Let matrix B be the adjoint of a square matrix A, l be the identify matrix of same order as A. If k (≠ 0) is the determinate of the matrix A, then what is AB equal to?

For realizing a binary half-subtractor having two inputs A and B, the current set of logical expression for the outputs D (A minus B) and X (borrow) are 1. The difference output D = A̅B + AB̅ 2. The borrow output B = AB̅ Which of the above statements is/are correct?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationship between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. Quantity 1: Area of the innermost square. A square is made by joining the midpoints of a square of area 200 sq. m. The outermost square is called Square 1, The square inside it is called Square 2. The next square is made by joining midpoints of square 2 and is called Square 3. This process goes on. Square 5 is the innermost square. Quantity 2: A man starts with a speed of 10 km/hr. He increases his speed by 10 km/hr every hour at the start and drives at the same speed for that hour. If he traveled a total distance of 550 km. Find the time Quantity 3: Height of cylinder Its volume is equal to the volume of a cone whose radius is 14 cm and height is 39.3 cm. The radius of the cylinder is 14 cm

A

Quantity 2 > Quantity 3 > Quantity 1

B

Quantity 1 > Quantity 2 > Quantity 3

C

Quantity 3 > Quantity 1 > Quantity 2

D

Quantity 1 = Quantity 2 < Quantity 3

E

Quantity 1 > Quantity 2 = Quantity 3

For a matrix A of order n, the det(adj(A)) = (det(A))n, where adj() is adjoint of matrix.

A

True

B

False

A planar truss tower structure is shown in the figure. Consider the following statements about the external and internal determinacies of the truss. P. Externally determinate Q. External static indeterminacy = 1 R. External Static Indeterminacy = 2 S. Internally Determinate T. Internal Static Indeterminacy = 1 U. Internal Static Indeterminacy = 2 Which one of the following options is correct?

A

P-False; Q-True; R-False; S-False; T-False; U-True

B

P-False; Q-True; R-False; S-False; T-True; U-False

C

P-False; Q-False; R-True; S-False; T-False; U-True

D

P-True; Q-True; R-False; S-True; T-False; U-True

Consider the following pattern of numbers: \(\dfrac{\begin{matrix} 8 \\\ 6 \ \\\ 4 \ \end{matrix}}{ \ 6} \ \ \dfrac{\begin{matrix} 10 \\\ 5 \ \\\ 6 \ \end{matrix}}{ \ 11} \ \ \dfrac{\begin{matrix} 15 \\\ 7 \ \\\ 8 \ \end{matrix}}{ \ 16} \ \ \dfrac{\begin{matrix} 13 \\\ 4 \ \\\ 8 \ \end{matrix}}{ \ ?}\) What is the number at ? in the above pattern?

A

17

B

19

C

21

D

23

The length of each side of square A is increased by 100 percent to make square B. Again the length of each side of square B is increased by 50 percent to make square C. By what percent is the area of square C greater than the sum of the areas of square A and B?

A

75%

B

80%

C

85%

D

90%

Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively. Let X, Y and Z represent the following operations: X: rotation of the square by 180 degree with respect to the S-Q axis. Y: rotation of the square by 180 degree with respect to the P-R axis. Z: rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T. Consider the following three distinct sequences of operation (which are applied in the left to right order). (1) XYZZ (2) XY (3) ZZZZ Which one of the following statements is correct as per the information provided above?

A

The sequence of operations (1) and (2) are equivalent

B

The sequence of operations (1) and (3) are equivalent

C

The sequence of operations (2) and (3) are equivalent

D

The sequence of operations (1), (2) and (3) are equivalent

A is a square matrix of order 3 such that its determinate is 4. What is the determinant of its transpose?

A

64

B

36

C

32

D

4

The average area of 3 square rooms I, II, and III are 1600 square meters. If one rectangular room(IV) area is added then the average area becomes 1400 square meters. If another room V, whose area is 400 square meters more than the IV room, replaces room I, then the average area of II, III, IV, and V room becomes 1350 square meters. Find the area of I room.

A

1300 square meters

B

1200 square meters

C

1400 square meters

D

1500 square meters

E

1800 square meters

Which of the following statements are true relating to payment of equal pay for equal work both for men and women?
1. ILO adopted equal remuneration Convention No. 100 in 1951.
2. India ratified ILO's Equal Remuneration Convention No. 100 in the year 1956.
3. Provisions relating to equal pay for equal work for both men and women are provided under Article 42 of the Indian Constitution.
4. The Equal Remuneration Ordinance was promulgated on 26^th September, 1975.

A

Both 1 and 4 are correct

B

Both 2 and 3 are correct

C

1, 3 and 4 are correct

D

1, 2 and 4 are correct

Let matrix B be the adjoint of a square matrix A, l be the identify matrix of same order as A. If k (≠ 0) is the determinate of the matrix A, then what is AB equal to?

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