JEE-Main - Grade 12 - Mathematics - Linear Programming - Introduction and Snapshot of Linear Programming - Study ref# 932

Introduction
In this chapter, we shall apply the
systems of linear inequalities/ equations to solve some real life problems of
the type as given below:
A furniture dealer deals in only two item
– tables and chairs. He has Rs. 50,000... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Importance and Snapshot of Linear Inequalities - Study ref# 617

Introduction:
In earlier classes, we have studied equations in one
variable and two variables and also solved some statement problems by
translating them in the form of equations. Now a natural question arises: ‘Is
it always possibl... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Importance and Snapshot of Linear Inequalities - Study ref# 618

Following sections must be covered to understand the
Linear Inequalities:
1. Inequalities
2. Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
3. Graphical Solution of Linear Inequalities in ... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Target Setup for Linear Inequalities - Study ref# 619

Student requires to achieve the following milestones to get better grip over Linear Inequalities. The milestones / targets are as follows:-Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%Chapter Test000%... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 2519

Solve -12x >30 ,when
(i) x is a natural number.
(ii) x is an integer. Answer: We have -12x >30, dividing both sides by – 12
(i... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 2520

Solve 3x + 8 > 2, when
(i) x is an integer (ii) x is a real number. Answer: We have , 3x + 8 > 2
Adding -8 on both sides,
3x + 8-8>2-8
3x> -6
Dividing by 3 on both sides,
... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 2521

Answer: We have ,
Transferring the term 2x to LHS and the term – 3 to RHS,
read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 2522

Answer: We have,
Transferring the term to LHS,
Taking LCM in LHS,
Multiplying both sides by 6,
... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 3030

Solve the following system of inequalities: Answer: We have And Since there is no real number x satisfying both the inequalities (1) and (2), the given system of inequalities has no solution.... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 3031

For all x>0, prove
and Answer: Since x>0, we have
If x < 0, then choose x =-y
where y is +ive
∴ multiply by
minus sign and change the sign
... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 3032

For any real x≠0,
prove
Answer: Since both sides of the inequality are positive,
is
equivalent to
which is true.... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 3033

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 3034

If such
that a, b ≥ 0 then
prove that
Answer: Since ,
we may choose a=sinθ,
b=cosθ
L.H.S
∴L.H.S.≥ by (1) and (2).... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 3255

Solve 24x < 100 when
(i)
x is a natural number
(ii)
x i... read more

JEE-Main - Grade 11 - Mathematics - Linear Inequalities - Study ref# 3256

Solve 5x – 3 < 7, Then
(i)
x is an integer
(ii)
x is a ... read more

JEE-Main - Grade 12 - Mathematics - Linear Programming - Study ref# 9638

Reshma wishes to mix two types of food P
and Q in such a way that the vitamin contents of the mixture contain at least
8 units of vitamin A and 11 units of vitamin B. Food P costs Rs. 60/kg and
Food Q costs Rs.80/kg. Food P contains 3 units/... read more

JEE-Main - Grade 12 - Mathematics - Linear Programming - Study ref# 9639

One kind of cake requires 200 g of flour
and 25g of fat, and another kind of cake requires 100g of flour and 50 g of
fat. Find the maximum number of cakes which can be made from 5kg of flour and
1kg of fat assuming that there is no shortage ... read more

JEE-Main - Grade 12 - Mathematics - Linear Programming - Study ref# 9640

A manufacture producers nuts and bolts.
It takes 1 hour of work on machine A and 3 hours on machine B to produce a
package of nuts. It takes 3 hours on machine A and 1 hour on machine B to
produce a package of bolts. He earns a profits... read more

JEE-Main - Grade 12 - Mathematics - Linear Programming - Study ref# 9641

A cottage industry manufactures pedestal
lamps and wooden shades, each requiring the use of a grinding/ cutting
machine and a sprayer. It takes 2 hours on grinding /cutting machine and 3
hours on the sprayer to
manufacture a pedestal lam... read more

JEE-Main - Grade 12 - Mathematics - Linear Programming - Study ref# 9642

A diet is to contain at least 80 units of
vitamin A and 100 units of minerals. Two foods and are available. Food
costs Rs.4 per unit
food and costs Rs.6 per unit.
... read more

JEE-Main - Grade 12 - Mathematics - Linear Programming - Study ref# 9643

A farmer mixes two brands P and Q of
cattle feed. Brand P, costing Rs. 250 per bag contains 3 units of nutritional
element A, 2.5 units of element B and 2 units of element C. Brand Q costing Rs.200
per bag contains, 1.5 units of nutritional ... read more