Q63.The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1, 3, 5, 8, if repetition of digits is allowed, is (1) 21 (2) 20 (3) 22 (4) 18
What This Question Tests
This question requires careful case analysis based on the definitions of the modulus function to simplify the equation into standard quadratic forms and then find the number of real roots.
Concepts Tested
Formulas Used
|x| = x for x >= 0
|x| = -x for x < 0
๐ NCERT Sections This Tests
1.3 โ Define The Following Terms:
Chemistry Class 11 ยท Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
3.23 โ The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 ร 10โ5Sโ1
Chemistry Class 11 ยท Chapter 3
3.23 The rate constant for the decomposition of hydrocarbons is 2.418 ร 10โ5sโ1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
5.18 โ What Is Crystal Field Splitting Energy? How Does The Magnitude Of Do Decide
Chemistry Class 11 ยท Chapter 5
5.18 What is crystal field splitting energy? How does the magnitude of Do decide the actual configuration of d orbitals in a coordination entity?
๐ Question Details
- Chapter
- Quadratic Equations
- Topic
- Equations involving modulus function
- Year
- 2023
- Shift
- 15 Apr Shift 1
- Q Number
- Q63
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
More from this Chapter
Q83.If the difference between the roots of the equation x2 + ax + 1 = 0 is less than โ5, then the set of possible values of a is JEE Main 2007 JEE Main Previous Year Paper (1) (โ3, 3) (2) (โ3, โ) (3) (3, โ) (4) (โโ, โ3)
Q72.The quadratic equations x2 โ6x + a = 0 and x2 โcx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is (1) 1 (2) 4 (3) 3 (4) 2
Q61.If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is (1) greater than 4ab (2) less than 4ab (3) greater than โ4ab (4) less than - 4ab
Q61.The value of k for which the equation (K โ2)x2 + 8x + K + 4 = 0 has both roots real, distinct and negative is (1) 6 (2) 3 (3) 4 (4) 1