Math [Class XII]

Class/Course - Class XII

Subject - Math

Total Number of Question/s - 3349

• 1. Relations and Functions - Quiz
  
  
• 2. Inverse Trigonometric Functions - Quiz
  
  1. For the equation cos^-1x + cos^-12x + π = 0, the number of real solution is
  a) 1
  b) 2
  c) 0
  d) ∞
  

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  2. The solution of sin^-1x - sin^-12x = $\frac{\pm \pi}{3}$ is
  a) $\pm\frac{1}{3}$
  b) $\pm\frac{1}{4}$
  c) $\pm \frac{\sqrt{3}}{2}$
  d) $\pm\frac{1}{2}$
  

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• 3. Matrices - Quiz
  
  
• 4. Determinants and Matrices - Quiz
  
  1. If $\begin{bmatrix} sin^{2}\alpha &cos^{2}\alpha \\ cos^{2}\alpha& sin^{2}\alpha \end{bmatrix}$ = 0, α ε (0,π), then the values of α are
  a) $\frac{\pi}{2}$ and $\frac{\pi}{12}$
  b) $\frac{\pi}{2}$ and $\frac{\pi}{6}$
  c) $\frac{\pi}{4}$ and $\frac{3\pi}{4}$
  d) $\frac{\pi}{6}$ and $\frac{\pi}{3}$
  e) $\frac{\pi}{2}$ and $\frac{\pi}{3}$
  

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  2. If matrix A = $\begin{bmatrix} 1 & 0 & -1\\ 3& 4 &5 \\ 0 & 6 & 7 \end{bmatrix}$ and its inverse is denoted by A^-1 = $\begin{bmatrix} a_{11} & a_{12} &a_{13}\\ a_{21}& a_{22} &a_{23} \\ a_{31} &a_{32} & a_{33} \end{bmatrix}$, then the value of a₂₃ =
  a) $\frac{21}{20}$
  b) $\frac{1}{5}$
  c) $-\frac{1}{5}$
  d) $\frac{2}{5}$
  

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• 5. Continuity and Differentiability - Quiz
  
  1. The function f(x) = [x]² - [x²], (where [y] is the greatest integer less than or equal to y), is discontinuous at
  a) All integers
  b) All integers except 0 and 1
  c) All integers except 0
  d) All integers except 1
  

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  2. A = {1,2,3,4}, B = {1,2,3,4,5,6} are two sets and function f : A → B is defined by f(x) = x + 2, ∀ x ε A, then the function f is
  a) Bijective
  b) Onto
  c) One-one
  d) Many-one
  

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• 6. Differentiation and Application of Derivatives - Quiz
  
  1. f(x) = x⁵ - 5x⁴ + 5x³ + 1 has
  a) Two maximum and two minimum value
  b) Two maximum and one minimum value
  c) One maximum and one minimum value
  d) None of these
  

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  2. If y = $tan^{-1}\left (\frac{cosx}{1 + sinx} \right )$, then $\frac{dy}{dx}$ is equal to
  a) $\frac{1}{2}$
  b) 2
  c) -2
  d) $\frac{-1}{2}$
  e) -1
  

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• 7. Integrals - Quiz
  
  
• 8. Application of Integrals - Quiz
  
  1. $int_{\pi/4}^{3\pi/4}\frac{dx}{1 + cosx}$ is equal to
  a) 2
  b) 2
  c) $\frac{1}{2}$
  d) $-\frac{1}{2}$
  

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  2. If [x] is the greatest integer function not greater than x, then $\int_{0}^{11}\left [x \right ]dx$ =
  a) 55
  b) 45
  c) 66
  d) 35
  

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• 9. Differential Equations - Quiz
  
  1. Solution of $\frac{dy}{dx}$ = $\frac{xlogx^{2} + x}{siny + ycosy}$ is
  a) ysiny = x²logx + c
  b) ysiny = x² + c
  c) ysiny = x² + logx + c
  d) ysiny = xlogx + c
  

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  2. A solution of the differential equation $\left (\frac{dy}{dx} \right )^{2} - x\frac{dy}{dx} + y$ = 0 is
  a) y = 2
  b) y = 2x
  c) y = 2x - 4
  d) y = 2x² - 4
  

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• 10. Vector Algebra - Quiz
  
  1. If ABCDEF is regular hexagon, then $\overrightarrow{AD}$ + $\overrightarrow{EB}$ + $\overrightarrow{FC}$ =
  a) 0
  b) 2$\overrightarrow{AB}$
  c) $3\overrightarrow{AB}$
  d) $4\overrightarrow{AB}$
  

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  2. If a and b are two unit vectors such that a + 2b and 5a - 4b are perpendicular to each other, then the angle between a and b is
  a) 45⁰
  b) 60⁰
  c) $cos^{-1}\left (\frac{1}{3} \right )$
  d) $cos^{-1}\left (\frac{2}{7} \right )$
  

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• 11. Three Dimensional Geometry - Quiz
  
  1. In the space the equation by + cz + d = 0 represents a plane perpendicular to the plane
  a) YOZ
  b) Z = k
  c) ZOX
  d) XOY
  

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  2. The equation of the plane containing the lines
  $\frac{x - 1}{2}$ = $\frac{y + 1}{-1}$= $\frac{z}{3}$ and $\frac{x}{2}$ = $\frac{y - 2}{-1}$ = $\frac{z + 1}{3}$ is
  a) 8x - y + 5z - 8 = 0
  b) 8x + y - 5z - 7 = 0
  c) x - 8y + 3z + 6 = 0
  d) 8x + y - 5z + 7 = 0
  e) x + y + z - 6 = 0
  

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• 12. Linear Programming - Quiz
  
  1. For the following shaded area, the linear constraints except x ≥ 0 and y ≥ 0, are
  
  a) 2x + y ≤ 2, x - y ≤ 1, x + 2y ≤ 8
  b) 2x + y ≥ 2, x - y ≤ 1, x + 2y ≤ 8
  c) 2x + y ≥ 2, x - y ≥ 1, x + 2y ≤ 8
  d) 2x + y ≥ 2, x - y ≥ 1, x + 2y ≥ 8
  

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  2. The L.P. problem MaxZ = x₁ + x₂ such that -2x₁ + x₂ ≤ 1 , x₁ ≤ 2, x₁ + x₂ ≤ 3 and x₁, x₂ ≥ 0 has
  a) One solution
  b) Three solution
  c) An infinite no. of solution
  d) None of these
  

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• 13. Probability - Quiz
  
  1. Among 15 players, 8 are batsman and 7 are bowlers . Find the probability that a team is chosen of 6 batsman and 5 bowlers
  a) $\frac{^{8}C_{6} \times ^{7}C_{5}}{^{15}C_{11}}$
  b) $\frac{^{8}C_{6} + ^{7}C_{5}}{^{15}C_{11}}$
  c) $\frac{15}{28}$
  d) None of these
  

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  2. An unbiased coin is tossed. If the result is a head, a pait of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4, ..., 12 is picked andt he number on the card is noted. The probability that the noted number is either 7 or 8 is
  a) 0.24
  b) 0.244
  c) 0.024
  d) None of these
  

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• 14. Statistics and Dynamics - Quiz
  
  
• 15. Indefinite Integration - Quiz
  
  1. If $\int \frac{1}{x + x^{5}}dx$ = f(x) + c, then the value of $\int \frac{x^{4}}{x + x^{5}}dx$ is
  a) logx - f(x) + c
  b) f(x) + logx + c
  c) f(x) - logx + c
  d) None of these
  

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  2. $\int \frac{x + sinx}{1 + cosx}dx$ is equal to
  a) $-xtan\frac{x}{2}+ c$
  b) $xtan\frac{x}{2}+ c$
  c) xtanx + c
  d) $\frac{1}{2}xtanx + c$
  

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• 16. Definite Integration and Area under the curve - Quiz
  
  1. The intercepts on x-axis made by tangents to the curve, y = $\int_{0}^{x}|t| dt, x \epsilon R$, which are parallel to the line y = 2x, are equal to
  a) ±1
  b) ±2
  c) ±3
  d) ±4
  

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  2. Let a,b,c be non-zero real numbers such that $\int_{0}^{3}\left (3ax^{2} + 2bx + c \right )dx$ = $\int_{1}^{3}\left (3ax^{2} + 2bx + c \right )dx$, then
  a) a + b + c = 3
  b) a + b + c = 1
  c) a + b + c = 0
  d) a + b + c = 2
  

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