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Home> Class-12> Mathematics >2022 Solutions
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| 1. Choose and write the correct options : If f(x)=8x^3 and g(x) = 1/x^3, then the value of gof is : (A) 8x^3 (B) 512x^3 |
| 2. Fill in the blanks : (i) In set A={4, 5, 6}, number of equivalence relations containing (4, 5) is _______. |
| 3. Match the correct pairs : |
| 4. Give answers in one word / sentence each : (i) What is the optimal value function ? (ii) What is the chance that leap year will |
| 5. Write true or false in the following statements : (i) The value of d / dx tanx is secx tanx. (ii) Equation of a plane in normal form |
| 6. Find the rate of change of the area of a circle with respect to its radius 1=3cm. |
| 7. Find the slope of the tangent to the curve y=3x^4–4x at x=4. |
| 8. If P(B)=0.5 and P(A∩B)=0.25, then compute P(A/B). |
| 9. If P(A)=3/5 and P(B)=1/5, calculate P(A∩B) if A and B are independent events. |
| 10. Find the direction cosines of a line which makes equal angles with the coordinate axes. |
| 11. Find the angle between pair of lines x/2=y/2=z/1 and (x-5)/4=(y-2)/1=(z-3)/8 |
| 12. Find the least distance between the lines given by ¯r=i ̂+2j ̂-4k ̂+λ (2i ̂+3j ̂+6k ̂) and ¯r=3i ̂+3j ̂-5k ̂+μ (2i ̂+3j ̂+6k ̂) |
| 13. Find the equation of the plane with intercepts 2, 3 and 4 on the x, y and z – axis respectively. |
| 14. Find the unit vector in the direction of vector ¯PQ, where P and Q are the points (1, 2, 3) and (4, 5, 6) respectively. |
| 15. Find the position vector of the midpoint of the vector joining the points P (2, 3, 4) and Q (4, 1, –2). |
| 16. ∫cos2x dx का मान परिकलित कीजिए । |
| 17. Calculate the value of I=∫ex•sinx dx. |
| 18. Find the value of Integral∫_2^3〖x^5•dx〗. |
| 19. Find the value of Integral ∫_0^(π/2)▒√(sinx )/(√(sinx )+√(cosx )) .dx. |
| 20. Examine that the relation R in the set {1,2,3} given by R={(1,1),(2,2),(3,3),(1,2),(2,3)} is reflexive but neither symmetric nor transitive. |
| 21. Show that the function f:R→R defined as f(x)=x2, is neither one–one nor onto. |
| 22. Find AB, if A=[(0 -1,0 2)] and B=[(3 5,0 0)]. |
| 23. If A=[(3 √3 2,4 2 0)], then show that (A')' = A. |
| 24. Differentiate ax with respect to x, where a is positive integer. |
| 25. Differentiate (log x)cos x with respect to x. |
| 26. Write the function tan^(-1)〖(√((1-cosx)/(1+cosx ))),0 |
| 27. Prove that sin^(-1)〖3/5-sin^(-1) 8/17=sin^(-1) 13/85〗. |
| 28. Express the matrix B=[(2 -2 -4,-1 3 4,1 -2 -3)] is a symmetric matrix. |
| 29. Find the values of x and y from the following equation : |
| 30. Find two numbers whose sum is 24 and whose product is as large as possible. |
| 31. Find the equation of the tangent and normal to the curve x2/3 +y2/3 = 2 at (1, 1). |
| 32. Solve the following linear programming problem graphically : Minimise Z = 200x + 500y |
| 33. Solve the following linear programming problem graphically : Maximize Z = 4x + y Subject to the constraints : |
| 34. Solve the following tabular |(x+1 3 5,2 x+2 5,2 3 x+4)|=0 |
| 35. Prove that : |(-a^2 ab ac,ab -b^2 bc,ac bc -c^2 )|=4a^2 b^2 c^2 |
| 36. Discuss the continuity of the function f given by |
| 37. Find the value of dy/dx, if x = a (t + sin t), y = a (1 – cos t) |
| 38. Find the area of the circle x^2 + y^2 = a^2. |
| 39. Find the area enclosed by the ellipse x^2/a^2 +y^2/b^2 =1. |
| 40. Solve the differential equation dy/dx=e^(x-y)+x•e^(-y). |
| 41. Solve the differential equations dy/dx=√(1-y^2 )/√(1-x^2 ). |
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