CBSE 10th Maths Question Paper 2026 (Set 4)

Using the distance formula d = sqrt((x2-x1)^2 + (y2-y1)^2), where x1=a cos θ + b sin θ, y1=0, x2=0, y2=a sin θ - b cos θ. d = sqrt((0 - (a cos θ + b sin θ))^2 + ((a sin θ - b cos θ) - 0)^2) = sqrt((a cos θ + b sin θ)^2 + (a sin θ - b cos θ)^2) = sqrt(a^2 cos^2 θ + b^2 sin^2 θ + 2ab sin θ cos θ + a^2 sin^2 θ + b^2 cos^2 θ - 2ab sin θ cos θ) = sqrt(a^2(sin^2 θ + cos^2 θ) + b^2(sin^2 θ + cos^2 θ)) = sqrt(a^2 + b^2). Option A is correct.

Volume of cone = (1/3)πr^2h. Volume of two spherical scoops = 2 * (4/3)π(r/2)^3 = 2 * (4/3)π(r^3/8) = (1/3)πr^3. Since volume of cone equals volume of two scoops, (1/3)πr^2h = (1/3)πr^3, which simplifies to h = r. We need h : 2r = r : 2r = 1 : 2. Wait, re-evaluating the question: if h=r, ratio is 1:2. Let's check the options. If the question implies the volume of the cone matches the two scoops, h/r = 1, so h/2r = 1/2. Option D (2:1) would be the answer if it asked 2r:h.

For infinitely many solutions, a1/a2 = b1/b2 = c1/c2. Here, k/6 = -1/-2 = -2/-3. Since -1/-2 = 1/2 and -2/-3 = 2/3, 1/2 is not equal to 2/3. Thus, the condition for infinitely many solutions can never be met for any value of k. Option D is correct.

Area of circle = πr^2 = (22/7) * 7 * 7 = 154 cm^2. Since there are 16 identical sectors, the area of each sector = 154 / 16 = 77 / 8. Wait, calculation: 154/16 = 77/8. Checking the options, if the question meant 14 sectors or different values. Given the options, 77/4 (A) would be 154/8. Let's re-calculate: 154/16 = 77/8. Option A is 77/4 (which is 154/8). If the sector division was 8 instead of 16, it would be 77/4.

The empirical relation is Mode = 3(Median) - 2(Mean). Mode = 3(40) - 2(43) = 120 - 86 = 34. Option A is correct.