Solve the following system of linear inequalities. 3x − 9 ≥ 0, 4x − 10 ≤ 6.
[1, 4]
[3, 1]
[-3, -4]
[3, 4]
A girl A is reading a book having 446 pages and she has already finished reading 271 pages. She wants to finish reading this book within a week. What is the minimum number of pages she should read per day to complete reading the book within a week?
5 pages
15 pages
25 pages
35 pages
If a and b are the roots of the equation x² − px + q = 0, find the value of 1/a+1/b.
p/q
q/p
-p/q
1/q
Find the complete set of values of a for which the quadratic x² − ax + a +2=0 has equal roots.
2+√12
2±√12
2-√12
None
Find the number of solutions of x² + |x − 1| = 1.
1
2
3
None
Solve √x + 14 < x + 2.
x < 2
x > 2.
x = 2.
None
Solve the equation √6 − 4x − x² = x + 4.
x = −2
x = 1
x = −1
x = −3
Construct a cubic polynomial function having zeros at x = 2/5 , 1 + √3 such that f(0) = −8.
−10x³ + 24x² + 12x − 8
−7x³ + 4x² + 12x − 8
10x³ + 24x² + 12x − 8
7x³ + 4x² + 12x − 5
Find the sum of 1+2+3+ ··· + (n − 1) + n, n ∈ N
n(n + 1)
n(n + 1)/2
(n + 1)/2
n/2
The equations x² − 6x + a = 0 and x² − bx +6=0 have one root in common. The other root of the first and the second equations are integers in the ratio 4:3. Find the common root.
1
2
3
4
Find the values of p for which the difference between the roots of the equation x² + px +8=0 is 2.
p = 5
p = ±5
p = 6
p = ±6
Simplify: √(x² − 10x + 25).
|x − 5|
|x + 5|
|x − 3|
|x +3|
Find the square root of 7 − 4√3.
2 − √3.
2 + √3.
7 − √3.
7 +√3.
If the logarithm of 324 to base a is 4, then find a.
2√2
√2
3√2
None
If log₂ x + log₄ x + log₁₆ x = 7/2, find the value of x.