Unit-1:Algebra
(a)Real numbers
(b)Polynomials
(c)Pair of linear equations in two variables
Q1.
{(21)2-1} is divisible by which number?
(a)6 (b)7 (c)8 (d)9
Solution.
(8)
Note:As we know that n2 - 1 is divisible by 8, if n is an odd positive integer.
Solution
Q2.
Product of (21).(22)(23) is divisible by which set of numbers.
(a)6,3 (b)4,8 (c)4,5 (d)11,8
Solution.
(6,3)
Note: we know that,the product of three consecutive positive integer is divisible by 6.
Solution
Q3.
H.C.F of 96 and 404 is 4 find their L.C.M ?
(a)444 (b)6086 (c)2432 (d)9696
Solution.
(9696)
Note : H.C.F x L.C.M = Product of two numbers.
Solution
Q4.
Find the number of places of decimals after which the decimal expansion terminates, of 27/8
(a)1 (b)2 (c)3 (d)4
Solution.
(3)
27/8 = 27/(23) = 27/(23)x 58
Note : Let x = p/q be a rational number, such that the prime
factorisation of q is of the form 2m)x 5n, where m,n are non-negative integers. Then, x has a decimal expansion
which terminates after t places of decimals, where t is the larger of m and n.
Solution
Q5.
Find the HCF of 7 and 19.
(a)1 (b)2 (c)3 (d)4
Solution.
(1)
Note : If p and q are two prime numbers then their HCF will be 1.
Solution
Q6.
What is the total number of factors of 31?
(a)2 (b)3 (c)4 (d)1
Solution.
(2)
Note : The total number of factors of a prime number is 2 (1 and number itself).
Solution
Q7.
A 4 degree polynomial is called a _____.
(a)Linear equation (b)Cubic equation (c)Quadratic equation (d)Bioquadratic equation
Solution.
Bioquadratic equation
Solution
Q8.
A graph of polynomial f(x) = x2 -2x + 20
(a)Opens downwords (b)Opens upwords (c)Straight line (d)can't say
Solution.
(Opens upwords)
Note : The coefficient of x2 is 1 (a positive real number), the parabola opens upwords.
Solution
Q9.
Find the LCM of 23 and 41.
(a)23 (b)43 (c)943 (d)1
Solution.
(943)
Note : LCM of two prime numbers a and b is ab.
Solution
Q10.
Formula to find the vertex of parabola.
(a)(-b/2a , -d/4a) (b)(b/2a , -d/4a) (c)(-b/2a, d/4a) (d)(-b/4a, 0)
Solution.
(-b/2a, d/4a)
Solution
