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Mathematics · 2016 · Shift 0

18 questions from this JEE Main paper

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2016 · Shift 0
Mathematics

Mathematics · 2016 · Shift 0

18 questions from this JEE Main paper

Limits Continuity and Differentiability2 questions Complex Numbers1 questions Statistics1 questions Probability1 questions Differential Equations1 questions Area Under the Curves1 questions Indefinite Integrals1 questions Matrices and Determinants2 questions Application of Derivatives1 questions Hyperbola1 questions Circle1 questions Straight Lines and Pair of Straight Lines1 questions Sequences and Series1 questions Permutations and Combinations1 questions Quadratic Equation and Inequalities1 questions Functions1 questions

Q20.For $x \in R, f (x) = ∣ lo g 2 - sin x ∣$ and $g (x) = f (f (x)),$ then :
Mathematics · Limits Continuity and Differentiability · MCQ
Q21.Let $p = x \to 0^{+} lim (1 + tan^{2} x)^{\frac{1}{2 x}}$ then $l o g p$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q22.A value of $θ$ for which $\frac{2 + 3 i s i n θ}{1 - 2 i s i n θ}$ is purely imaginary, is :
Mathematics · Complex Numbers · MCQ
Q23.If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?
Mathematics · Statistics · MCQ
Q24.Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_{1}$ is the event that die $A$ shows up four, $E_{2}$ is the event that die $B$ shows up two and $E_{3}$ is the event that the sum of numbers on both dice is odd, then…
Mathematics · Probability · MCQ
Q25.If a curve $y = f (x)$ passes through the point $(1, - 1)$ and satisfies the differential equation, $y (1 + x y) d x = x d y$ , then $f (- \frac{1}{2})$ is equal to :
Mathematics · Differential Equations · MCQ
Q26.The area (in sq. units) of the region ${(x, y) : y^{2} \geq 2 x an d x^{2} + y^{2} \leq 4 x, x \geq 0, y \geq 0}$ is :
Mathematics · Area Under the Curves · MCQ
Q27.The integral $\int \frac{2 x ^{12} + 5 x ^{9}}{( x ^{5} + x ^{3} + 1 ) ^{3}} d x$ is equal to :
Mathematics · Indefinite Integrals · MCQ
Q28.The system of linear equations $x + λ y - z = 0 λ x - y - z = 0 x + y - λ z = 0$ has a non-trivial solution for :
Mathematics · Matrices and Determinants · MCQ
Q29.If $A = [5 a 3 - b 2]$ and $A$ adj $A = A A^{T},$ then $5 a + b$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q30.A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $= r$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum, then:
Mathematics · Application of Derivatives · MCQ
Q31.The eccentricity of the hyperbola whose length of the latus rectum is equal to $8$ and the length of its conjugate axis is equal to half of the distance between its foci, is :
Mathematics · Hyperbola · MCQ
Q32.If one of the diameters of the circle, given by the equation, $x^{2} + y^{2} - 4 x + 6 y - 12 = 0,$ is a chord of a circle $S$ , whose centre is at $(- 3, 2)$ , then the radius of $S$ is :
Mathematics · Circle · MCQ
Q33.Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7 x - y - 5 = 0$ . If its diagonals intersect at $(- 1, - 2)$ , then which one of the following is a vertex of this rhombus?
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q34.If the $2^{n d}, 5^{t h} an d 9^{t h}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :
Mathematics · Sequences and Series · MCQ
Q35.If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is :
Mathematics · Permutations and Combinations · MCQ
Q36.The sum of all real values of $x$ satisfying the equation $(x^{2} - 5 x + 5)^{x^{2} + 4 x - 60} = 1$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q37.If $f (x) + 2 f (\frac{1}{x}) = 3 x, x e q 0$ , and $S = {x \in R : f (x) = f (- x)}$ ; then $S :$
Mathematics · Functions · MCQ