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Mathematics · 2017 · Shift 1

18 questions from this JEE Advanced paper
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Mathematics · 2017 · Shift 1

18 questions from this JEE Advanced paper

Probability1 questionsLimits Continuity and Differentiability3 questionsComplex Numbers1 questionsHyperbola3 questionsMatrices and Determinants2 questionsParabola2 questionsSequences and Series1 questionsEllipse1 questionsPermutations and Combinations1 questionsApplication of Derivatives3 questions
  1. Q19.Let X and Y be two events such that P(X)=31​, P(X∣Y)=21​ and P(Y∣X)=52​. Then
    Mathematics · Probability · Multiple correct
  2. Q20.Let f : R → (0, 1) be a continuous function. Then, which of the following function(s) has (have) the value zero at some point in the interval (0, 1) ?
    Mathematics · Limits Continuity and Differentiability · Multiple correct
  3. Q21.Let a, b, x and y be real numbers such that a − b = 1 and y e 0. If the complex number z = x + iy satisfies Imolimits(z+1az+b​)=y, then which of the following is(are) possible…
    Mathematics · Complex Numbers · Multiple correct
  4. Q22.If 2x−y+1=0 is a tangent to the hyperbola a2x2​−16y2​=1 then which of the following CANNOT be sides of a right angled triangle?
    Mathematics · Hyperbola · Multiple correct
  5. Q23.Let [x] be the greatest integer less than or equals to x. Then, at which of the following point(s) the function f(x)=xcos(π(x+[x])) is discontinuous?
    Mathematics · Limits Continuity and Differentiability · Multiple correct
  6. Q24.Which of the following is(are) NOT the square of a 3 × 3 matrix with real entries?
    Mathematics · Matrices and Determinants · Multiple correct
  7. Q25.If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x + y = p, and mid-point (h, k), then which of the following is(are) possible value(s) of p, h and k?
    Mathematics · Parabola · Multiple correct
  8. Q26.For a real number α, if the system ​1αα2​α1α​α2α1​​​xyz​​=​1−11​​…
    Mathematics · Matrices and Determinants · Numerical
  9. Q27.The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?
    Mathematics · Sequences and Series · Numerical
  10. Q28.Let f : R → R be a differentiable function such that f(0) = 0, f(2π​)=3 and f'(0) = 1. If g(x)=x∫π/2​[f′(t)cosect−cottcosectf(t)]dt for x∈(0,2π​]…
    Mathematics · Limits Continuity and Differentiability · Numerical
  11. Q29.For how many values of p, the circle x2 + y2 + 2x + 4y − p = 0 and the coordinate axes have exactly three common points?
    Mathematics · Ellipse · Numerical
  12. Q30.Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated; and let y be the number of such words where exactly one letter is repeated twice and no other…
    Mathematics · Permutations and Combinations · Numerical
  13. Q31.By appropriately matching the information given in the three columns of the following table. Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively. For a=2​, if a tangent is… Includes table
    Mathematics · Hyperbola · MCQ
  14. Q32.By appropriately matching the information given in the three columns of the following table. Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively. The tangent to a suitable conic… Includes table
    Mathematics · Hyperbola · MCQ
  15. Q33.By appropriately matching the information given in the three columns of the following table. Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively. If a tangent to a suitable conic… Includes table
    Mathematics · Parabola · MCQ
  16. Q34.By approximately matching the information given in the three columns of the following table. Let f(x) = x + loge x − x loge x, x ∈(0, ∞) Column 1 contains information about zeroes of f(x), f'(x) and f"(x). Column 2 contains… Includes table
    Mathematics · Application of Derivatives · MCQ
  17. Q35.By approximately matching the information given in the three columns of the following table. Let f(x) = x + loge x − x loge x, x ∈(0, ∞) Column 1 contains information about zeroes of f(x), f'(x) and f"(x). Column 2 contains… Includes table
    Mathematics · Application of Derivatives · MCQ
  18. Q36.By approximately matching the information given in the three columns of the following table. Let f(x) = x + loge x − x loge x, x ∈(0, ∞) Column 1 contains information about zeroes of f(x), f'(x) and f"(x). Column 2 contains… Includes table
    Mathematics · Application of Derivatives · MCQ