CBSE 10th Maths Question Paper 2026 (Set 1)

Using the distance formula d = √[(x2 - x1)² + (y2 - y1)²]. Here, x1 = a cos θ + b sin θ, y1 = 0, x2 = 0, y2 = a sin θ - b cos θ. Distance squared = (0 - (a cos θ + b sin θ))² + ((a sin θ - b cos θ) - 0)² = a² cos² θ + b² sin² θ + 2ab sin θ cos θ + a² sin² θ + b² cos² θ - 2ab sin θ cos θ = a²(cos² θ + sin² θ) + b²(sin² θ + cos² θ) = a² + b². Therefore, distance = √(a² + b²). Since the options given are written as powers, Option D is the intended result representing a²+b².

Volume of cone = (1/3)πr²h. Volume of two spherical scoops = 2 * (4/3)π(r/2)³ = 2 * (4/3)π(r³/8) = (1/3)πr³. Since the cone is completely filled, (1/3)πr²h = (1/3)πr³, which implies h = r. We need the ratio h : 2r = r : 2r = 1 : 2. Wait, re-calculating: 2 * (4/3)π(r/2)^3 = 2 * (4/3)π * r^3 / 8 = πr^3/3. Thus 1/3 * πr^2h = 1/3 * πr^3 => h=r. The ratio h:2r is 1:2. There may be a calculation error in the prompt's options or interpretation; based on standard geometry, 1:2 is correct.

For infinitely many solutions, the condition is a1/a2 = b1/b2 = c1/c2. Here, k/6 = -1/-2 = -2/-3. Since -1/-2 = 1/2 and -2/-3 = 2/3, and 1/2 is not equal to 2/3, the ratios are inconsistent for any value of k. Thus, no such k exists.

Area of circle = πr² = (22/7) * 7 * 7 = 154 cm². Since the circle is divided into 16 identical sectors, the area of each sector = 154 / 16 = 77 / 8 cm². Note: Option A says 77/4, but 154/16 is 77/8. Re-checking: 22*7/16 = 154/16 = 77/8.

The empirical relation is Mode = 3(Median) - 2(Mean). Given Mean = 43 and Median = 40. Mode = 3(40) - 2(43) = 120 - 86 = 34.