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Q) A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and AB = 24 cm, find the radius of the circle. Q25 A – Sample Question Paper – Set 1 – Maths Standard – CBSE 2026 Ans: Let’s first draw a diagram for the given question: By Pythagorus […]
Q) Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + tan θ + cot θ Ans: Here, let’s start by simplifying the LHS in given equation: LHS = = = Let’s make the denominators equal: LHS = = = We know that a3
Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + tan θ + cot θ Read More »
Q) Calculate the mean of the following data : Ans: Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with frequency: We know that, mean of grouped data is given by: Mean of grouped data = Therefore, Mean value = = 10.57 Hence, the mean value of the given data is
Q. Solve for X : Ans: Given equation is: ∴ ∴ 4 (2 X + 3) – 5 X = 3 X (2X + 3) ∴ 8 X + 12 – 5 X = 6 X 2 + 9 X ∴ 12 = 6 X 2 + 6 X ∴ 6 X 2 + 6 X
Q. The sum of two numbers is 18 and the sum of their reciprocals is 1/4 . Find the numbers. Ans: Let the numbers be X and Y Step 1: By 1st condition: X + Y = 18 or X = 18 – Y ….. (i) Step 2: By 2nd condition: By simplifying this equation, we
The sum of two numbers is 18 and the sum of their reciprocals is 1/4 . Find the numbers. Read More »
Q) ABCD is a trapezium with AB ǁ DC. AC and BD intersect at E. If Δ AED ~ Δ BEC, then prove that AD = BC. Ans: Let’s start with the diagram for he given question: Step 1: We are given AB ǁ DC, hence let’s look at △AEB and △CED: Here we
Q) Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube. Ans: Let’s draw the diagram for the given question: If the radius of the sphere is R, then volume of the sphere, VS = If the side of the cube is X, then volume
Q) The interior of a building is in the form of a cylinder of base radius 12 m and height 3.5 m surmounted by a cone of equal base and slant height 14 m. Find the internal curved surface area of the building. Ans: Let’s draw the diagram for the given question: Now the curved
The interior of a building is in the form of a cylinder of base radius 12 m Read More »
Q) The vertices of a quadrilateral ABCD are A(6, – 2), B(9, 2), C(5, – 1) and D(2, – 5). Prove that ABCD is a rhombus, and not a square. Ans: Let’s quickly understand the comparisons of a Square and a Rhombus: Key Similarities: 1. Both are polygons with all four sides equal in length 2.
The vertices of a quadrilateral ABCD are A(6, – 2), B(9, 2), C(5, – 1) and D(2, – 5). Read More »
Q) Student-teacher ratio expresses the relationship between the number of students enrolled in a school and the number of teachers employed by the school. This ratio is important for a number of reasons. It can be used as a tool to measure teachers’ workload as well as the allocation of resources. A survey was conducted