Q.649·Miscellaneous·2024·EasyLet y dx + (x – y^3) dy = 0 be a differential equation. What is the solution of the differential equation?View question
Q.650·Miscellaneous·2024·EasyLet I = ∫(0 to π/2) (f(x)/g(x)) dx, where f(x) = sin x and g(x) = sin x + cos x + 1. What is I equal to?View question
Q.651·Miscellaneous·2024·EasyLet L: x + y + z + 4 = 0 = 2x - y - z + 8 be a line and P: x + 2y + 3z + 1 = 0 be a plane. What are the direction ratios of the line?View question
Q.652·Miscellaneous·2024·EasyThe area bounded by the parabola y^2 = kx and the line x = k, where k > 0, is 4/3 square units What is the area of the parabola bounded by the latus rectum?View question
Q.653·Miscellaneous·2024·EasyLet y dx + (x – y^3) dy = 0 be a differential equation. What are the order and degree respectively of the differential equation?View question
Q.654·Miscellaneous·2024·EasyLet 2 ∫[(x² – 1)/(x² + 1)] dx = U(x) V(x) – 3ln |U(x) + V(x)| + V(x) + c What is U(x) V(x) equal to?View question
Q.656·Miscellaneous·2024·EasyIf f(2x) = 4x^2 + 1, then for how many real values of x will f(2x) be the GM of f(x) and f(4x)?View question
Q.657·Miscellaneous·2024·EasyIf f(x) = [x]^2 – 30[x] + 221 = 0, where [x] is the greatest integer function, then what is the sum of all integer solutions?View question
Q.658·Miscellaneous·2024·EasyLet f(x) f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value of f(1/2)?View question
Q.659·Miscellaneous·2024·EasyLet f(x) = [x]^2 – [x^2]. What is f(0.999) + f(1.001) equal toView question
Q.660·Miscellaneous·2024·EasyLet f(x) = [x]^2 – [x^2]. Consider the following statements: I. f(x) is continuous at x = 0. II. f(x) is continuous at x = 1. Which of the statements given above is/are correct?View question
Q.661·Miscellaneous·2024·EasyLet z = [y] and y = [x] - x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?View question
Q.662·Miscellaneous·2024·EasyLet L: x + y + z + 4 = 0 = 2x - y - z + 8 be a line and P: x + 2y + 3z + 1 = 0 be a plane. What is the point of intersection of L and P?View question
Q.663·Miscellaneous·2024·EasyIf f(x) = 4x + 1 and g(x) = kx + 2 such that f o g(x) = g o f(x), then what is the value of k?View question
Q.664·Miscellaneous·2024·EasyWhat is the minimum value of the function f(x) = log10(x^2 + 2x + 1)?View question
Q.665·Miscellaneous·2024·EasyThe area bounded by the parabola y^2 = kx and the line x = k, where k > 0, is 4/3 square units. What is the value of k?View question
Q.666·Miscellaneous·2024·EasyLet x – 3y + 4 = 0 and 2x – 7y + 8 = 0 be two lines of regression computed from some bivariate data. If b<sub>yx</sub> and b<sub>xy</sub> are regression coefficients of lines of regression of y on x and x on y respectively, then what is the value of b<sub>xy</sub> + 7b<sub>yx</sub>?View question