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Mathematics · 2017 · 8 Apr · Shift 1

24 questions from this JEE Main paper

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2017 · 8 Apr · Shift 1
Mathematics

Mathematics · 2017 · 8 Apr · Shift 1

24 questions from this JEE Main paper

Limits Continuity and Differentiability1 questions Permutations and Combinations1 questions Sequences and Series1 questions Binomial Theorem1 questions Functions1 questions Matrices and Determinants3 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Ellipse1 questions Inverse Trigonometric Functions1 questions Probability2 questions Statistics1 questions Vector Algebra1 questions Circle2 questions Area Under the Curves1 questions Definite Integration1 questions Hyperbola1 questions Differential Equations1 questions Differentiation1 questions Indefinite Integrals1 questions

Q25. $x \to 3 lim$ $\frac{3 x - 3}{2 x - 4 - 2}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :
Mathematics · Permutations and Combinations · MCQ
Q27.If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then $\frac{a + b}{a - b}$ is equal to :
Mathematics · Sequences and Series · MCQ
Q28.If (27)999 is divided by 7, then the remainder is :
Mathematics · Binomial Theorem · MCQ
Q29.Let f(x) = 210.x + 1 and g(x)=310.x $-$ 1. If (fog) (x) = x, then x is equal to :
Mathematics · Functions · MCQ
Q30.The number of real values of $λ$ for which the system of linear equations 2x + 4y $- λ$ z = 0 4x + $λ$ y + 2z = 0 $λ$ x + 2y + 2z = 0 has infinitely many solutions, is :
Mathematics · Matrices and Determinants · MCQ
Q31.Let A be any 3 $\times$ 3 invertible matrix. Then which one of the following is not always true ?
Mathematics · Matrices and Determinants · MCQ
Q32.Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x $-$ 1 and it leaves remainder 6 when divided by x + 1; then :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q33.Let z $\in$ C, the set of complex numbers. Then the equation, 2|z + 3i| $-$ |z $-$ i| = 0 represents :
Mathematics · Complex Numbers · MCQ
Q34.Consider an ellipse, whose center is at the origin and its major axis is along the x-axis. If its eccentricity is $\frac{3}{5}$ and the distance between its foci is 6, then the area (in sq. units) of the quadrilatateral inscribed in the…
Mathematics · Ellipse · MCQ
Q35.The value of tan-1 $[\frac{1 + x ^{2} + 1 - x ^{2}}{1 + x ^{2} - 1 - x ^{2}}], ∣ x ∣ < \frac{1}{2}, x e 0,$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q36.If $S = ⎩ ⎨ ⎧ x \in [0, 2 π] : 0 sin x cos x cos x 0 sin x - sin x cos x 0 = 0 ⎭ ⎬ ⎫,$ then $x \in S \sum tan (\frac{π}{3} + x)$ …
Mathematics · Matrices and Determinants · MCQ
Q37.Three persons P, Q and R independently try to hit a target. I the probabilities of their hitting the target are $\frac{3}{4}, \frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by P or Q but not by R is…
Mathematics · Probability · MCQ
Q38.An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :
Mathematics · Probability · MCQ
Q39.The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly…
Mathematics · Statistics · MCQ
Q40.The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8 i - 6 j$ and $3 i + 4 j - 12 k,$ is :
Mathematics · Vector Algebra · MCQ
Q41.If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles $cos^{- 1} (\frac{1}{7})$ and sec $-$ 1 (7) at the center respectivey, then the distance between…
Mathematics · Circle · MCQ
Q42.The area (in sq. units) of the smaller portion enclosed between the curves, x2 + y2 = 4 and y2 = 3x, is :
Mathematics · Area Under the Curves · MCQ
Q43.The integral $\int_{\frac{π}{12}}^{\frac{π}{4}} \frac{8 c o s 2 x}{( t a n x + c o t x ) ^{3}} d x$ equals :
Mathematics · Definite Integration · MCQ
Q44.The locus of the point of intersection of the straight lines, tx $-$ 2y $-$ 3t = 0 x $-$ 2ty + 3 = 0 (t $\in$ R), is :
Mathematics · Hyperbola · MCQ
Q45.The curve satisfying the differential equation, ydx $-$ (x + 3y2)dy = 0 and passing through the point (1, 1), also passes through the point :
Mathematics · Differential Equations · MCQ
Q46.If a point P has co-ordinates (0, $-$ 2) and Q is any point on the circle, x2 + y2 $-$ 5x $-$ y + 5 = 0, then the maximum value of (PQ)2 is :
Mathematics · Circle · MCQ
Q47.If y = $[x + x^{2} - 1]^{15} + [x - x^{2} - 1]^{15},$ then (x2 $-$ 1) $\frac{d ^{2} y}{d x ^{2}} + x \frac{d y}{d x}$ is equal to :
Mathematics · Differentiation · MCQ
Q48.The integral $\int 1 + 2 cot x (csc x + cot x) d x (0 < x < \frac{π}{2})$ is equal to : (where C is a constant of integration)
Mathematics · Indefinite Integrals · MCQ