Let a function f : N $\to$ N be defined by

$f(n) = \left[ {\matrix{ {2n,} & {n = 2,4,6,8,......} \cr {n - 1,} & {n = 3,7,11,15,......} \cr {{{n + 1} \over 2},} & {n = 1,5,9,13,......} \cr } } \right.$ then, f is

1

If the system of linear equations$2x + 3y - z = - 2$$x + y + z = 4$$x - y + |\lambda |z = 4\lambda - 4$where, $\lambd…

Topic: JEE Main 2022 (28 June Morning Shift)

2

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple…

Topic: JEE Main 2022 (28 June Morning Shift)

3

Let A1, A2, A3, ....... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = ${1 \over {1296}…

Topic: JEE Main 2022 (28 June Morning Shift)

4

Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral $\int\limits_0^1 {[ - 8{x^…

Topic: JEE Main 2022 (28 June Morning Shift)

5

Let f : R $\to$ R be defined as$f(x) = \left[ {\matrix{ {[{e^x}],} & {x < 0} \cr {a{e^x} + [x - 1],} & {0 \le x <…

Topic: JEE Main 2022 (28 June Morning Shift)

6

The area of the region S = {(x, y) : y2 $\le$ 8x, y $\ge$ $\sqrt2$x, x $\ge$ 1} is

Topic: JEE Main 2022 (28 June Morning Shift)

7

Let the solution curve $y = y(x)$ of the differential equation$\left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \ove…

Topic: JEE Main 2022 (28 June Morning Shift)

8

Let y = y(x) be the solution of the differential equation $x(1 - {x^2}){{dy} \over {dx}} + (3{x^2}y - y - 4{x^3}) = 0$,…

Topic: JEE Main 2022 (28 June Morning Shift)

9

The number of real solutions of :- ${x^7} + 5{x^3} + 3x + 1 = 0$ is equal to ____________.

Topic: JEE Main 2022 (28 June Morning Shift)

10

The probability, that in a randomly selected 3-digit number at least two digits are odd, is :

Topic: JEE Main 2022 (28 June Morning Shift)