ}$, find the area of the shaded region. Question 21- Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region. Question 22- If the roots of the equation $(c^{2}- ab) x^{2}- 2(a^{2}-bc)x – ac = 0$ in x are equal, then show that either a = 0 or $a^{3}+b^{3}+ c^{3} = 3abc$

To practice more questions, students must solve the CBSE board sample papers for class 10. Stay tuned for further updated on CBSE and other competitive exams. To access interactive Maths and Science videos download BYJU’S app.