NTSE Mathematics Algebra MCQs Set 01

Question: If (x + p) is the HCF of (x2 + bx + a) and (x2 + cx + d) then the value of p is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: What are the number of integer solutions of the equation 7x+ 3y = 123, for x, y > 0 ?

• a) 4
• b) 5
• c) 4
• d) 6

Answer: 5

Question:  x² - 5x + 6 = 0 and x² + mx + 3 = 0 have a common root. Then m = ?

• a)

  

• b) -4
• c) Either (a) or (b)
• d) Both (a) and (b)

Answer: Either (a) or (b)

Question: The difference between two numbers is 5 difference in their squares is 65. The larger number is

• a) 9
• b) 10
• c) 11
• d) 12

Answer: 9

Question: If 

   , then  is equal to

• a) 9
• b)

  

• c) 7
• d) 11

Answer: 7

Question: The sum of the series 5 + 13 + 21 + ..... + 181 is

• a) 2139
• b) 6500
• c) 7500
• d) 3750

Answer: 2139

Question: What must be added to ¹/_x to make it equal to x ?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The value of (a^1/8 + a^-1/8) (a^1/8 – a^-1/8) (a^1/4 + a^-1/4) (a^1/2 + a^-1/2) is         

• a) (a + a^-1)            
• b) (a – a^-1)                 
• c) (a² – a^-2)              
• d) (a^1/2 – a^-1/2)

Answer:  (a – a^-1)                 

Question: If (x - 2) is a factor of  (x² + 3qx - 2q) then the value of q is

• a) 2
• b) -2
• c) 1
• d) -1

Answer: -1

Question: The arithmetic mean of two numbers is 34 and their geometric mean is 16. Find the numbers.

• a) 60,8
• b) 64,4
• c) 56,12
• d) 52,16

Answer: 64,4

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

Question: If log₁₀ 0.1 = log5x, find x.

• a) 5
• b) 1/5
• c) 10
• d) 1/10

  

Answer: 1/5

Question: The sum of ages of a father and son is 45 years. Five years ago, the product of their ages was 4 times the age of the father at that time. The present age of the father is

• a) 30 yrs
• b) 31 yrs
• c) 36 yrs
• d) 41 yrs

Answer: 36 yrs

Question: If a, b and c are is GP and a^1/x = b^1/y = c^1/z then x, y and z are in

• a) AP
• b) GP
• c) HP
• d) None of these

Answer: AP

Question: If a, b and c in GP, then log a log b and log c are in

• a) AP
• b) GP
• c) HP
• d) None of these

Answer: AP

Question: If one of the roots of the quadratic equation is 2 +√3 then find the quadratic equation   

• a) x2 - (2 +√3) x+ 1 = 0                                                
• b) x2 + (2 + √3) x + 1 =0         
• c) x2 - 4x + 1 =0                                                        
• d) x2 + 4x - 1 = 0

Answer:  x2 - 4x + 1 =0                                                        

Question: If α and β are the roots of the equations in which α- β = - 5 and  αβ = -6. Find the quadratic equation       

• a) x2 - x - 6 = 0          
• b) x2 + x - 6 = 0       
• c) x2 + x + 6 = 0      
• d) x2 - x + 6 = 0

Answer: x2 - x - 6 = 0           

Question: The mid points of sides of a square of side 12 m are joined to form another square inside it. The mid points of the inner square are further joined to form another square within it. This process goes on infinitely. Find the sum of areas of all such squares formed.

• a) 144 m2                
• b) 288 m2                      
• c) 280 m2               
• d) Infinite

Answer: 288 m2                      

Question: Calculate the value of 

• a) 1+√3          
• b) 1-√3                  
• c) Both of these
• d) None of these

Answer: 1+√3              

Question: The digit at the ten’s place of a two digit number is three times the digit at one’s place. If the sum of this number and the number formed by reversing its digits is 88, find the number.

• a) 62
• b) 26
• c) 64
• d) 46

Answer: 62

Question: If

and 3 (m + n) = 13 then find the value of x :

• a) 4
• b) 8
• c) 10
• d) 16

Answer: 8

Question: If

 and  2 x + 1 = y + 1 = P = 5; find value of q

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If

then the value of x is : 

• a) - 7
• b) 7/2
• c) 7
• d) -14

Answer: 7

Question: Find three consecutive integers such that four times the first plus one - half the second minus twice the third is equal to 24.

• a) 11, 12 and 13
• b) 12, 13 and 14
• c) 13, 14 and 15
• d) 10, 11 and 12

Answer: 11, 12 and 13

Question: Michal is 6 years older than Sabrina. Find years ago, Michal was thrice as old as Sabrina, find Michal’s present age?

• a) 8 years
• b) 14 years
• c) 16 years
• d) 28 years

Answer: 14 years

Question: If P = x + 1 and

then the value of x is :

• a) 1
• b) 1/2
• c) 2
• d) -1

Answer: 1

Question: If

then  

• a) 1148
• b) 1150
• c) 1154
• d) 1156

Answer: 1154

Question: If

than 

• a) 8
• b) -8
• c) 8
• d) 4

Answer: 8

Question: if a2 + b2 + c2 = 16 and ab + bc + ca = 10 then a + b + c =  

• a) 6
• b) -6
• c) 8
• d) 6

Answer: 6

Question: If a + b = 10, ab = 21 then a3 + b3 =

• a) 370
• b) 365
• c) 360
• d) 355

Answer: 370

Question: if x = - 2, y = 1 then value of (4y2 - 9x2) (16y4 + 36 x2y2 + 81x4) is :     

• a) 46592
• b) -46592
• c) 46592
• d) None of these

Answer: -46592