MHT-CET
Q. Evaluate ∫(5x^4)dx. (2020)
-
A.
(5/5)x^5 + C
-
B.
(1/5)x^5 + C
-
C.
(5/4)x^4 + C
-
D.
(1/4)x^4 + C
Solution
The integral of 5x^4 is (5/5)x^5 + C = x^5 + C.
Correct Answer: A — (5/5)x^5 + C
Learn More →
Q. Find the area of the triangle formed by the points (0, 0), (4, 0), and (0, 3). (2022) 2022
Solution
Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.
Correct Answer: A — 6
Learn More →
Q. Find the area of the triangle formed by the points A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2022)
Solution
The points are collinear, hence the area = 0.
Correct Answer: A — 0
Learn More →
Q. Find the coefficient of x^2 in the expansion of (2x + 3)^6.
-
A.
540
-
B.
720
-
C.
810
-
D.
960
Solution
The coefficient of x^2 is given by 6C2 * (2)^2 * (3)^4 = 15 * 4 * 81 = 4860.
Correct Answer: A — 540
Learn More →
Q. Find the coefficient of x^2 in the expansion of (x + 4)^5. (2023)
-
A.
80
-
B.
100
-
C.
120
-
D.
160
Solution
The coefficient of x^2 is C(5,2)(4)^3 = 10 * 64 = 640.
Correct Answer: A — 80
Learn More →
Q. Find the coefficient of x^3 in the expansion of (2x - 3)^4. (2022)
-
A.
-54
-
B.
-108
-
C.
108
-
D.
54
Solution
The coefficient of x^3 is C(4,3) * (2)^3 * (-3)^1 = 4 * 8 * (-3) = -96.
Correct Answer: B — -108
Learn More →
Q. Find the coefficient of x^4 in the expansion of (2x - 3)^6.
-
A.
540
-
B.
720
-
C.
810
-
D.
900
Solution
The coefficient of x^4 is C(6,4) * (2)^4 * (-3)^2 = 15 * 16 * 9 = 2160.
Correct Answer: A — 540
Learn More →
Q. Find the coefficient of x^4 in the expansion of (3x + 2)^5. (2022)
-
A.
240
-
B.
360
-
C.
480
-
D.
600
Solution
The coefficient of x^4 is C(5,4)(3)^4(2)^1 = 5 * 81 * 2 = 810.
Correct Answer: B — 360
Learn More →
Q. Find the coefficient of x^5 in the expansion of (2x - 3)^6. (2022)
-
A.
-540
-
B.
540
-
C.
-720
-
D.
720
Solution
The coefficient of x^5 is C(6,5) * (2)^5 * (-3)^1 = 6 * 32 * (-3) = -576.
Correct Answer: A — -540
Learn More →
Q. Find the coefficient of x^5 in the expansion of (2x - 3)^7. (2023)
-
A.
168
-
B.
252
-
C.
336
-
D.
504
Solution
The coefficient of x^5 is C(7,5) * (2)^5 * (-3)^2 = 21 * 32 * 9 = 6048.
Correct Answer: B — 252
Learn More →
Q. Find the coefficient of x^5 in the expansion of (2x - 3)^8.
-
A.
-6720
-
B.
6720
-
C.
-3360
-
D.
3360
Solution
The coefficient of x^5 is C(8,5) * (2)^5 * (-3)^3 = 56 * 32 * (-27) = -6720.
Correct Answer: A — -6720
Learn More →
Q. Find the coefficient of x^5 in the expansion of (x + 1)^7.
Solution
The coefficient of x^5 is C(7,5) = 21.
Correct Answer: C — 35
Learn More →
Q. Find the constant term in the expansion of (x - 2/x)^6. (2022)
Solution
The constant term occurs when the power of x is zero. Setting 6 - 2k = 0 gives k = 3. The term is C(6,3)(-2)^3 = -64.
Correct Answer: A — -64
Learn More →
Q. Find the coordinates of the midpoint of the line segment joining A(2, 3, 4) and B(4, 5, 6). (2023)
-
A.
(3, 4, 5)
-
B.
(2, 3, 4)
-
C.
(4, 5, 6)
-
D.
(5, 6, 7)
Solution
Midpoint M = ((2+4)/2, (3+5)/2, (4+6)/2) = (3, 4, 5).
Correct Answer: A — (3, 4, 5)
Learn More →
Q. Find the derivative of f(x) = sin(x) + cos(x).
-
A.
cos(x) - sin(x)
-
B.
-sin(x) - cos(x)
-
C.
sin(x) + cos(x)
-
D.
-cos(x) + sin(x)
Solution
The derivative f'(x) = d/dx(sin(x) + cos(x)) = cos(x) - sin(x).
Correct Answer: A — cos(x) - sin(x)
Learn More →
Q. Find the derivative of f(x) = tan(x). (2022) 2022
-
A.
sec^2(x)
-
B.
csc^2(x)
-
C.
sec(x)
-
D.
tan^2(x)
Solution
The derivative f'(x) = d/dx(tan(x)) = sec^2(x).
Correct Answer: A — sec^2(x)
Learn More →
Q. Find the derivative of f(x) = x^5 + 3x^3 - 2x.
-
A.
5x^4 + 9x^2 - 2
-
B.
5x^4 + 6x^2 - 2
-
C.
3x^2 + 5x^4 - 2
-
D.
5x^4 + 3x^2 - 2
Solution
The derivative f'(x) = d/dx(x^5 + 3x^3 - 2x) = 5x^4 + 9x^2 - 2.
Correct Answer: A — 5x^4 + 9x^2 - 2
Learn More →
Q. Find the derivative of f(x) = x^5 - 3x^3 + 2. (2022)
-
A.
5x^4 - 9x^2
-
B.
5x^4 + 9x^2
-
C.
3x^2 - 9x
-
D.
5x^4 - 3x^2
Solution
The derivative f'(x) = d/dx(x^5 - 3x^3 + 2) = 5x^4 - 9x^2.
Correct Answer: A — 5x^4 - 9x^2
Learn More →
Q. Find the determinant of E = [[3, 2], [1, 4]]. (2022)
Solution
Det(E) = (3*4) - (2*1) = 12 - 2 = 10.
Correct Answer: A — 10
Learn More →
Q. Find the determinant of E = [[4, 2], [1, 3]]. (2023)
Solution
Det(E) = (4*3) - (2*1) = 12 - 2 = 10.
Correct Answer: A — 10
Learn More →
Q. Find the determinant of F = [[4, 5], [6, 7]]. (2020)
Solution
Det(F) = (4*7) - (5*6) = 28 - 30 = -2.
Correct Answer: A — -2
Learn More →
Q. Find the determinant of H = [[3, 1], [2, 5]]. (2021)
Solution
Determinant of H = (3*5) - (1*2) = 15 - 2 = 13.
Correct Answer: A — 7
Learn More →
Q. Find the determinant of J = [[5, 2], [1, 3]]. (2020)
Solution
The determinant of J is calculated as (5*3) - (2*1) = 15 - 2 = 13.
Correct Answer: A — 10
Learn More →
Q. Find the determinant of the matrix D = [[4, 2], [3, 1]]. (2023)
Solution
The determinant of D is calculated as (4*1) - (2*3) = 4 - 6 = -2.
Correct Answer: A — -2
Learn More →
Q. Find the determinant of the matrix \( E = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). (2021)
Solution
The determinant is \( 3*4 - 2*1 = 12 - 2 = 10 \).
Correct Answer: A — 10
Learn More →
Q. Find the dimensions of a rectangle with a fixed area of 50 square units that minimizes the perimeter. (2022) 2022
-
A.
5, 10
-
B.
7, 7.14
-
C.
10, 5
-
D.
8, 6.25
Solution
For minimum perimeter, the rectangle should be a square. Thus, side = sqrt(50) ≈ 7.07.
Correct Answer: B — 7, 7.14
Learn More →
Q. Find the distance between the parallel planes x + 2y + 3z = 4 and x + 2y + 3z = 10. (2023)
Solution
Distance = |d1 - d2| / √(a² + b² + c²) = |4 - 10| / √(1² + 2² + 3²) = 6 / √14.
Correct Answer: A — 2
Learn More →
Q. Find the equation of the line parallel to y = 3x + 2 and passing through (4, 5).
-
A.
y = 3x - 7
-
B.
y = 3x + 5
-
C.
y = 3x + 2
-
D.
y = 3x - 2
Solution
Since the line is parallel, it has the same slope. Using point-slope form: y - 5 = 3(x - 4) gives y = 3x - 7.
Correct Answer: A — y = 3x - 7
Learn More →
Q. Find the equation of the line parallel to y = 3x + 2 that passes through the point (4, 1).
-
A.
y = 3x - 11
-
B.
y = 3x + 1
-
C.
y = 3x + 2
-
D.
y = 3x - 2
Solution
Since the line is parallel, it has the same slope (3). Using point-slope form: y - 1 = 3(x - 4) gives y = 3x - 11.
Correct Answer: A — y = 3x - 11
Learn More →
Q. Find the equation of the line parallel to y = 5x - 3 that passes through the point (2, 1).
-
A.
y = 5x - 9
-
B.
y = 5x + 1
-
C.
y = 5x - 7
-
D.
y = 5x + 3
Solution
Since the slope is the same (5), using point-slope form: y - 1 = 5(x - 2) gives y = 5x - 9.
Correct Answer: A — y = 5x - 9
Learn More →
Showing 211 to 240 of 1443 (49 Pages)
