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Mathematics · 2022 · 25 Jun · Shift 1

20 questions from this JEE Main paper

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2022 · 25 Jun · Shift 1
Mathematics

Mathematics · 2022 · 25 Jun · Shift 1

20 questions from this JEE Main paper

Definite Integration1 questions Functions3 questions Matrices and Determinants2 questions Differentiation1 questions Binomial Theorem1 questions Limits Continuity and Differentiability1 questions Probability1 questions Differential Equations3 questions Vector Algebra2 questions Parabola1 questions Complex Numbers1 questions Permutations and Combinations2 questions Circle1 questions

Q24.The value of $0 \int π \frac{e ^{c o s x} s i n x}{( 1 + c o s ^{2} x ) ( e ^{c o s x} + e ^{- c o s x} )} d x$ is equal to:
Mathematics · Definite Integration · MCQ
Q25.Let f : N $\to$ R be a function such that $f (x + y) = 2 f (x) f (y)$ for natural numbers x and y. If f(1) = 2, then the value of $α$ for which $k = 1 \sum 10 f (α + k) = \frac{512}{3} (2^{20} - 1)$ holds, is :
Mathematics · Functions · MCQ
Q26.Let A be a 3 $\times$ 3 real matrix such that $A 110 = 110; A 101 = - 1 01$ …
Mathematics · Matrices and Determinants · MCQ
Q27.Let f : R $\to$ R be defined as $f (x) = x^{3} + x - 5$ . If g(x) is a function such that $f (g (x)) = x, \forall^{'} x^{'} \in R$ , then g'(63) is equal to .
Mathematics · Differentiation · MCQ
Q28.If $\frac{1}{2 . 3 ^{10}} + \frac{1}{2 ^{2} . 3 ^{9}} + ..... + \frac{1}{2 ^{10} . 3} = \frac{K}{2 ^{10} . 3 ^{10}}$ , then the remainder when K is divided by 6 is :
Mathematics · Binomial Theorem · MCQ
Q29.Let f(x) be a polynomial function such that $f (x) + f^{'} (x) + f^{''} (x) = x^{5} + 64$ . Then, the value of $x \to 1 lim \frac{f ( x )}{x - 1}$ is equal to:
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.Let E1 and E2 be two events such that the conditional probabilities $P (E_{1} ∣ E_{2}) = \frac{1}{2}$ , $P (E_{2} ∣ E_{1}) = \frac{3}{4}$ and $P (E_{1} \cap E_{2}) = \frac{1}{8}$ . Then :
Mathematics · Probability · MCQ
Q31.Let $A = [02 - 2 0]$ . If M and N are two matrices given by $M = k = 1 \sum 10 A^{2 k}$ and $N = k = 1 \sum 10 A^{2 k - 1}$ then MN2 is :
Mathematics · Matrices and Determinants · MCQ
Q32.Let $g : (0, \infty) \to R$ be a differentiable function such that $\int (\frac{x ( c o s x - s i n x )}{e ^{x} + 1} + \frac{g ( x ) ( e ^{x} + 1 - x e ^{x} )}{( e ^{x} + 1 ) ^{2}}) d x = \frac{x g ( x )}{e ^{x} + 1} + c$ …
Mathematics · Differential Equations · MCQ
Q33.Let $f : R \to R$ and $g : R \to R$ be two functions defined by $f (x) = lo g_{e} (x^{2} + 1) - e^{- x} + 1$ and $g (x) = \frac{1 - 2 e ^{2 x}}{e ^{x}}$ . Then, for which of the following range of $α$ , the inequality $f (g (\frac{( α - 1 ) ^{2}}{3})) > f (g (α - \frac{5}{3}))$ …
Mathematics · Functions · MCQ
Q34.Let $a = a_{1} i + a_{2} j + a_{3} k$ $a_{i} > 0$ , $i = 1, 2, 3$ be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of $a$ on the…
Mathematics · Vector Algebra · MCQ
Q35.Let $y = y (x)$ be the solution of the differential equation $(x + 1) y^{'} - y = e^{3 x} (x + 1)^{2}$ , with $y (0) = \frac{1}{3}$ . Then, the point $x = - \frac{4}{3}$ for the curve $y = y (x)$ is :
Mathematics · Differential Equations · MCQ
Q36.If the solution curve $y = y (x)$ of the differential equation $y^{2} d x + (x^{2} - x y + y^{2}) d y = 0$ , which passes through the point (1, 1) and intersects the line $y = 3 x$ at the point $(α, 3 α)$ , then value of $lo g_{e} (3 α)$ …
Mathematics · Differential Equations · MCQ
Q37.Let $x = 2 t$ , $y = \frac{t ^{2}}{3}$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $S A ⊥ B A$ , where A is any point on the conic. If k is the ordinate of the centroid of the $Δ$ SAB, then $t \to 1 lim k$ …
Mathematics · Parabola · MCQ
Q38.Let a circle C in complex plane pass through the points $z_{1} = 3 + 4 i$ , $z_{2} = 4 + 3 i$ and $z_{3} = 5 i$ . If $z (e z_{1})$ is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then $a r g (z)$ …
Mathematics · Complex Numbers · MCQ
Q39.The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is .
Mathematics · Permutations and Combinations · Numerical
Q40.Let $θ$ be the angle between the vectors $a$ and $b$ , where $∣ a ∣ = 4, ∣ b ∣ = 3$ and $θ \in (\frac{π}{4}, \frac{π}{3})$ . Then $(a - b) \times (a + b)^{2} + 4 (a . b)^{2}$ …
Mathematics · Vector Algebra · Numerical
Q41.Let the abscissae of the two points P and Q be the roots of $2 x^{2} - r x + p = 0$ and the ordinates of P and Q be the roots of $x^{2} - s x - q = 0$ . If the equation of the circle described on PQ as diameter is $2 (x^{2} + y^{2}) - 11 x - 14 y - 22 = 0$ …
Mathematics · Circle · Numerical
Q42.Let $f : R \to R$ be a function defined by $f (x) = (2 (1 - \frac{x ^{25}}{2}) (2 + x^{25}))^{\frac{1}{50}}$ . If the function $g (x) = f (f (f (x))) + f (f (x))$ , then the greatest integer less than or equal…
Mathematics · Functions · Numerical
Q43.Let A be a 3 $\times$ 3 matrix having entries from the set { $-$ 1, 0, 1}. The number of all such matrices A having sum of all the entries equal to 5, is .
Mathematics · Permutations and Combinations · Numerical