Prove the following identities: Question 35. = 4xyz Solution: Considering the determinant, we have R1⇢R1 – R2 – R3 C2⇢C2 – C3 △ = [-2x((z)(-y) –… Read More
Tag Archives: RD Sharma Class-12
Prove the following identities: Question 18. = -2 Solution: Considering the determinant, we have R2⇢R2 – R1 and R3⇢R3 – R2 △ = 1[2(a + 2)… Read More
Question 1. A diet of two foods F1 and F2 contains nutrients thiamine, phosphorus, and iron. The amount of each nutrient in each of the… Read More
Question 1 (i). Verify Lagrange’s mean value theorem for the following function on the indicated interval. In each case find a point ‘c’ in the… Read More
Question 1: If y=sin x and x changes from π/2 to 22/14, what is the approximate change in y? Solution: According to the given condition,… Read More
Question 9: Using differentials, find the approximate values of the following: (xiv) Solution: Considering the function as y = f(x) = cos x Taking x… Read More
Question 11. Sketch the region {(x, y) : 9x2 + 4y2 = 36} and find the area enclosed by it, using integration. Solution: 9×2 +… Read More
Question 1. Using integration, find the area of region bounded between the line x = 2 and parabola y2 = 8x Solution: Here, Given equations… Read More
Question 21. If and , find Solution: Here, Differentiate it with respect to t using chain rule, And, Differentiate it with respect to t using quotient rule,… Read More
Question 21. Draw a rough sketch of the curve and find the area between x-axis, the curve and the ordinates x = 0, x = π… Read More
Question 1. Find , when: x = at2 and y = 2at Solution: Given that x = at2, y = 2at So, Therefore, Question 2. Find ,… Read More
Question 1. Show that and are coplanar. Also, find the equation of the plane containing them. Solution: We know, the lines and are coplanar if: Since, , the lines are… Read More
Question 1. Evaluate the following determinant: (i) Solution: Considering the determinant, we have As R1 and R2 are identical Hence, △ = 0 (ii) Solution:… Read More
Question 11. Find, when and Solution: Here, Differentiating it with respect to t using quotient rule, and, Differentiating it with respect to t using quotient rule,… Read More
Evaluate the following integrals: Question 41. ∫cos-1((1 – x2)/(1 + x2))dx Solution: Given that, I = ∫cos-1((1 – x2)/(1 + x2))dx) Let us considered x… Read More
