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Mathematics · 2019 · 9 Jan · Shift 2

24 questions from this JEE Main paper

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2019 · 9 Jan · Shift 2
Mathematics

Mathematics · 2019 · 9 Jan · Shift 2

24 questions from this JEE Main paper

Sequences and Series1 questions Definite Integration2 questions Parabola1 questions 3D Geometry1 questions Hyperbola1 questions Permutations and Combinations2 questions Differentiation1 questions Indefinite Integrals1 questions Matrices and Determinants2 questions Statistics1 questions Straight Lines and Pair of Straight Lines1 questions Quadratic Equation and Inequalities2 questions Complex Numbers1 questions Area Under the Curves1 questions Differential Equations1 questions Inverse Trigonometric Functions1 questions Limits Continuity and Differentiability1 questions Vector Algebra1 questions Probability1 questions Functions1 questions

Q24.Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also three consecutive terms of a G.P., then $\frac{a}{c}$ equal to :
Mathematics · Sequences and Series · MCQ
Q25.If $0 \int \frac{π}{3} \frac{t a n θ}{2 k s e c θ} d θ = 1 - \frac{1}{2}, (k > 0),$ then value of k is :
Mathematics · Definite Integration · MCQ
Q26.Let A(4, $-$ 4) and B(9, 6) be points on the parabola, y2 = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of $Δ$ ACB is maximum. Then, the area (in sq. units) of $Δ$ ACB, is :
Mathematics · Parabola · MCQ
Q27.If the lines x = ay + b, z = cy + d and x = a'z + b', y = c'z + d' are perpendicular, then :
Mathematics · 3D Geometry · MCQ
Q28.A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :
Mathematics · Hyperbola · MCQ
Q29.The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repitition of digits allowed) is equal to :
Mathematics · Permutations and Combinations · MCQ
Q30.If x $=$ 3 tan t and y $=$ 3 sec t, then the value of $\frac{d ^{2} y}{d x ^{2}}$ at t $= \frac{π}{4},$ is :
Mathematics · Differentiation · MCQ
Q31.Let f be a differentiable function from R to R such that $∣ f (x) - f (y) ∣ \leq 2 ∣ x - y ∣^{\frac{3}{2}},$ for all $x, y \in$ R. If $f (0) = 1$ then $0 \int 1 f^{2} (x) d x$ …
Mathematics · Definite Integration · MCQ
Q32.If $f (x) = \int \frac{5 x ^{8} + 7 x ^{6}}{( x ^{2} + 1 + 2 x ^{7} ) ^{2}} d x, (x \geq 0), f (0) = 0,$ then the value of $f (1)$ is :
Mathematics · Indefinite Integrals · MCQ
Q33.If $A = e^{t} e^{t} e^{t} e^{- t} cos t - e^{- t} cos t - e^{- t} sin t 2 e^{- t} sin t e^{- t} sin t - e^{- t} sin t + e^{- t} co s o l imi t s t - 2 e^{- t} cos t$ …
Mathematics · Matrices and Determinants · MCQ
Q34.A data consists of n observations : x1, x2, . . . . . . ., xn. If $i = 1 \sum n (x_{i} + 1)^{2} = 9 n$ and $i = 1 \sum n (x_{i} - 1)^{2} = 5 n,$ then the standard deviation of this…
Mathematics · Statistics · MCQ
Q35.Let the equations of two sides of a triangle be 3x $-$ 2y + 6 = 0 and 4x + 5y $-$ 20 = 0. If the orthocentre of this triangle is at (1, 1), then the equation of its third side is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q36.Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements…
Mathematics · Permutations and Combinations · MCQ
Q37.If both the roots of the quadratic equation x2 $-$ mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q38.Let z0 be a root of the quadratic equation, x2 + x + 1 = 0, If z = 3 + 6iz $_{0}^{81} -$ 3iz $_{0}^{93}$ , then arg z is equal to :
Mathematics · Complex Numbers · MCQ
Q39.If the system of linear equations x $-$ 4y + 7z = g 3y $-$ 5z = h $-$ 2x + 5y $-$ 9z = k is consistent, then :
Mathematics · Matrices and Determinants · MCQ
Q40.The area of the region A = {(x, y) : 0 $\leq$ y $\leq$ x |x| + 1 and $-$ 1 $\leq$ x $\leq$ 1} in sq. units, is :
Mathematics · Area Under the Curves · MCQ
Q41.Let f : [0,1] $\to$ R be such that f(xy) = f(x).f(y), for all x, y $\in$ [0, 1], and f(0) $e$ 0. If y = y(x) satiesfies the differential equation, $\frac{d y}{d x}$ = f(x) with y(0) = 1, then y $(\frac{1}{4})$ + y $(\frac{3}{4})$ …
Mathematics · Differential Equations · MCQ
Q42.If x = sin $-$ 1(sin10) and y = cos $-$ 1(cos10), then y $-$ x is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q43.For each x $\in$ R, let [x] be the greatest integer less than or equal to x. Then $x \to 0^{-} lim \frac{x ( [ x ] + ∣ x ∣ ) s i n [ x ]}{∣ x ∣}$ is…
Mathematics · Limits Continuity and Differentiability · MCQ
Q44.Let $a = i + j + 2 k, b = b_{1} i + b_{2} j + 2 k$ , $c = 5 i + j + 2 k$ be three vectors…
Mathematics · Vector Algebra · MCQ
Q45.An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not…
Mathematics · Probability · MCQ
Q46.The number of all possible positive integral values of $α$ for which the roots of the quadratic equation, 6x2 $-$ 11x + $α$ = 0 are rational numbers is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q47.Let A = {x $\in$ R : x is not a positive integer}. Define a function $f$ : A $\to$ R as $f (x)$ = $\frac{2 x}{x - 1}$ , then $f$ is :
Mathematics · Functions · MCQ