CBSE EXAMINATION PAPER-2025

A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway. The total area of the lawn and the walkway is 360 square metres. The width of the walkway is the same on all sides. The dimensions of the lawn itself are 12 metres by 10 metres.

Based on the information given above, answer the following questions :

A lighthouse stands tall on a cliff by the sea, watching over ships that pass by. One day a ship is seen approaching the shore and from the top of the lighthouse, the angles of depression of the ship are observed to be 30° and 45° as it moves from point P to point Q. The height of the lighthouse is 50 metres.

Based on the information given above, answer the following questions :

If tan 3θ =√3 , then θ/2 equals:

If x is the LCM of 4, 6, 8 and y is the LCM of 3, 5, 7 and p is the LCM of x and y, then which of the following is true?

The value of 'k' for which the system of linear equations 6x + y= 3k and 36x + 6y = 3 have infinitely many solutions is:

If α and β are the zeroes of polynomial p(x) = x² - ax - b, then the value of (α +β +αβ ) is equal to:

If x/12- 3/x= 0, then the values of x are:

The line represented by x/4 +y/6 =1 intersects x-axis and y-axis respectively at P and Q. The coordinates of the mid-point of line segment PQ are:

Two of the vertices of ΔPQR are P(-1, 5) and Q(5, 2). The coordinates of a point which divides PQ in the ratio 2 : 1 are:

If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other at an angle of 80° as shown in the given figure, then the measure of ∠POA is:

If in two Δ DEF and Δ PQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is not true?

The measurements of Δ LMN and Δ ABC are shown in the figure given below. The length of side AC is:

If the area of a sector of a circle of radius 36 cm is 54π cm², then the length of the corresponding arc of the sector is:

A die is thrown once. The probability of getting a number which is not a factor of 36 is:

Zeroes of the polynomial p(x) = x² - 3√2x + 4 are:

In the given figure in Δ ABC, AD ⊥ BC and ∠BAC = 90°. If BC = 16 cm and DC = 4 cm, then the value of x is:

Assertion (A) : A ladder leaning against a wall, stands at a horizontal distance of 6 m from the wall. If the height of the wall up to which the ladder reaches is 8 m, then the length of the ladder is 10 m.

Reason (R): The ladder makes an angle of 60 with the ground.

Assertion (A) : If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre of the circle.

Reason (R): A parallelogram circumscribing a circle is a rhombus.

If 4k = tan² 60° - 2 cosec² 30° - 2 tan² 30°, then find the value of k.

The probability of guessing the correct answer of a certain test question is x / 12. If the probability of not guessing the correct answer is 5 / 6 then find the value of x.

Find the value (s) of 'K' so that the quadratic equation 4x² + kx + 1 = 0 has real and equal roots.

Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts.

Prove that ( 5√3+2/3) is an irrational number given that √3 is an irrational number.

Prove that: √sec A -1/ √sec A + 1  + √sec A +1/ √sec A -1= 2cosec A

Prove that:(1/ cos A -cos A) (1/ sin A - sin A) = 1 / tan A + cot A

Three unbiased coins are tossed simultaneously. Find the probability of getting:

(a) exactly two tails

(b) at least one head

(c) at most two heads

In the given figure, PC is a tangent to the circle at C. AOB is the diameter which when extended meets the tangent at P. Find ∠CBA and ∠BCO, if ∠PCA = 110°.

The perimeter of an isosceles triangle is 32 cm. If each equal side is 5/ 6 th of the base, find the area of the triangle.

In the given figure, PA, QB and RC are perpendicular to AC. If PA = x units, QB = y units and RC = z units, prove that 1/x + 1/z = 1/y .

Sides AB and BC and median AD of triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that Δ ABC ~ ΔPQR.