NAT IIP Physical Science Mathematics Preparation Online Test for Pakistani Students

In a school, there are 150 students. Out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for Physics class. The student enrolled for English cannot attend any other class, but the students of mathematics and Physics can take two courses at a time. Find the number of students who have taken both physics and mathematics

• 40 A
• 30 B
• 50 C
• 20 D

The circle (x-2)²+ (y+3)²= 4 is not concentric with the circle

• (x-2)²+ (y+3)²= 9 A
• (x+2)²+ (y-3)²= 4 B
• (x-2)²+ (y+3)²= 8 C
• (x-2)²+ (y+3)²= 5 D

• 
  A
• 
  B
• 
  C
• None of these D

If any two rows (or any two columns) of a square matrix are inter changed, the determinant of the resultant matrix is

• Same as the original determinant A
• Additive inverse of the original determinant
  B
• Both A and B C
• Adj of the original matrix D

Which of the vectors have opposite direction?

• 
  A
• 
  B
• 
  C
• Both A and B D

If a statement S(n) is true for n = 1 and the truth of S(n) for n + K implies the truth of S(n) for S(n) = K + 1, then S(n) true for all

• All Real numbers A
• All integers B
• Positive integers C
• All complex numbers D

The equation of the normal to the circle x²+ y²= 25 at(4, 3) is

• 3x - 4y = 0 A
• 3x - 4y = 5 B
• 4x + 3y = 5 C
• 4x + 3y = 25 D

The sum of the series 1+5+9+13+17+21+25+29 is

• 140 A
• 130 B
• 120 C
• 110 D

• 
  A
• -3/4 B
• 1/16 C
• 1/4 D

The nth term of of A.P:1,5,9,15,....................... is given by

• 4n - 3 A
• 4n + 1 B
• 3n - 4 C
• 4n + 3 D

Total number of terms in the expansion of (a + b)⁵+ (a - b)⁵after simplification are

• 3 A
• 1 B
• 4 C
• 7 D

• 2 A
• 1 B
• 0 C
• 
  D

The center of a circle of radius 10 is on the origin. Which of the following points lies with in the circle

• (10, 0) A
• (8, 8) B
• (8, 4) C
• (0, 10) D

• 
  A
• 
  B
• 
  C
• 
  D

In which quadrant is the solution of the equation sin x - 1 = 0

• II quadrants A
• II and III quadrants B
• III and IV quadrants C
• I quadrant D