Numbers & Algebra - Numbers and Algebra MCQ

11:

When x + y + z = 9 and xy + yz + zx = 11, then x3 - y3 - z3 - 3xyz equals

A.	384
B.	192
C.	432
D.	48
	Answer Report Discuss
	Option: C Explanation : x³ - y³ - z³- 3xyz = (x+y+z)(x²+y²+z²-xy-yz-zx) = 9[(x + y + z)2 - 3(xy + yz + zx)] = 9(81 - 33) = 432. Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

12:

HCF and LCM of two numbers is given. It is possible to ind out the two numbers uniquely if
I. either sum or difference between the two numbers is known.
II. HCF of two numbers = LCM of two numbers.
III. (LCM/HCF)= Prime number.

A.	I and II only
B.	II only
C.	II and III only
D.	I, II and III
	Answer Report Discuss
	Option: D Explanation : Let HCF be h and LCM be l. I. Let, numbers be ah and bh. Then abh = and (a + b)h = m => (a — b)h = n Using these ah and bh can be uniquely determined. Thus, I is true II. II. If HCF = LCM, then two numbers are equal and same as HCF or LCM. Thus, II is true. III. LCM/HCF = prime i.e. l/h =P Then one of the numbers is equal to h and other is equal to E. Thus, III is true. Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

13:

A number when divided by sum of 555 and 445 gives two times their diference as quotient and 30 as remainder. The number is

A.	1220
B.	1250
C.	22030
D.	220030
	Answer Report Discuss
	Option: D Explanation : Number = (555+445)(555-445)2+30 = (555+445)2110+30 = 220000+30 = 220030 Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

14:

What is the remainder when 2050 x 2071 x 2095 is divided by 23?

A.	17
B.	12
C.	6
D.	3
	Answer Report Discuss
	Option: C Explanation : 2050 x 2071 x 2095 =(23x89+3)x(23x90+1)x(23x91+2) =(23[89 x 90+ 89 + 90 x 3]+ 3)x(23 x 91+2) =(23 K+ 3) (23 * 91 + 2) ) =(23 [K 91 + K* 2 + 91 * 3]+ 6) = 23 * L + 6 (where K and L are constants). Hence remainder is 6. Click on Discuss to view users comments. Sakshi singh said: (7:38pm on Friday 21st July 2017) but sir remainder 17 are also come .if we calculate it well, some quick arithmetic as followed by using multiples of 23 like 230,2300 etc. 2300-230=2070 is clearly a multiple of 23.(2070-2050)(2070-2071)(2070-2095)=20(-1)(-25) by 23500/23remainder is come 17. Write your comments here: Updating your Comments.. Updating your Comments..

15:

HCF of y3 - 4y and 4y (y3 + 8) is

A.	y(y + 2)
B.	y - 2
C.	2 (y + 2)
D.	(y + 2)(y²- 2y + 4)
	Answer Report Discuss
	Option: A Explanation : y³-4y = y(y²-4) = y(y-2)(y+2) 4y(y³+8) =4y(y+2)(y²-2y+4) ∴ HCF = y(y + 2). Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

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