MHT-CET
Q. Find the integral of sin(x). (2020)
-
A.
-cos(x) + C
-
B.
cos(x) + C
-
C.
sin(x) + C
-
D.
-sin(x) + C
Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer: A — -cos(x) + C
Learn More →
Q. Find the integral of sin(x)dx. (2020)
-
A.
-cos(x) + C
-
B.
cos(x) + C
-
C.
sin(x) + C
-
D.
-sin(x) + C
Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer: A — -cos(x) + C
Learn More →
Q. Find the integral of x^5 dx. (2020)
-
A.
(1/6)x^6 + C
-
B.
(1/5)x^6 + C
-
C.
(1/4)x^6 + C
-
D.
(1/7)x^6 + C
Solution
The integral is (1/6)x^6 + C.
Correct Answer: B — (1/5)x^6 + C
Learn More →
Q. Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6 units. (2022)
-
A.
√49
-
B.
√45
-
C.
√36
-
D.
√50
Solution
Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7 units.
Correct Answer: A — √49
Learn More →
Q. Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6. (2023)
-
A.
√49
-
B.
√36
-
C.
√45
-
D.
√50
Solution
Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7.
Correct Answer: A — √49
Learn More →
Q. Find the limit: lim (x -> 1) (x^4 - 1)/(x - 1) (2023)
-
A.
0
-
B.
1
-
C.
4
-
D.
Undefined
Solution
Factoring gives ((x - 1)(x^3 + x^2 + x + 1))/(x - 1). For x ≠ 1, this simplifies to x^3 + x^2 + x + 1. Thus, lim (x -> 1) = 4.
Correct Answer: A — 0
Learn More →
Q. Find the limit: lim (x -> 3) (x^2 - 9)/(x - 3) (2023)
Solution
The expression can be factored as ((x - 3)(x + 3))/(x - 3). For x ≠ 3, this simplifies to x + 3. Thus, lim (x -> 3) (x + 3) = 6.
Correct Answer: A — 0
Learn More →
Q. Find the magnitude of the vector A = 3i - 4j. (2020)
Solution
|A| = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5.
Correct Answer: A — 5
Learn More →
Q. Find the maximum area of a triangle with a base of 10 m and height varying. (2020)
Solution
Area = 1/2 * base * height. Max area occurs when height is maximized, thus Area = 1/2 * 10 * 10 = 50.
Correct Answer: B — 50
Learn More →
Q. Find the maximum area of a triangle with a base of 10 units and height as a function of the base. (2021)
Solution
Area = 1/2 * base * height. Max area occurs when height is maximized at 10 units, giving Area = 50.
Correct Answer: B — 50
Learn More →
Q. Find the maximum height of the projectile modeled by h(t) = -16t^2 + 32t + 48. (2020)
Solution
The maximum occurs at t = -b/(2a) = -32/(2*-16) = 1. h(1) = 64.
Correct Answer: A — 48
Learn More →
Q. Find the maximum height of the projectile modeled by h(t) = -16t^2 + 64t + 48. (2020)
Solution
The maximum occurs at t = -b/(2a) = 64/(2*16) = 2. h(2) = -16(2^2) + 64(2) + 48 = 80.
Correct Answer: B — 64
Learn More →
Q. Find the maximum value of the function f(x) = -2x^2 + 8x - 3. (2021) 2021
Solution
The function is a downward-opening parabola. The maximum occurs at x = -b/(2a) = -8/(2*-2) = 2. f(2) = -2(2^2) + 8(2) - 3 = 8.
Correct Answer: B — 8
Learn More →
Q. Find the midpoint of the line segment joining the points (2, 3) and (4, 7). (2022) 2022
-
A.
(3, 5)
-
B.
(2, 5)
-
C.
(4, 5)
-
D.
(3, 4)
Solution
Midpoint = ((2+4)/2, (3+7)/2) = (3, 5).
Correct Answer: A — (3, 5)
Learn More →
Q. Find the minimum value of f(x) = x^2 - 4x + 7. (2021)
Solution
The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4*2 + 7 = 3.
Correct Answer: A — 3
Learn More →
Q. Find the minimum value of f(x) = x^2 - 4x + 7. (2021) 2021
Solution
The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4*2 + 7 = 3.
Correct Answer: A — 3
Learn More →
Q. Find the minimum value of the function f(x) = 2x^2 - 8x + 10. (2022)
Solution
The minimum occurs at x = 2. f(2) = 2(2^2) - 8(2) + 10 = 6.
Correct Answer: B — 4
Learn More →
Q. Find the particular solution of dy/dx = 4y with the initial condition y(0) = 2.
-
A.
y = 2e^(4x)
-
B.
y = e^(4x)
-
C.
y = 4e^(x)
-
D.
y = 2e^(x)
Solution
The general solution is y = Ce^(4x). Using the initial condition y(0) = 2, we find C = 2, thus y = 2e^(4x).
Correct Answer: A — y = 2e^(4x)
Learn More →
Q. Find the particular solution of dy/dx = 4y, given y(0) = 2.
-
A.
y = 2e^(4x)
-
B.
y = e^(4x)
-
C.
y = 4e^(2x)
-
D.
y = 2e^(x/4)
Solution
The general solution is y = Ce^(4x). Using the initial condition y(0) = 2, we find C = 2, thus y = 2e^(4x).
Correct Answer: A — y = 2e^(4x)
Learn More →
Q. Find the point of inflection for f(x) = x^3 - 6x^2 + 9x. (2022)
-
A.
(1, 4)
-
B.
(2, 3)
-
C.
(3, 0)
-
D.
(0, 0)
Solution
f''(x) = 6x - 12. Setting f''(x) = 0 gives x = 2. f(2) = 3.
Correct Answer: C — (3, 0)
Learn More →
Q. Find the point on the curve y = x^3 - 3x^2 + 4 that has a horizontal tangent. (2023)
-
A.
(0, 4)
-
B.
(1, 2)
-
C.
(2, 2)
-
D.
(3, 4)
Solution
To find horizontal tangents, set the derivative y' = 3x^2 - 6x = 0. This gives x = 0 and x = 2. The point (1, 2) has a horizontal tangent.
Correct Answer: B — (1, 2)
Learn More →
Q. Find the real part of the complex number 4 + 5i. (2023)
Solution
The real part of the complex number 4 + 5i is 4.
Correct Answer: A — 4
Learn More →
Q. Find the roots of the equation x² + 2x - 8 = 0. (2022)
-
A.
-4 and 2
-
B.
4 and -2
-
C.
2 and -4
-
D.
0 and 8
Solution
Factoring gives (x + 4)(x - 2) = 0, hence the roots are 4 and -2.
Correct Answer: B — 4 and -2
Learn More →
Q. Find the slope of the tangent line to f(x) = 2x^3 - 3x^2 + 4 at x = 1. (2021)
Solution
f'(x) = 6x^2 - 6. f'(1) = 6(1)^2 - 6 = 0.
Correct Answer: B — 2
Learn More →
Q. Find the solution of the differential equation dy/dx = y^2.
-
A.
y = 1/(C - x)
-
B.
y = C/(x - 1)
-
C.
y = Cx
-
D.
y = e^(x)
Solution
This is a separable equation. Integrating gives y = 1/(C - x).
Correct Answer: A — y = 1/(C - x)
Learn More →
Q. Find the solution of the differential equation y' = 3y + 6.
-
A.
y = Ce^(3x) - 2
-
B.
y = Ce^(3x) + 2
-
C.
y = 2e^(3x)
-
D.
y = 3Ce^(x)
Solution
This is a linear first-order equation. The integrating factor is e^(3x). The solution is y = Ce^(3x) + 2.
Correct Answer: B — y = Ce^(3x) + 2
Learn More →
Q. Find the solution of the equation dy/dx = y^2 - 1.
-
A.
y = tan(x + C)
-
B.
y = C/(1 - Cx)
-
C.
y = 1/(C - x)
-
D.
y = C/(x + 1)
Solution
This is a separable equation. The solution is y = tan(x + C).
Correct Answer: A — y = tan(x + C)
Learn More →
Q. Find the solution of the equation y' + 2y = 0.
-
A.
y = Ce^(-2x)
-
B.
y = Ce^(2x)
-
C.
y = 2Ce^x
-
D.
y = Ce^x
Solution
This is a first-order linear differential equation. The solution is y = Ce^(-2x).
Correct Answer: A — y = Ce^(-2x)
Learn More →
Q. Find the term containing x^3 in the expansion of (x - 1)^5.
Solution
The term containing x^3 is C(5,3) * x^3 * (-1)^2 = 10 * x^3 * 1 = 10.
Correct Answer: C — -10
Learn More →
Q. Find the term independent of x in the expansion of (x^2 - 2x + 3)^4. (2022)
Solution
The term independent of x occurs when the powers of x cancel out. The term is 81.
Correct Answer: A — 81
Learn More →
Showing 331 to 360 of 1717 (58 Pages)
