CBSE 12th Math (Term 1) Paper 2021-22 | Class 12 Year Wise Previous Years Questions

Mathematics

1. Differential of $$\log [\log (\log {x^5})]$$ w.r.t. x is 2. The number of all possible matrices of order 2 $$\times$$ 3 with each entry 1 or 2 is 3. A function f : R $$\to$$ R is defined as f(x) = x3 + 1. Then the function has 4. If $$\sin y = x\cos (a + y)$$, then $${{dx} \over {dy}}$$ is 5. The points on the curve $${{{x^2}} \over 9} + {{{y^2}} \over {25}} = 1$$, where tangent is parallel to x-axis are 6. Three points P(2x, x + 3), Q(0, x) and R(x + 3, x + 6) are collinear, then x is equal to 7. The principal value of $${\cos ^{ - 1}}\left( {{1 \over 2}} \right) + {\sin ^{ - 1}}\left( { - {1 \over {\sqrt 2 }}} \ri 8. If $${({x^2} + {y^2})^2} = xy$$, then $${{dy} \over {dx}}$$ is 9. If a matrix A is both symmetric and skew symmetric, then A is necessarily a 10. Let set X = {1, 2, 3} and a relation R is defined in X as : R = {(1, 3), (2, 2), (3, 2)}, then minimum ordered pairs whi 11. A Linear Programming Problem is as follows:Minimize z = 2x + ysubject to the constraints x $$\ge$$ 3, x $$\le$$ 9, y $$\ 12. The function $$f(x) = \left\{ {\matrix{ {{{{e^{3x}} - {e^{ - 5x}}} \over x},} & {if\,x \ne 0} \cr {k,} & {if\,x 13. If Cij denotes the cofactor of element pij of the matrix $$P = \left[ {\matrix{ 1 & { - 1} & 2 \cr 0 & 2 & { - 3 14. The function $$y = {x^2}{e^{ - x}}$$ is decreasing in the interval 15. If R = {(x, y); x, y $$\in$$ Z, x2 + y2 $$\le$$ 4} is a relation in set Z, then domain of R is 16. The system of linear equations5x + ky = 5,3x + 3y = 5; will be consistent if 17. The equation of the tangent to the curve y (1 + x2) = 2 $$-$$ x, where it crosses the x-axis is 18. If $$\left[ {\matrix{ {3c + 6} & {a - d} \cr {a + d} & {2 - 3b} \cr } } \right] = \left[ {\matrix{ {12} & 19. The principal value of $${\tan ^{ - 1}}\left( {\tan {{9\pi } \over 8}} \right)$$ is 20. For two matrices $$P = \left[ {\matrix{ 3 & 4 \cr { - 1} & 2 \cr 0 & 1 \cr } } \right]$$ and $${Q^T} = 21. The function $$f(x) = 2{x^3} - 15{x^2} + 36x + 6$$ is increasing in the interval 22. If $$x = 2\cos \theta - \cos 2\theta $$ and $$y = 2\sin \theta - \sin 2\theta $$, then $${{dy} \over {dx}}$$ is 23. What is the domain of the function $${\cos ^{ - 1}}(2x - 3)$$ ? 24. A matrix $$A = {[{a_{ij}}]_{3 \times 3}}$$ is defined by $${a_{ij}} = \left\{ {\matrix{ {2i + 3j} & , & {i j} \cr 25. If a function f defined by $$f(x) = \left\{ {\matrix{ {{{k\cos x} \over {\pi - 2x}}} & , & {if\,x \ne {\pi \over 2} 26. For the matrix $$X = \left[ {\matrix{ 0 & 1 & 1 \cr 1 & 0 & 1 \cr 1 & 1 & 0 \cr } } \right]$$, (X2 $$-$ 27. Let X = {x2 : x $$\in$$ N} and the function f : N $$\to$$ X is defined by f(x) = x2, x $$\in$$ N. Then this function is 28. The corner points of the feasible region for a Linear Programming problem are P(0, 5), Q(1, 5), R(4, 2) and S(12, 0). Th 29. The equation of the normal to the curve ay2 = x3 at the point (am2, am3) is 30. If A is a square matrix of order 3 and |A| = $$-$$ 5, then |adj A| is 31. The simplest form of $${\tan ^{ - 1}}\left[ {{{\sqrt {1 + x} - \sqrt {1 - x} } \over {\sqrt {1 + x} + \sqrt {1 - x} }} 32. If for the matrix $$A = \left[ {\matrix{ \alpha & { - 2} \cr { - 2} & \alpha \cr } } \right]$$, | A3 | = 1 33. If $$y = \sin (m{\sin ^{ - 1}}x)$$, then which one of the following equations is true? 34. The principal value of $$[{\tan ^{ - 1}}\sqrt 3 - {\cot ^{ - 1}}( - \sqrt 3 )]$$ is 35. The maximum value of $${\left( {{1 \over x}} \right)^{x}}$$ is 36. Let matrix $$X = [{x_{ij}}]$$ is given by $$X = \left[ {\matrix{ 1 & { - 1} & 2 \cr 3 & 4 & { - 5} \cr 2 & 37. A function f : R $$\to$$ R defined by f(x) = 2 + x2 is 38. A Linear Programming Problem is as follows:Maximize/Minimize objective function Z = 2x $$-$$ y + 5Subject to the constra 39. If x = $$-$$4 is a root of $$\left| {\matrix{ x & 2 & 3 \cr 1 & x & 1 \cr 3 & 2 & x \cr } } \right| = 0 40. The absolute maximum value of the function $$f(x) = 4x - {1 \over 2}{x^2}$$ in the interval $$\left[ { - 2,{9 \over 2}} 41. In a sphere of radius r, a right circular cone of height h having maximum curved surface area is inscribed. The expressi 42. The corner points of the feasible region determined by a set of constraints (linear inequalities) are P(0, 5), Q(3, 5), 43. If curves y2 = 4x and xy = c cut at right angles, then the value of c is 44. The inverse of the matrix $$X = \left[ {\matrix{ 2 & 0 & 0 \cr 0 & 3 & 0 \cr 0 & 0 & 4 \cr } } \right]$ 45. For an L.P.P. the objective function is Z = 4x + 3y, and the feasible region determined by a set of constraints (linear 46. In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were ins 47. In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were ins 48. In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were ins 49. In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were ins 50. In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were ins

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CBSE 12th Math (Term 1) Paper 2021-22

MCQ (Single Correct Answer)

-0

The function $$y = {x^2}{e^{ - x}}$$ is decreasing in the interval

(0, 2)

(2, $$\infty$$)

($$-$$ $$\infty$$, 0)

($$-$$ $$\infty$$, 0) $$\cup$$ (2, $$\infty$$)

CBSE 12th Math (Term 1) Paper 2021-22

MCQ (Single Correct Answer)

-0

If R = {(x, y); x, y $$\in$$ Z, x² + y² $$\le$$ 4} is a relation in set Z, then domain of R is

{0, 1, 2}

{$$-$$2, $$-$$1, 0, 1, 2}

{0, $$-$$1, $$-$$2}

{$$-$$1, 0, 1}

CBSE 12th Math (Term 1) Paper 2021-22

MCQ (Single Correct Answer)

-0

The system of linear equations

5x + ky = 5,

3x + 3y = 5; will be consistent if

k $$\ne$$ $$-$$3

k = $$-$$5

k = 5

k $$\ne$$ 5

CBSE 12th Math (Term 1) Paper 2021-22

MCQ (Single Correct Answer)

-0

The equation of the tangent to the curve y (1 + x²) = 2 $$-$$ x, where it crosses the x-axis is

x $$-$$ 5y = 2

5x $$-$$ y = 2

x + 5y = 2

5x + y = 2

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