Extra Questions of Real Numbers, Polynomials and Pair of Linear Equations in Two Variables
1.) If a and b are two positive integers such that a=14b. Find the HCF of a and b.
Ans : b
2.) If the HCF of 55 and 99 is expressible in the form 55m-99, then the value of m is _____.
Ans : 2
3.) If p(x) is a polynomial of at least degree one and p(k)=0, then k is known as
a) value of p(x)
b) zero of p(x)
c) contant term of p(x)
d) none of these.
Ans : b) zero of p(x)
4.) The pair of linear equations 2x+3y=5 and 4x+6y=10 is
a) inconsistent
b) consistent
c) dependent consistent
d) none of these.
Ans : a) inconsistent
5.) The HCF of 1001 and 385 is __
Ans : 1
6.) Graph of y=f(x) is given below. Find the zeros of f(x).
Ans : -4, -1, 2
7.) Given below are three equations. Two of them have infinite solution and two have unique solution. state the two pairs:
i) 3x-2y=4
ii) 6x+2y=4
iii) 9x-6y=12
Ans :
Pairs having infinitely many solutions
3x-2y=4 & 9x-6y=12
Pairs having unique solution
3x-2y=4 & 6x+2y=4
8.) If two positive integers a and b are written as a=x³y² and b=xy³, where x, y are prime numbers, then HCF (a,b) is
a) xy
b) xy²
c) x³y³
d) x²y²
Also, find LCM of (a,b)
Ans : HCF = xy²
LCM = x³y³
9.) If one of the zeroes of the quadratic polynomial (k-1)x²+kx+1 is -3, then the value of k is
a) 4/3
b) -4/3
c) 2/3
d) -2/3
Ans : a) 4/3
10.) The pair of equations x=a and y=b graphically represents lines which are
a) parallel
b) intersecting at (b,a)
c) coincident
d) intersecting at (a,b)
Ans : d) intersecting at (a,b)
11.) Find pairs of natural number whose least common multiple is 78 and the greatest divisor is 13.
Ans : 26 and 39 OR 13 and 78
12.) Find the zeroes of √3x²+10x+7√3
Ans : x=-√3 and x=-7/√3
13.) Solve the following pair of linear equations by subsitution method y-5=0; 3x+4y-20=0
14.) The ratio of the LCM and HCF of 5, 15, 20 is :
a) 9:1
b) 4:3
c) 11:1
d) 12:1
Ans : d) 12:1
15.) Zeroes of p(z)=z²-27 are ___ and ___.
Ans : 3√3 and -3√3
16.) Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to the no. of points where the graph of the polynomial
a) intersect y-axis
b) intersect x-axis.
c) intersect y-axis or intersect x-axis.
d) none of these.
17.) The pair of equations x=4 and y=3 graphically represent lines which are
a) parallel
b) intersecting at (3,4)
c) coincident
d) intersecting at (4,3)
18.) The decimal expansion of the rational number 43/2⁴.5³, will terminate after how many places of decimal.
Ans : 0.0214
19.) Sum and product of zeroes of quadratic polynomial are 0 and √15 respectively. Find the quadratic polynomial.
20.) For what value of p will the following pair of linear equations have infinitely many solutions?
(p-3)x+3y=p; px+py=12
Ans : p=6
21.) Two alarm clock ring their alarms at regular intervals of 50 seconds and 48 seconds. If they first beep together at 12 noon then what time will they beep again for the first time?
a) 12:20 PM
b) 12:12 PM
c) 12:11 PM
d) None of these.
Ans : a) 12:20 PM
22.) If A=2n+13, B=n+7, where n is a natural number, then HCF of A and B is
a) 2
b) 1
c) 3
d) 4
Ans : b) 1
23.) If graph of a polynomial does not intersects the x-axis but intersects y-axis in one point, then number of zeroes of the polynomial is equal to
a) 0
b) 1
c) 0 or 1
d) None of these.
Ans : c) 0 or 1
24.) If x=a, y=b is the solution of the pair of equations x-y=2 and x+y=4, then the respective values of a and b are
a) 3,5
b) 5,3
c) 3,1
d) -1, -3
Ans c) 3, 1
25.) If the zeroes of the quadratic polynomial x²+(a+1)x+b are 2 and -3, then
a) a=-7, b=-1
b) a=5, b=-1
c) a=2, b=-6
d) a=0, b=-6
Ans : d) a=0, b=-6
26.) Which of the following is not the graph of a quadratic polynomial?
