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Mathematics · 2012 · Shift 0

22 questions from this JEE Main paper

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2012 · Shift 0
Mathematics

Mathematics · 2012 · Shift 0

22 questions from this JEE Main paper

Sets and Relations1 questions Statistics1 questions Limits Continuity and Differentiability2 questions Application of Derivatives3 questions Vector Algebra2 questions Probability1 questions Differential Equations1 questions Definite Integration1 questions Area Under the Curves1 questions Indefinite Integrals1 questions 3D Geometry1 questions Ellipse1 questions Circle1 questions Straight Lines and Pair of Straight Lines1 questions Binomial Theorem1 questions Permutations and Combinations1 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions

Q23.Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y $\subseteq$ X, Z $\subseteq$ X and Y $\cap$ Z is empty, is :
Mathematics · Sets and Relations · MCQ
Q24.Let x1, x2,........., xn be n observations, and let $\overline{x}$ be their arithematic mean and $σ^{2}$ be their variance. Statement 1 : Variance of 2x1, 2x2,......., 2xn is 4 $σ^{2}$ . Statement 2 : : Arithmetic mean of 2x1,…
Mathematics · Statistics · MCQ
Q25.If $f : R \to R$ is a function defined by $f (x) = [x] cos (\frac{2 x - 1}{2}) π$ , where [x] denotes the greatest integer function, then $f$ is
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.Consider the function, $f (x) = ∣ x - 2 ∣ + ∣ x - 5 ∣, x \in R$ Statement - 1 : $f^{'} (4) = 0$ Statement - 2 : $f$ is continuous in [2, 5], differentiable in (2, 5) and $f$ (2) = $f$ (5)
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.Let $a, b \in R$ be such that the function $f$ given by $f (x) = I n ∣ x ∣ + b x^{2} + a x, x e 0$ has extreme values at $x = - 1$ and $x = 2$ Statement-1 : $f$ has local maximum at $x = - 1$ and at $x = 2$ . Statement-2 : $a = \frac{1}{2}$ …
Mathematics · Application of Derivatives · MCQ
Q28.Let $a$ and $b$ be two unit vectors. If the vectors $c = a + 2 b$ and $d = 5 a - 4 b$ are perpendicular to each other, then the angle…
Mathematics · Vector Algebra · MCQ
Q29.Three numbers are chosen at random without replacement from ${1, 2, 3, ..8} .$ The probability that their minimum is $3,$ given that their maximum is $6,$ is :
Mathematics · Probability · MCQ
Q30.The population $p (t)$ at time $t$ of a certain mouse species satisfies the differential equation $\frac{d p ( t )}{d t} = 0.5 p (t) - 450.$ If $p (0) = 850,$ then the time at which the population becomes zero is…
Mathematics · Differential Equations · MCQ
Q31.If $g (x) = 0 \int x cos 4 t d t,$ then $g (x + π)$ equals
Mathematics · Definite Integration · Multiple correct
Q32.The area between the parabolas $x^{2} = \frac{y}{4}$ and $x^{2} = 9 y$ and the straight line $y = 2$ is :
Mathematics · Area Under the Curves · MCQ
Q33.If the $\int \frac{5 t a n x}{t a n x - 2} d x = x + a ln ∣ sin x - 2 cos x ∣ + k,$ then $a$ is equal to :
Mathematics · Indefinite Integrals · MCQ
Q34.A line is drawn through the point $(1, 2)$ to meet the coordinate axes at $P$ and $Q$ such that it forms a triangle $O P Q,$ where $O$ is the origin. If the area of the triangle $O P Q$ is least, then the slope of the line $P Q$ is :
Mathematics · Application of Derivatives · MCQ
Q35.If the line $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4}$ and $\frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1}$ intersect, then $k$ is equal to :
Mathematics · 3D Geometry · MCQ
Q36.A spherical balloon is filled with $4500 π$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72 π$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the…
Mathematics · Application of Derivatives · MCQ
Q37.An ellipse is drawn by taking a diameter of thec circle $(x - 1)^{2} + y^{2} = 1$ as its semi-minor axis and a diameter of the circle $x^{2} + (y - 2)^{2} = 4$ is semi-major axis. If the centre of the…
Mathematics · Ellipse · MCQ
Q38.The length of the diameter of the circle which touches the $x$ -axis at the point $(1, 0)$ and passes through the point $(2, 3)$ is :
Mathematics · Circle · MCQ
Q39.If the line $2 x + y = k$ passes through the point which divides the line segment joining the points $(1, 1)$ and $(2, 4)$ in the ratio $3 : 2$ , then $k$ equals :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q40.If $n$ is a positive integer, then $(3 + 1)^{2 n} - (3 - 1)^{2 n}$ is :
Mathematics · Binomial Theorem · MCQ
Q41.Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:
Mathematics · Permutations and Combinations · MCQ
Q42.The equation $e^{s i n x} - e^{- s i n x} - 4 = 0$ has:
Mathematics · Quadratic Equation and Inequalities · MCQ
Q43.If $z e 1$ and $\frac{z ^{2}}{z - 1}$ is real, then the point represented by the complex number z lies :
Mathematics · Complex Numbers · MCQ
Q44.Let $A B C D$ be a parallelogram such that $A B = q, A D = p$ and $∠ B A D$ be an acute angle. If $r$ is the vector that coincide with the altitude…
Mathematics · Vector Algebra · MCQ