Central Board of Secondary Education (CBSE) has issued the official date of examination for class 10th board exams. This exam is crucial from the examination aspect, as it help us in obtaining the desired stream for forthcoming studies.

Students who wish to get in an engineering line requires to excel in the maths examination. The subject requires a proper understanding and skills to score well in final boards. As 2 marks question are direct types and can be framed from any small topic, so practicing the given questions can be helpful in acquiring a good score. We at BYJUâ€™S provide students of class 10th with Important 2 marks question to practice and prepare for maths board examination. If students wants to practice more then they can solve the CBSE 10th Sample Papers.

Students preparing for CBSE Class 10 Maths Board Examination are suggested to practice the given problems for Mathematics:

**Important 2 Marks Questions for Class 10 Maths Board are as follows-**

**Question 1- **Find the value of k for which the roots of the quadratic equation \(2x^{2}+ kx + 8 = 0\), will have equal value.

**Question 2- **Determine the AP whose third term is 5 and seventh term is 9.

**Question 3- **If any point is equidistant from the points (a+b, b-a) and (a-b, a+b), prove that bx = ay.

**Question 4- **If the line segment joining the points A(2,1) and B (5,-8) is trisected at the points P and Q, find the coordinates of P.

**Question 5- **If, from an external point P of a circle with centre O, two tangents PA and PB are drawn such that \(\angle BPA = 120\), then show that OP = 2PA.

**Question 6- **Prove that the tangent drawn to a circle at the end points of a diameter are parallel to each other.

**Question 7- **Find the value of p for which the numbers 2p-1, 3p+1, 11 are in A.P. Hence find the numbers.

**Question 8- **Find the coordinates of the points of trisection of the line segment joining the points A (7,-2) and B (1,-5).

**Question 9- **Find the coordinates of the point on x-axis, which is equidistant from the points (-2,5) and (2,-3).

**Question 10- **A circle touches all the four sides of a quadrilateral ABCD. Prove that

AB + CD = BC + DA

**Question 11- **Which term of the A.P. 8, 14, 20, 26, â€¦â€¦.. Will be 72 more than its 41st term?

**Question 12- **A line intersect the y-axis at the points P and Q respectively. If (2,-5) is the midpoint of PQ, then find the coordinates of P and Q.

**Question 13-** Solve for x: \(4\sqrt{3}x^{2} + 5x -2\sqrt{3} = 0\)

**Question 14- **Prove that the perpendicular drawn from the point of contact to the tnagent, passes through the centre of the circle.

**Question 15- **Show that in two concentric circle, is bisected at the point of contact.

**Question 16- **Find the ratio in which the point (-3,k) divides the line segment joining the points (-5,-4) and (-2,3). Hence find the value of k.

**Question 17- **If the nth term of an A.P. is given by tn= 3n + 4, find the common difference of the A.P. and the sum of its first five terms.

**Question 18- **Â In the figure below, the radius of incircle of \(\Delta ABC\) of area 84 cm2 is 4 cm and the lengths of the segment AP and BP into which side AB is divided by the point of contact are 6 cm and 8 cm. Find the lengths of the sides AC and BC.

Find the value of k for which the roots of the quadratic equation 2x^2+kx+8=0, will have equal value.

Solution of this question

If the roots of quadratic equation are equal, then the discriminant is zero.

Therefore,

D = 0

b^2 – 4ac = 0

Here, a=2, b=k and c=8

k^2 – 4*2*8 = 0

k^2 – 64 = 0

k^2 = 64

k = Â±8

The value of k.

\bf{\red{\underline{\bf{Explanation\::}}}}

Explanation:

â€‹

We have 2xÂ² + kx + 8 = 0

A/q

Discriminate (D) = 0

a = 2

b = k

c = 8

Formula use :

\boxed{\bf{b^{2}-4ac=0}}}

\begin{gathered}\longrightarrow\sf{b^{2} -4ac=0}\\\\\longrightarrow\sf{(k)^{2} -4\times 2\times 8=0}\\\\\longrightarrow\sf{(k)^{2} -64=0}\\\\\longrightarrow\sf{(k)^{2} =64}\\\\\longrightarrow\sf{k=\pm\sqrt{64} }\\\\\longrightarrow\sf{\green{k=\pm8}}\end{gathered}

âŸ¶b

2

âˆ’4ac=0

âŸ¶(k)

2

âˆ’4Ã—2Ã—8=0

âŸ¶(k)

2

âˆ’64=0

âŸ¶(k)

2

=64

âŸ¶k=Â±

64

â€‹

âŸ¶k=Â±8

â€‹

Thus;

The value of k is Â±8 .

for equal roots

D=0 , b^2-4ac=0

[k]^2-4*2*8=0

k^2-64=0

k^2= 64

k = 8