If \(y = a + b\log_e x\) then which of the following is true?

A circle touches the \(y\)-axis at \((0,4)\) and passes through the point \((-2,0)\). Then the radius of the circle is

Let \(A(1,3)\) and \(B(5,1)\) be two points. If a line with slope \(m\) intersects AB at an angle of \(45^\circ\), then the possible values of \(m\) are

Which of the following numbers is divisible by \(3^{10} + 2\) ?

The number of integers greater than 5000 and divisible by 5 that can be formed with the digits 1, 3, 5, 7, 8, 9 where no digit is repeated is

If \(a_1, a_2, \ldots, a_8\) are the roots of the equation \(x^8 + x^7 + \cdots + x + 1 = 0\), then the value of \(a_1^{2025} + a_2^{2025} + \cdots + a_8^{2025}\) is

Area of a regular octagon inscribed in a circle of radius 1 unit is

Two swimmers, Ankit and Bipul, start swimming from the opposite ends of a swimming pool at the same time. Ankit can cover the length of the pool once in 10 minutes. Bipul can cover the length of the pool once in 15 minutes. They swim back and forth for 80 minutes without stopping…

The sum of the first 5 terms of a geometric progression is the same as the sum of the first 7 terms of the same progression. If the sum of the first 9 terms is 24, then the \(4^{th}\) term of the progression is