Solution - Mathematics MCQsMathematics MCQs for A-Level, FSc, Class 11, 12 students ORMathematics MCQs for Engineering Universities Admission Test

1. 3 3 ? (A) 3(B) 3(C) 3i(D) 3i(E) None of these

Solution:

We can write 3 3i Hence, 23 3 3 3( 1) 3i i i Answer is: 3

2. ?xdb

dx

(A) xb(B) bx(C) lnxb b(D) lnxb x(E) lnxb x x

Solution:

Remember: lnx xda a a

dx Hence, lnx xd

b b adx

Answer

3. If a b

Ac d

Then 1 ?A

(A) ad bc(B) ad bc

(C) 1 a b

c dad bc

(D) 1 d b

c aad bc

(E) 1 d b

c aad bc

Solution:

Remember, if a b

Ac d

Then its inverse is: 1 1 d bA

c aad bc

Hence, 1 1 d bA

c aad bc

Answer

4. If

2

1sin

2

a

xdx

Then ?a

(A) 0(B) 1(C)

(D) 2

(E) 3

Solution:

2

sin cos

2

a axdx x

= cos cos cos 0 cos

2a a a

1

2OR

1cos

2a

Hence, 3

a

Answer

5. Find the values of x and y from the following equations:

3 2 4

2

x y

x y

(A) 2x and 4y (B) 4x and 6y

(C) 3

2x and

2

3y

(D) 8

5x and

2

5y

(E) 4

3x and

3

5y

Solution:

3 2 4

2

x y

x y

Multiply eq:2 with 3.3 2 4

3 3 6

x y

x y

5 2y 5 2y

2

5y

Now put value of y in eq:2, 2x y 2

25

x

8

5x

Hence, answer is (D).

6. If 2

( )3

xf x

Then 1( ) ?f x

(A) 3 2x (B) 2 3x

(C) 3

2x (D) Does not exist(E) None of these

Solution:

2( )

3

xf x

Step.1 Replace ( )f x by y2

3

xy

Step.2 Replace y with x , and x with y2

3

yx

Step.3 Solve for y .2 3y x 3 2y x

Step.4 Replace y by 1( )f x

1( ) 3 2f x x Answer

7. Matrix A has 4 rows and 3 columns, and Matrix B has 5 rows and 2 columns. The Matrix AB will have?(A) 4 rows and 2 columns(B) 5 rows and 3 columns(C) 2 rows and 4 columns(D) 3 rows and 5 columns(E) 3 rows and 2 columns

Solution:

If rows = m , and columns = n , thenm n n p (Columns of 1st are equal to rows of 2nd). Cancel n , hence result is m pHence, In the Matrix AB there are rows of 1st, and columns of 2nd. That is, 4 rows and 2 columns. (A) is answer

8. Given that the Matrix 2 3

4 a

is singular. Find the value of ?a

(A) 2(B) 2(C) 3(D) 6(E) 6

Solution:

Since the Matrix is singular, therefore Matrix 2 3

04 a

Now, 2 12 0a 2 12a

6a Answer

9. 4(1 ) ?i (A) 2(B) 2i(C) 4(D) 4i(E) 6i

Solution:

We can write 4 2 2(1 ) {(1 ) }i i = 2{(1 2 1)}i = 2(2 )i = 24i = 4( 1) = 4 Answer

10. (log )(log ) ?yx xyxy x

(A) 1(B) x

(C) y(D) xy

(E) yx

Solution:

(log )(log ) logy yx xy xxy x x y Answer