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Mathematics · 2014 · Shift 2

20 questions from this JEE Advanced paper

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JEE Advanced
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2014 · Shift 2
Mathematics

Mathematics · 2014 · Shift 2

20 questions from this JEE Advanced paper

Probability3 questions Trigonometric Functions and Equations1 questions Inverse Trigonometric Functions1 questions Parabola2 questions Complex Numbers1 questions Quadratic Equation and Inequalities1 questions Mathematical Induction and Binomial Theorem1 questions Permutations and Combinations1 questions Ellipse1 questions Differential Equations1 questions Differentiation1 questions Properties of Triangle1 questions Definite Integration4 questions Functions1 questions

Q21.Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is
Mathematics · Probability · MCQ
Q22.For $x \in (0, π),$ the equation $sin x + 2 sin 2 x - sin 3 x = 3$ has
Mathematics · Trigonometric Functions and Equations · MCQ
Q23.Match List $I$ with List $I I$ and select the correct answer using the code given below the lists: List- $I$ (P.) Let $y (x) = cos (3 cos^{- 1} x), x \in [- 1, 1], x e \pm \frac{3}{2} .$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q24.Box $1$ contains three cards bearing numbers $1, 2, 3;$ box $2$ contains five cards bearing numbers $1, 2, 3, 4, 5;$ and box $3$ contains seven cards bearing numbers $1, 2, 3, 4, 5, 6, 7.$ A card is drawn from each of the boxes. Let $x_{i}$ be number…
Mathematics · Probability · MCQ
Q25.Box $1$ contains three cards bearing numbers $1, 2, 3;$ box $2$ contains five cards bearing numbers $1, 2, 3, 4, 5;$ and box $3$ contains seven cards bearing numbers $1, 2, 3, 4, 5, 6, 7.$ A card is drawn from each of the boxes. Let $x_{i}$ be number…
Mathematics · Probability · MCQ
Q26.Let $a, r, s, t$ be nonzero real numbers. Let $P (a t^{2}, 2 a t), Q, R (a r^{2}, 2 a r)$ and $S (a s^{2}, 2 a s)$ be distinct points on the parabola $y^{2} = 4 a x$ . Suppose that $P Q$ is…
Mathematics · Parabola · MCQ
Q27.Let $z_{k}$ = $cos (\frac{2 k π}{10}) + i sin (\frac{2 k π}{10}); k = 1, 2...., 9$ List-I P. For each $z_{k}$ = there exits as $z_{j}$ such that $z_{k}$ . $z_{j}$ = 1 Q. There exists a $k \in {1, 2, ...., 9}$ …
Mathematics · Complex Numbers · MCQ
Q28.The quadratic equation $p (x) = 0$ with real coefficients has purely imaginary roots. Then the equation $p (p (x)) = 0$ has
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.Coefficient of $x^{11}$ in the expansion of $(1 + x^{2})^{4} (1 + x^{3})^{7} (1 + x^{4})^{12}$ is
Mathematics · Mathematical Induction and Binomial Theorem · MCQ
Q30.Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered…
Mathematics · Permutations and Combinations · MCQ
Q31.The common tangents to the circle $x^{2} + y^{2} = 2$ and the parabola $y^{2} = 8 x$ touch the circle at the points $R$ and the parabola at the points $R$ , $S$ . Then the area of the quadrilateral $P QR S$ is
Mathematics · Ellipse · MCQ
Q32.Let $a, r, s, t$ be nonzero real numbers. Let $P (a t^{2}, 2 a t), Q, R (a r^{2}, 2 a r)$ and $S (a s^{2}, 2 a s)$ be distinct points on the parabola $y^{2} = 4 a x$ . Suppose that $P Q$ is…
Mathematics · Parabola · MCQ
Q33.The function $y = f (x)$ is the solution of the differential equation $\frac{d y}{d x} + \frac{x y}{x ^{2} - 1} = \frac{x ^{4} + 2 x}{1 - x ^{2}}$ in $(- 1, 1)$ satisfying $f (0) = 0$ . Then $- \frac{3}{2} \int \frac{3}{2} f (x) d (x)$ …
Mathematics · Differential Equations · MCQ
Q34.Let $f : [0, 2] \to R$ be a function which is continuous on $[0, 2]$ and is differentiable on $(0, 2)$ with $f (0) = 1$ . Let $F (x) = 0 \int x^{2} f (t) d t$ for $x \in [0, 2]$ …
Mathematics · Differentiation · MCQ
Q35.In a triangle the sum of two sides is $x$ and the product of the same sides is $y$ . If $x^{2} - c^{2} = y$ , where $c$ is the third side of the triangle, then the ratio of the in radius to the circum-radius of the triangle is
Mathematics · Properties of Triangle · MCQ
Q36.The following integral $\frac{π}{4} \int \frac{π}{2} (2 csc x)^{17} d x$ is equal to
Mathematics · Definite Integration · MCQ
Q37.List - $I$ P. The number of polynomials $f (x)$ with non-negative integer coefficients of degree $f (0) = 0$ , satisfying $f (0) = 0$ and $\int_{0}^{1} f (x) d x = 1,$ is Q. The number of points in the interval $[- 13, 13]$ …
Mathematics · Definite Integration · MCQ
Q38.Given that for each $a \in (0, 1), h \to 0^{+} lim h \int 1 - h t^{- a} (1 - t)^{a - 1} d t$ exists. Let this limit be $g (a) .$ In addition, it is given that the…
Mathematics · Definite Integration · MCQ
Q39.Given that for each $a \in (0, 1), h \to 0^{+} lim h \int 1 - h t^{- a} (1 - t)^{a - 1} d t$ exists. Let this limit be $g (a) .$ In addition, it is given that the…
Mathematics · Definite Integration · MCQ
Q40.Let f1 : R $\to$ R, f2 : [0, $\infty$ ) $\to$ R, f3 : R $\to$ R, and f4 : R $\to$ [0, $\infty$ ) be defined by $f_{1} (x) = {∣ x ∣ e^{x} i f x < 0, i f x \geq 0;$ … Includes diagram
Mathematics · Functions · MCQ