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Mathematics · 2019 · 8 Apr · Shift 2

21 questions from this JEE Main paper

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2019 · 8 Apr · Shift 2
Mathematics

Mathematics · 2019 · 8 Apr · Shift 2

21 questions from this JEE Main paper

Vector Algebra1 questions Ellipse1 questions Complex Numbers1 questions Definite Integration1 questions Sequences and Series1 questions Quadratic Equation and Inequalities1 questions 3D Geometry1 questions Matrices and Determinants1 questions Limits Continuity and Differentiability2 questions Binomial Theorem1 questions Differentiation1 questions Area Under the Curves1 questions Straight Lines and Pair of Straight Lines2 questions Functions1 questions Statistics1 questions Probability1 questions Application of Derivatives1 questions Permutations and Combinations1 questions Indefinite Integrals1 questions

Q25.Let $a \to = 3 i \land + 2 j \land + x k \land$ and $b \to = i \land - j \land + k \land$ , for some real…
Mathematics · Vector Algebra · MCQ
Q26.In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at (0,5 $3$ ), then the length of its latus rectum is :
Mathematics · Ellipse · MCQ
Q27.If $z = \frac{3}{2} + \frac{i}{2} (i = - 1)$ , then (1 + iz + z5 + iz8)9 is equal to :
Mathematics · Complex Numbers · MCQ
Q28.Let $f (x) = 0 \int x g (t) d t$ where g is a non-zero even function. If ƒ(x + 5) = g(x), then $0 \int x f (t) d t$ equals-
Mathematics · Definite Integration · MCQ
Q29.If three distinct numbers a, b, c are in G.P. and the equations ax2 + 2bx + c = 0 and dx2 + 2ex + ƒ = 0 have a common root, then which one of the following statements is correct?
Mathematics · Sequences and Series · MCQ
Q30.The number of integral values of m for which the equation (1 + m2 )x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q31.If a point R(4, y, z) lies on the line segment joining the points P(2, –3, 4) and Q(8, 0, 10), then the distance of R from the origin is :
Mathematics · 3D Geometry · MCQ
Q32.Let the number 2,b,c be in an A.P. and A = $124 1 b b^{2} 1 c c^{2}$ . If det(A) $\in$ [2, 16], then c lies in the interval :
Mathematics · Matrices and Determinants · MCQ
Q33.Let ƒ : R $\to$ R be a differentiable function satisfying ƒ'(3) + ƒ'(2) = 0. Then $x \to 0 lim (\frac{1 + f ( 3 + x ) - f ( 3 )}{1 + f ( 2 - x ) - f ( 2 )})^{\frac{1}{x}}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q34.If the fourth term in the binomial expansion of $(x^{(\frac{1}{1 + l o g _{10} x})} + x^{\frac{1}{12}})^{6}$ is equal to 200, and x > 1, then the value of x is :
Mathematics · Binomial Theorem · MCQ
Q35.If ƒ(1) = 1, ƒ'(1) = 3, then the derivative of ƒ(ƒ(ƒ(x))) + (ƒ(x))2 at x = 1 is :
Mathematics · Differentiation · MCQ
Q36.Let S( $α$ ) = {(x, y) : y2 $\leq$ x, 0 $\leq$ x $α$ } and A( $α$ ) is area of the region S( $α$ ). If for a $λ$ , 0 < $λ$ < 4, A( $λ$ ) : A(4) = 2 : 5, then $λ$ equals
Mathematics · Area Under the Curves · MCQ
Q37.If the system of linear equations x – 2y + kz = 1 2x + y + z = 2 3x – y – kz = 3 has a solution (x,y,z), z $e$ 0, then (x,y) lies on the straight line whose equation is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.Let ƒ(x) = ax (a > 0) be written as ƒ(x) = ƒ1 (x) + ƒ2 (x), where ƒ1 (x) is an even function of ƒ2 (x) is an odd function. Then ƒ1 (x + y) + ƒ1 (x – y) equals
Mathematics · Functions · MCQ
Q39.A student scores the following marks in five tests : 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is
Mathematics · Statistics · MCQ
Q40.The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :
Mathematics · Probability · MCQ
Q41.The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is
Mathematics · Application of Derivatives · MCQ
Q42.The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0,1,2,3,4,5 (repetition of digits is allowed) is :
Mathematics · Permutations and Combinations · MCQ
Q43.Let ƒ : [–1,3] $\to$ R be defined as $f (x) = ⎩ ⎨ ⎧ ∣ x ∣ + [x] x + ∣ x ∣ x + [x],,, - 1 \leq x < 1 1 \leq x < 2 2 \leq x \leq 3$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q44.Suppose that the points (h,k), (1,2) and (–3,4) lie on the line L1 . If a line L2 passing through the points (h,k) and (4,3) is perpendicular to L1 , then $\frac{k}{h}$ equals :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q45.If $\int \frac{d x}{x ^{3} ( 1 + x ^{6} ) ^{2/3}} = x f (x) (1 + x^{6})^{\frac{1}{3}} + C$ where C is a constant of integration, then the function ƒ(x) is equal to
Mathematics · Indefinite Integrals · MCQ