NTSE Mathematics Algebra MCQs Set 02

Question: If we divide 3y4 - y3 + 12y2 + 2 by 3y2 - 1 then remainder is :

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Factors of (x + )3 - (x - 1)3 are :  

• a) 2 (x2 + 1)            
• b) 3x2 + 1                       
• c) 2 (2x2 + 1     
• d) 2 (3x2 + 1)

Answer: 2 (3x2 + 1)

Question: Factors of x3 + 3x2 + 3x - 7 are :          

• a) (x - 1) (x2 + 4x + 7   
• b) (x + 1) (x2 + 4x + 7)          
• c) (x + 1) (x2 + 4x - 7) 
• d) (x - 1) (x2 - 4x + 7)
  
  

Answer:  (x - 1) (x2 + 4x + 7   

Question: The value of k for which x + k is a factor of x3 + kx2 - 2x + k + 4 is           

• a) - 5
• b) 2
• c)

  

• d)

  

Answer:

Question: The solution of the equation 7^{1 + x} + 1 = 50 is  

• a) 0
• b) 1
• c) 2
• d) None of these

Answer: 1

Question: f(x), g(x) are two polynomial with integer co-efficient such that their H.C.F. is 1 and L.C.M. is (x2 - 4) (x4 - 1). If f(x) = x3 - 2x2 - x + 2 then g(x) is.      

• a) x3 - 2x2 + x + 2       
• b) x3 + 2x2 + x - 2                
• c) x3 + 2x2 + x + 2      
• d) x3 -2x2 - x - 2

Answer: x3 + 2x2 + x + 2      

Question: The H.C.F of (x3 - 1) and (x4 + x2 + 1) is -       

• a) x+ 1
• b)  x2 + x + 1                    
• c) x2 - x + 1               
• d) x - 1

Answer:  x2 + x + 1                    

Question: The volume of a box is given by V - x3 - 2x2 - 24x. If the depth be the smallest of the dimensions, it is-

• a)  x - 3
• b) x - 6
• c) x - 4
• d) x - 8

Answer: x - 6

Question: The area of a rectangle is given by A = 8x2 - 2x - 15. if the length be larger that the breadth, it is - 

• a) 3x + 5
• b) 5x + 3
• c) 4x + 5
• d) 2x + 3

Answer: 4x + 5

Question: Taking positive roots, the expression 

when simplifies reduces to

• a) 999
• b) 1000
• c) 1001
• d) 1

Answer: 1

More Questions.....................

Question: If [(23)9 - (23)8]/22 = (23^)x, then x equals. 

• a) 7
• b) 8
• c) 9
• d) 1

Answer: 8

Question: The value of (553 + 453)/(552 - 55 × 45 + 452)

• a) 100
• b) 105
• c) 125
• d) 75

Answer: 100

Question: 

 then the value of   is

• a) 84 - 28 - 2            
• b) 84 + 2                                  
• c) 84 - 28 + 2           
• d) 84 + 28 - 2

Answer:  84 - 28 + 2           

Question: The value of x satisfying the equation (considering only positive root)

• a) 6
• b) 3
• c) √3
• d) 9/2

Answer: 3

Question: D is a real number with non terminating digits a1 and a2 after the decimal point. Let D = 0. a1a2a1a2....... with a1 & a2 both not zero which of the following when multiplied by D will necessarily give an integer ? 

• a) 18
• b) 198
• c) 125
• d) 75

Answer: 198

Question: The pair of equations 3^x+y = 81, 81^x-y = 3 has                      

• a) No solution
• b) The solution
•  
• c) The solution x = 2, y = 2
• d) The solution 

Answer:

The solution 

Question: Solve for the non-zero values of u and v from the following : u - 4v = 3uv 2u + 5v = 19uv.

• a) u = -1, v =1/7
• b) u = 1, v = -1/7
• c) u = -1, v = 1/7
• d) u = 1, v = 1/7

Answer: u = 1, v = 1/7

Question: For what values of  α will the system of linear equations αx+ 3y = α- 3 and 12x + α y   = α  have a unique solution ?

• a) 6
• b) -6
• c) ±6                     
• d) Any real value except ±6

Answer: Any real value except ±6

Question: Obtain the condition for the following system of linear equations to have a unique solution. ax + by = c and Ix + my = n

• a) al  ≠ bm            
• b) ab ≠ ml                     
• c) am ≠ bl                
• d) am = bl

Answer: am ≠ bl                

Question: Find the value of c such that the system of linear equations : cx + 3y =3, 12x+ cy = 6 represents a pair of parallel lines.

• a) 6
• b) -6
• c) ±6
• d) Any real value except  ± 6

Answer: -6

Question: The ratio of the number of boys and the number of girls in a class of 45 students was 5 : 4. Seven new students joined the class. How many of them must be boys so that the ratio of the number of boys and the number of girls becomes 7 : 6 ?

• a) 3
• b) 4
• c) 6
• d) 8

Answer: 3

Question: The roots of the equation x^2/3 + x^1/3 - 2 = 0 are

• a) 1, 4
• b) 1, -4
• c) 1, -8
• d) 1, 8

Answer: 1, -8

Question: Solve :

• a) 20
• b) -20
• c) -8
• d) 8

Answer: 8

Question: If the equation x2 - 2kx - 2x - k2 = 0 has equal roots, the value of k must be           

• a) Zero
• b) Either zero or -1/2
• c) -1/2
• d) Either 1/2 or -1/2

Answer: -1/2

Question:  Find the H.C.F. of the polynomials in each of the following problems :

x2 + 2x - 3 and x3 + 5x2 - 2x - 24

• a) (x + 3) (x + 4) (x - 2)
• b) (x + 3) (x - 1)
• c) x - 3
• d) x+ 3

Answer: x+ 3

Question: Find the L.C.M. of the following expressions in each problem -

x3 - b3 and a4 + a2b2 + b4 

• a) (a3 - b3) (a2 - ab + b2)                                       
• b) (a3 + b3) (a2 - ab + b2)   
• c) (a3 - b3) (a2 + ab + b2)                                          
• d) (a3 - b3) (a2 - ab - b2)
  
  

Answer: (a3 - b3) (a2 - ab + b2)                                       

Question: Solve the following equation :

• a) 9
• b) 4
• c) 9, 4
• d) 9, -4

Answer: 9

Question: Solve for x

• a) -2, 3
• b) 3, 2
• c) -3, 2
• d) -3, -2

Answer: -3, 2

Question: For what value of k, (4 - k) x2 + (2k + 4) x + (8 k +1) = 0, is a perfect square :

• a) k = 1,2
• b) k = 1, -2
• c) k = 0, 3
• d) k = -1, -3

Answer: k = 0, 3

Question: In a competition, two students while solving a quadratic equation, committed the following mistakes : (i) One of them made a mistake in the constant term and got the roots as 5 and 9. (ii) Another one committed as error in the coefficient of x and he got the roots as 12 and 4. But in the meantime, they realized that they were wrong and they managed to get it right jointly. Find the quadratic equation.

• a) x2 + 4x + 14 = 0  
• b) 2x2 + 7x - 24 = 0
• c) x2 - 14x + 48 = 0 
• d) 3x2 - 17x + 52 = 0

Answer: x2 - 14x + 48 = 0