NAT-IE Pre Engineering Mathematics Hard Test

The values of n such that, in the binomial expansion of (1 - x)ⁿ, co-efficient of x², co-efficient of x²is 3, are

• -2, -3 A
• 2, -3 B
• -2, 3 C
• None of these D

• 15 A
• 15 i B
• -15 i C
• -15 D

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 2 B
• 3 C
• 4 D

• 
  A
• 
  B
• 
  C
• 
  D

The common difference of the sequence 7,4,1, .......... is

• 1 A
• -3 B
• 5 C
• 0 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If 4 - x > 5, then

• x > 1 A
• x > -1 B
• x < 1 C
• x < -1 D

• 
  A
• 
  B
• 
  C
• None D

The gradient of the line joining (1, 4) and (-2, 5) is

• 3/8 A
• -2 2/3 B
• -1/3 C
• 2 D

If A and B are matrices such that AB=BA=I then

• A and B are multiplicative inverse of each other
  A
• A and B are additive inverses of each other
  B
• . A and B are singular matrices C
• A and B are equal D

Two matrices A and B are conformable

for multiplication (AB) if and only if

• Both A,B have the same number of columns
  
  A
• Both A and B do not have the same order
  
  B
• Number of col A is same as number of rows of B
  
  C
• Number of rows of A is same as number of col of B
  
  D

The conic is a parabola if

• e < 1 A
• e > 1 B
• e = 1 C
• e = 0 D

In the expansion of (a + b)ⁿin every term the sum of the exponents of a and b is

• n A
• n + 1 B
• 2n - 1 C
• 2n + 1 D

• A + B A
• C²/AB B
• A²/BC C
• B²/AC D

• 
  A
• 
  B
• 
  C
• 
  D

• 1/2 A
• 3/5 B
• 4/5 C
• 1 D

Which is in the solution set of 4x - 3y < 2

• (3, 0) A
• (4, 1) B
• (1, 3) C
• None D

The magnitude of a vector can never be

• Zero A
• Negative B
• Positive C
• Absolute D