Mathematics Solved MCQs Maths Solved MCQs for ECAT Mathematics SOLVED MCQs for Engineering Collages Admission Test ECAT

Mathematics Solved MCQs

Mathematics Solved MCQs for ECATMathematics SOLVED MCQs for Engineering                   Collages Admission Test ECAT

1.  3   3  ?

 

(A)   3

(B)    3

 

(C)   3i

(D)   3i

 

(E)  None of these

 

Solution:

We can write  3  3i Hence, 3i  3i  3i²    3( 1)   3

Answer is:  3

 

2. _dx^d b^x    ?

(A)   b^x

 

(B)   bx

 

(C)   b^x ln b

 

(D)   b^x ln x

(E)    b ^x x ln x

 

Solution:

 

Remember: _dx^d a^x    a^x ln a Hence, _dx^d b^x    b^x ln a Answer

3.  If A   ^{a   b  Then} A ¹    ?

 

^{c   d}

(A)   ad  bc

 

(B)    ad  bc

 

(C)		1		a	b
		ad  bc   c			d
(D)		1		d	b
		ad  bc   c			a
(E)		1		d	b
		ad  bc   c			a

Solution:
Remember, if		A	a	b	Then its inverse is: A 1		1	d	b
			c	d			ad  bc   c		a
Hence, A 1		1		d	b	Answer
		ad  bc   c			a
4. If a sin xdx  1			Then a  ?
		2
2
(A) 0
(B) 1
(C)
(D)
	2
(E)
	3

Solution:

 

a sin xdx   cos x				a	=   cos a  cos		cos a  0   cos a	1	OR cos a	1
				2		2		2		2
2
Hence, a		Answer
	3

5.  Find the values of x and y from the following equations: 3x 2y 4

 

x  y  2

 

(A)    x  2 and y  4

 

(B)    x  4 and y  6

 

(C)    x  ³₂ and y  ²₃

 

(D)    x  ⁸₅ and y  ₅²

 

(E)    x ⁴₃ and y ³₅ Solution:

3x 2y 4 x y 2

 

Multiply eq:2 with 3. 3x 2 y 4

 

3x  3y   6

 

5y 2 5y 2

 

y  ₅²

Now put value of y in eq:2, x  y  2

 

x ²₅ 2 x ⁸₅

Hence, answer is (D).

 

 

6. If	f ( x)	x  2	Then	f 1 (x)  ?
	3

(A)   3x  2

 

(B)    2x  3

 

(C)           ³

 

x  2

 

(D)   Does not exist

(E)  None of these

Solution:

 

f ( x)			x  2
3
Step.1 Replace						f ( x)	by y
y		x  2
3
Step.2 Replace						y with x , and x with y
x	y  2
3
Step.3 Solve for y .
y  2  3x
y  3x  2
Step.4 Replace						y by	f 1 (x)

f ¹ (x)  3x  2 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 , then

m  n   n  p (Columns of 1^st are equal to rows of 2^nd). Cancel n , hence result is m  p

 

Hence, In the Matrix AB there are rows of 1^st, and columns of 2^nd. That is, 4 rows and 2 columns. (A) is answer

 

2   3

8. Given that the Matrix                is singular. Find the value of a ?

^{4  a}

(A)   2

(B)    2

 

(C)   3

 

(D)   6

(E)    6

 

Solution:
Since the Matrix is singular, therefore Matrix				2	3	0
Now, 2a  12  0				4	a
2a   12
a   6 Answer
9. (1  i)4	?
(A) 2
(B) 2i
(C)  4
(D) 4i
(E)  6i
Solution:
We can write (1  i)4		{(1  i)2 }2	= {(1  2i  1)}2		= (2i)2  = 4i2  = 4( 1)		=  4 Answer
10. (logx	xy)(logxy xy )  ?
(A) 1
(B) x

(C)    y

 

(D)    xy

 

(E)    x^y

 

Solution:

 

(log_x xy)(log_xy x^y )  log_x x^y    y Answer