CBSE Class 10 Mathematics (Standard) Guess Paper 2027

Area of a segment of a circle of radius 'r' and central angle 60 degrees is : (A) (pi r²)/2 - (1/2) r² (B) (2 pi r)/4 - (sqrt(3)/4) r² (C) (pi r²)/6 - (sqrt(3)/4) r² (D) (2 pi r)/4 - r² sin 60

A pair of dice is tossed. The probability of not getting the sum eight is (A) 5/36 (B) 31/36 (C) 5/18 (D) 5/9

[3/4 tan² 30 - sec² 45 + sin² 60] is equal to (A) -1 (B) 5/6 (C) -3/2 (D) 1/6

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are not parallel, then k has to be (A) 15/4 (B) not equal to 15/4 (C) any rational number (D) any rational number having 4 as denominator

The LCM of 960 and 240 is : (A) 960 (B) 240 (C) 60 (D) 15

A point on the x-axis divides the line segment joining the points A(2,-3) and B(5,6) in the ratio 1:2. The point is A) (4,0) B) (7/2, 3/2) C) (3,0) D) (0,3)

If alpha and beta are two zeroes of a polynomial f(x) = px² - 2x + 3p and alpha + beta = alpha*beta, then value of p is : (A) -2/3 (B) 2/3 (C) 1/3 (D) -1/3

In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is drawn at random. The probability that drawn ball is white in colour is A) 1/6 B) 3/8 C) 11/24 D) 5/8

The distance of the point A(4a, 3a) from x-axis is : (A) 3a (B) -3a (C) 4a (D) -4a

If triangle ABC ~ triangle DEF, AB = 6cm, DE = 9cm, EF = 6cm and FD = 12cm, then the perimeter of triangle ABC is (A) 28cm (B) 28.5cm (C) 18cm (D) 23cm

For any natural number n, 5ⁿ ends with the digit : (A) 0 (B) 5 (C) 3 (D) 2

From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be 45 degrees. The height (in metres) of the tower is : (A) 10 sqrt(3) (B) 30 sqrt(3) (C) 60 (D) 30

The graph of y = f(x) is given. The number of distinct zeroes of y = f(x) is : (A) 0 (B) 1 (C) 2 (D) 3 [Figure: curve crossing x-axis at A and touching it at another point]

If 2sin(5x) = sqrt(3), 0 <= x <= 90 degrees, then x is equal to (A) 10 deg (B) 12 deg (C) 20 deg (D) 50 deg

The median of a set of 9 distinct observations is 20.5. If each of the observations of the set is increased by 2, then the median of the new set (A) is increased by 2 (B) is decreased by 2 (C) is two times the original number (D) Remains same as that of original observations

Which of the following gives the middle most observation of the data? A) Median B) Mean C) Range D) Mode

In the given figure, a tangent has been drawn at a point P on the circle centred at O. If angle TPQ = 110 deg then angle POQ is equal to A) 110 deg B) 70 deg C) 140 deg D) 55 deg

The curved surface area of a cone having height 24 cm and radius 7 cm, is (A) 528 cm² (B) 1056 cm² (C) 550 cm² (D) 500 cm²

Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 cm². Reason (R) : The surface area of a cuboid of dimensions l x b x h is (lb + bh + hl). [Choose: both true R explains A / both true R does not explain A / A true R false / A false R true]

The tangents drawn at the extremities of the diameter of a circle are always : (A) parallel (B) perpendicular (C) equal (D) intersecting

Find the sum of first 30 terms of AP : -30, -24, -18, ..... .

If AP and DQ are medians of triangles ABC and DEF respectively, where triangle ABC ~ triangle DEF, then prove that AB/DE = AP/DQ

Find the zeroes of the polynomial p(x) = x² + (4/3)x - 4/3.

If sin theta + cos theta = sqrt(3), then find the value of sin theta * cos theta.

Find the point(s) on the x-axis which is at a distance of sqrt(41) units from the point (8, -5).

Solve the following system of equations graphically: 2x + y = 6, 2x - y - 2 = 0. Find the area of the triangle so formed by two lines and x-axis. [For Visually Impaired candidates: Five years hence, father's age will be three times the age of son. Five years ago, father was seven times as old as his son. Find their present ages.]

Prove that sqrt(5) is an irrational number.

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

In Figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that angle AOB = 90 degrees. [For Visually Impaired candidates: Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that angle APB = 2(angle OAB)]

Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the point of intersection.

Prove that (cosA - sinA + 1)/(cosA + sinA - 1) = cosecA + cotA

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.

A boy whose eye level is 1.35 m from the ground, spots a balloon moving with the wind in a horizontal line at some height from the ground. The angle of elevation of the balloon from the eyes of the boy at an instant is 60 deg. After 12 seconds, the angle of elevation reduces to 30 deg. If the speed of the wind is 3 m/s then find the height of the balloon from the ground. (Use sqrt(3) = 1.73)

If the mode of the following distribution is 55, then find the value of x. Hence, find the mean. Class Interval: 0-15, 15-30, 30-45, 45-60, 60-75, 75-90; Frequency: 10, 7, x, 15, 10, 12

An empty cone of radius 3cm and height 12cm is filled with ice-cream such that the lower part of the cone which is (1/6)th of the volume of the cone is unfilled (empty) but a hemisphere is formed on the top. Find the volume of the ice-cream.

From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed out. Find the total surface area of the remaining solid.

In Figure 1, a triangle ABC with angle B = 90 degrees is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC.

[case context: elder brother repays a bank loan of Rs 1,18,000 in monthly instalments starting at Rs 1,000 and increasing by Rs 100 every month (an AP)] Find the amount paid by him in the 30th instalment.