CBSE 10 Maths Question Paper-2019

If HCF (336, 54) = 6, find LCM (336, 54).

Find the nature of roots of the quadratic equation 2x² – 4x + 3 = 0.

Find the common difference of the Arithmetic Progression (A.P.) a1, a3, a-3, a3, a2-3,... (a ≠ 0).

Evaluate: sin² 60° + 2 tan 45° – cos² 30°.

Write the coordinates of a point P on x-axis which is equidistant from points A(-2, 0) and B(6, 0).

In Figure 1, ABC is an isosceles triangle right-angled at C with AC = 4 cm. Find the length of AB.

Write the smallest number which is divisible by both 306 and 657.

Find a relation between x and y if the points A(x, y), B(–4, 6), and C(–2, 3) are collinear.

The probability of selecting a blue marble at random from a jar is 1/5. The probability of selecting a black marble is 1/4. If the jar contains 11 green marbles, find the total number of marbles in the jar.

For what value of k, is the polynomial f(x) = 3x⁴ – 9x³ + x² + 15x + k completely divisible by 3x² – 5?

The larger of two supplementary angles exceeds the smaller by 18°. Find the angles.

Find the mode of the following frequency distribution: Class Interval: 25–30, 30–35, 35–40, 40–45, 45–50, 50–55, 55–60. Frequency: 25, 34, 50, 42, 38, 14.

Prove that 2 + 5√3 is an irrational number, given that √3 is an irrational number.

Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P, prove that AP × PC = BP × DP.

In Figure 3, PQ and RS are two parallel tangents to a circle with centre O. Prove that ∠AOB = 90°.

Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (–2, –5) and (6, 3).

Evaluate: 85tan65° tan45° tan25° tan5° cos37° cos47° sin3°.

In Figure 4, OA = 15 cm. Find the area of the shaded region (Use π = 3.14).

Find the total volume of a solid with hemispherical ends, total height 20 cm and diameter 7 cm.

Find the mean marks of the students based on the frequency distribution.

For the polynomial f(x) = 3x⁴ – 9x³ + x² + 15x + k, find the value of k so that f(x) is divisible by 3x² – 5.

Write all the values of p for which the quadratic equation x² + px + 16 = 0 has equal roots.

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

Amit finds a bird flying at a distance of 200 m from him at an elevation of 30°. Deepak finds the angle of elevation of the same bird to be 45°. Find the distance of the bird from Deepak.

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole.

Construct an equilateral triangle ABC with each side 5 cm. Then construct another triangle whose sides are 3/2 times the corresponding sides of triangle ABC.

Change the following data into ‘less than type’ distribution and draw its ogive.

Prove that tan(θ+θ) = secθ + 1/cotθ.

Which term of the Arithmetic Progression -7, -12, -17, -22, ... will be -82? Is -100 any term of the A.P.? Give reason for your answer.

In a class test, the sum of Arun’s marks in Hindi and English is 30. Had he got 2 marks more in Hindi and 3 marks less in English, the product of the marks would have been 210. Find his marks in the two subjects.