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Mathematics · 2014 · Shift 0

20 questions from this JEE Main paper

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2014 · Shift 0
Mathematics

Mathematics · 2014 · Shift 0

20 questions from this JEE Main paper

Statistics1 questions Limits Continuity and Differentiability1 questions Differential Equations1 questions Definite Integration1 questions Area Under the Curves1 questions Indefinite Integrals1 questions Matrices and Determinants2 questions Application of Derivatives1 questions Differentiation1 questions Probability1 questions Ellipse1 questions Straight Lines and Pair of Straight Lines2 questions Sequences and Series1 questions Quadratic Equation and Inequalities2 questions Complex Numbers1 questions Trigonometric Ratio and Identites1 questions 3D Geometry1 questions

Q25.The variance of first 50 even natural numbers is
Mathematics · Statistics · MCQ
Q26. $x \to 0 lim \frac{s i n ( π c o s ^{2} x )}{x ^{2}}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.Let the population of rabbits surviving at time $t$ be governed by the differential equation $\frac{d p ( t )}{d t} = \frac{1}{2} p (t) - 200.$ If $p (0) = 100,$ then $p (t)$ equals:
Mathematics · Differential Equations · MCQ
Q28.The integral $0 \int π 1 + 4 sin^{2} \frac{x}{2} - 4 sin \frac{x}{2} d x$ equals:
Mathematics · Definite Integration · MCQ
Q29.The area of the region described by $A = {(x, y) : x^{2} + y^{2} \leq 1$ and $y^{2} \leq 1 - x}$ is :
Mathematics · Area Under the Curves · MCQ
Q30.The integral $\int (1 + x - \frac{1}{x}) e^{x + \frac{1}{x}} d x$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q31.If $A$ is a $3 \times 3$ non-singular matrix such that $A A^{'} = A^{'} A$ and $B = A^{- 1} A^{'},$ then $B B^{'}$ equals:
Mathematics · Matrices and Determinants · MCQ
Q32.If $α, β e 0,$ and $f (n) = α^{n} + β^{n}$ and $3 1 + f (1) 1 + f (2) 1 + f (1) 1 + f (2) 1 + f (3) 1 + f (2) 1 + f (3) 1 + f (4)$ …
Mathematics · Matrices and Determinants · MCQ
Q33.If $x = - 1$ and $x = 2$ are extreme points of $f (x) = α lo g ∣ x ∣ + β x^{2} + x$ then
Mathematics · Application of Derivatives · MCQ
Q34.If $g$ is the inverse of a function $f$ and $f^{'} (x) = \frac{1}{1 + x ^{5}},$ then $g^{'} (x)$ is equal to:
Mathematics · Differentiation · MCQ
Q35.Let $A$ and $B$ be two events such that $P (\overline{A \cup B}) = \frac{1}{6}, P (A \cap B) = \frac{1}{4}$ and $P (\overline{A}) = \frac{1}{4},$ where $\overline{A}$ stands for the…
Mathematics · Probability · MCQ
Q36.The locus of the foot of perpendicular drawn from the centre of the ellipse $x^{2} + 3 y^{2} = 6$ on any tangent to it is :
Mathematics · Ellipse · MCQ
Q37.Let $a, b, c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4 a x + 2 a y + c = 0$ and $5 b x + 2 b y + d = 0$ lies in the fourth quadrant and is equidistant from the two axes then :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.Let $P S$ be the median of the triangle with vertices $P (2, 2)$ , $Q (6, - 1)$ and $R (7, 3)$ . The equation of the line passing through $(1, - 1)$ band parallel to PS is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is :
Mathematics · Sequences and Series · MCQ
Q40.Let $α$ and $β$ be the roots of equation $p x^{2} + q x + r = 0, p e 0.$ If $p, q, r$ in A.P. and $\frac{1}{α} + \frac{1}{β} = 4,$ then the value of $∣ α - β ∣$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q41.If $a \in R$ and the equation $- 3 (x - [x])^{2} + 2 (x - [x]) + a^{2} = 0$ (where [ $x$ ] denotes the greater integer $\leq x$ ) has no integral solution, then all possible values of a…
Mathematics · Quadratic Equation and Inequalities · MCQ
Q42.If z is a complex number such that $∣ z ∣ \geq 2$ , then the minimum value of $z + \frac{1}{2}$ :
Mathematics · Complex Numbers · MCQ
Q43.Let $f_{k} (x) = \frac{1}{k} (sin^{k} x + cos^{k} x)$ where $x \in R$ and $k \geq 1.$ Then $f_{4} (x) - f_{6} (x)$ equals :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q44.The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$ and $l^{2} = m^{2} + n^{2}$ is :
Mathematics · 3D Geometry · MCQ