Let f : R $\to$ R be defined as
$f(x) = \left[ {\matrix{ {[{e^x}],} & {x < 0} \cr {a{e^x} + [x - 1],} & {0 \le x < 1} \cr {b + [\sin (\pi x)],} & {1 \le x < 2} \cr {[{e^{ - x}}] - c,} & {x \ge 2} \cr } } \right.$
where a, b, c $\in$ R and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true?
Previous 10 Questions — JEE Main 2022 (28 June Morning Shift)
Nearest first
1
2
3
4
5
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)
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)
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)
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)
Let a function f : N $\to$ N be defined by$f(n) = \left[ {\matrix{ {2n,} & {n = 2,4,6,8,......} \cr {n - 1,} & {n…
Topic: JEE Main 2022 (28 June Morning Shift)
Next 10 Questions — JEE Main 2022 (28 June Morning Shift)
Ascending by ID
1
2
3
4
5
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)
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)
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)
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)
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)
