CBSE Class 10 Mathematics Board Paper 2026 — Set 5

An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting two hills at P and Q. If the parabolic curve is represented by the polynomial p(x)=−0.0025x²−0.025x+136 .

Observe the diagram and based on the above information, answer the following questions:

Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an elevated water tank and CD is a nearby multistorey building. The building is 54 metres away from the water tank.

From a window (W) of the building, the angle of elevation of the top of the tank is 45° and the angle of depression of its foot is 30°.

The value of k for which the equation kx² — 6x — 4 = 0 has real and equal roots, is

The line segment joining the points P(—4, —2) and Q(10, 4) is divided by y-axis in the ratio

If the zeroes of a polynomial p(x) are —3 and 8, then p(x) equals

n the given figure, PQ is tangent to the circle with centre O. S is a point on the circle such that ∠SQT = 55°. The measure of ∠QPS is

Devansh proved that ΔABC ∼ ΔPQR using SAS similarity criteria. If he found ∠C = ∠R, then which of the following was proved true?

While calculating mean of a grouped frequency distribution, step deviation method was used )x-a/h=u). It was found that x̅ = 64, h =5 and a = 62.5. The value of u̅ is

If aₙ represents the nᵗʰ term of the A.P. -15/4,-10/4,-5/4,.... then the value of a₁₆-a₁₂ is

The value of p for which roots of the quadratic equation x² — px + 6 = 0 are rational, is

Which of the following can not be the probability of an event ?

A card is drawn at random from a well shuffled deck of 52 playing cards.

The probability that it is either a ten or a king is

An arc of length 2.2 cm subtends an angle θ at the centre of the circle with radius 2.8 cm. The value of θ is

For an acute angle θ , if sin θ = 1/9 then value of 9 cosec θ+1 / 9cosec θ-1 is

Simplest form of : sec A /√sec² A -1 is

Assertion (A) : The system of linear equations 3x — 5y + 7 = 0 and —6 x+ 10 y + 14 = 0 is inconsistent. Reason (R) : When two linear equations don’t have unique solution, they always represent parallel lines.

Assertion (A) : H.C.F. (36 m², 18 m) =18 m, where m is a prime number.

Reason (R) :H.C.F. of two numbers is always less than or equal to the smaller number.

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

Vertices of a right triangle ABC with ∠B = 90° are A(3, 4), B(1, 1) and C(-8, 7). Find the value of tan A.

Using distance formula, prove that the points A(2, 3), B(-7, 0) and C(-1, 2) are collinear.

In the given figure, AB || DE and AC || DF. Show that ΔABC ~ ΔDEF. If BC =10 cm, EB=CF =5 cm and AB = 7 cm, then find the length DE.

For acute angles A and B and A + 2B and 2A + B are acute if tan (A + 2B) = √3 and sin (2A + B) = 1/√2, then find the measures of angles A and B.

Evaluate: sin³ 60° — tan 30°/cos² 45°

A bag contains 25 balls. Some them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is 3/5, then find the number of yellow balls.

A circle of diameter 20 cm is equally divided into five sectors. Find the area and perimeter of one of the sectors.

In an A.P., the 15ᵗʰ term exceeds the 8ᵗʰ term by 21. If the sum of the first 10 terms is 55, then form the A.P.

The sum of the first n terms of an A.P. is 2n²+13n. Find its nᵗʰ term and hence 10ᵗʰ term.

A circle centered at (2, 1) passes through the points A(5, 6) and B(-3, K). Find the value(s) of K. Hence find length of chord AB.

Prove that the point P dividing the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 3 : 2, lies on the line x - 3y = -1. Also find length of PA and PB.

Prove that :

tanθ /1-cotθ+ cot θ /1-tan θ =1=tan θ +cot θ.

Solve the system of linear equations : x = 4 and 3x — 2y = 6 graphically.

The dimensions of a window are 156 cm x 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Venkat can row a boat in still water at the speed of 12 km/h. He ferries tourists 15 km upstream and 18 km downstream in 3 hours. Find the speed of the stream.

D is the mid-point of side BC of Δ ABC. CE and BF intersect at O, a point on AD. AD is produced to G such that OD = DG.

Prove that

(i) OBGC is a parallelogram.

(ii) EF∥ BC

(iii) ΔAEF ~ ΔABC

Through the mid-point Q of side CD of a parallelogram ABCD, the line AR is drawn which intersects BD at P and produced BC at R.

Prove that

(i) AQ=QR

(ii) AP=2PQ

(iii) PR =2AP

The mean of the following frequency distribution is 28. If sum of all frequencies is 100, then find the values of p and q :

Find median and mode of the following distribution :

PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.