CBSE Class 10 Mathematics (Basic) Guess Paper 2027

The distance between the points (cos30°, sin30°) and (cos60°, −sin60°) is A) 0 unit B) √3 units C) 1 unit D) √2 units

The class mark of the median class of the following data is : (Class Interval / Frequency) 10–25 : 2, 25–40 : 3, 40–55 : 7, 55–70 : 6, 70–85 : 6, 85–100 : 6. (A) 40 (B) 55 (C) 47.5 (D) 62.5

The mid-point of the line segment joining the points (-1, 3) and (8, 3/2) is : (a) (7/2, -3/4) (b) (7/2, 9/2) (c) (9/2, -3/4) (d) (7/2, 9/4)

The seventh term of an A.P. whose first term is 28 and common difference − 4, is : (a) 0 (b) 4 (c) 52 (d) 56

The value of (tan² A – 1/cos² A) is : (A) more than 1 (B) 1 (C) 0 (D) – 1

The roots of quadratic equation 3x² − 4√3x + 4 = 0 are (A) not real (B) real and equal (C) rational and distinct (D) irrational and distinct

A quadratic polynomial whose zeroes are 2/5 and −1/5 is (A) 25x² + 5x − 2 (B) 5x² − 2x + 1 (C) 5x² + 2x − 1 (D) 25x² − 5x − 2

HCF (132, 77) is : (a) 11 (b) 77 (c) 22 (d) 44

(1 − tan² 30°)/(1 + tan² 30°) is equal to (A) cos 60° (B) sin 60° (C) 1 (D) tan² 60°

If the roots of quadratic equation 4x² - 5x + k = 0 are real and equal, then value of k is : (a) 5/4 (b) 25/16 (c) -5/4 (d) -25/16

In the given figure, PQ and PR are tangents to a circle centred at O. If ∠QPR = 35° then ∠QOR is equal to (A) 70° (B) 90° (C) 135° (D) 145°

If ΔABC ∼ ΔPQR (with AB = 3 cm, BC = 4 cm, AC = 5 cm and PR = 10 cm as shown), then perimeter of the triangle PQR (in cm) is A) 12 B) 24 C) 18 D) 20

In the given figure, BC and BD are tangents to the circle with centre O and radius 9 cm. If OB = 15 cm, then the length (BC + BD) is : (a) 18 cm (b) 12 cm (c) 24 cm (d) 36 cm

If the HCF of two positive integers a and b is 1, then their LCM is : (A) a + b (B) a (C) b (D) ab

Which of the following is not the criterion for similarity of triangles ? (A) AAA (B) SSS (C) SAS (D) RHS

In the given figure, which of the following angles represents the angle of depression ? [Observer at top with horizontal line; line of sight to Object; marked angles x, y, z at observer/horizontal and a at object] (A) x (B) y (C) z (D) a

The perimeter of the shaded region in the given figure is : [Circle with centre O; two radii r bounding a shaded sector, chord a subtending the sector, and arc l] (A) l (B) l + a (C) l + 2r (D) l + 2r + a

The ratio of the area of a quadrant of a circle to the area of the same circle is : (A) 1 : 2 (B) 2 : 1 (C) 1 : 4 (D) 4 : 1

Assertion (A) : The value of p for which the system of equations 4x + py + 8 = 0 and 2x + 2y + 2 = 0 is consistent is 4. Reason (R) : The system of equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂ is consistent with infinitely many solutions, if a₁/a₂ = b₁/b₂ = c₁/c₂. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.

ASSERTION (A): Two coins are tossed simultaneously. Possible outcomes are two heads, one head and one tail, two tails. Hence, the probability of getting two heads is 1/3. REASON (R): Probabilities of 'equally likely' outcomes of an experiment are always equal. A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). C) Assertion (A) is true but reason (R) is false. D) Assertion (A) is false but reason (R) is true.

Calculate mode of the following distribution: Class: 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 ; Frequency: 5 | 6 | 15 | 10 | 5 | 4.

In an AP, if a = 50, d = -4 and S_n = 0, then find the value of n.

Find the values of A and B (0 ≤ A < 90°, 0 ≤ B < 90°), if tan (A + B) = 1 and tan (A – B) = 1/√3.

Find the sum of the first twelve 2-digit multiples of 7, using an AP.

A chord of a circle of diameter 20 cm subtends an angle of 60° at the centre of the circle. Find the area of the corresponding minor segment of the circle. (Use π = 3.14 and √3 = 1.73)

Prove that : (1 + cot² A)/(1 + tan² A) = ((1 – cot A)/(1 – tan A))²

Find the mean using the step deviation method. Class: 0-10 | 10-20 | 20-30 | 30-40 | 40-50 ; Frequency: 6 | 10 | 15 | 9 | 10.

Solve the following system of equations graphically : x + 3y = 6; 2x – 3y = 12

Prove that √3 is an irrational number.

Find the ratio in which the y-axis divides the line segment joining the points (4, −5) and (−1, 2). Also find the point of intersection.

A solid is in the form of a cylinder with hemi-spherical ends of same radii. The total height of the solid is 20 cm and the diameter of the cylinder is 14 cm. Find the surface area of the solid.

Prove that a line drawn parallel to one side of a triangle intersecting other two sides in distinct points, divides the other two sides in the same ratio.

As observed from the top of a 75 m high lighthouse from the sea level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use √3 = 1.732)

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hr, it takes 2 hours less in the journey. Find the original speed of the train.

The difference of the squares of two positive numbers is 180. The square of the smaller number is 8 times the greater number. Find the two numbers.

A spherical glass vessel has a cylindrical neck 8 cm long and 1 cm in radius. The radius of the spherical part is 9 cm. Find the amount of water (in litres) it can hold, when filled completely.

In Figure 3, the tangent l is parallel to the tangent m drawn at points A and B respectively to a circle centred at O. PQ is a tangent to the circle at R. Prove that angle POQ = 90 degrees.

[Blood Donation Centre 2023 distribution of blood/Rhesus types (in %): O^- = x, O^+ = 30, A^- = 8, A^+ = 24, B^- = 6, B^+ = 18, {AB}^- = 1, {AB}^+ = 3.] Find the value of x.