Types of Inequalities

Q.

How to solve $\frac{5}{2x}=-10$?

Q.

Question 92

In the following question, state whether the given statement is true (T) or false (F).

Sum of two distinct whole number is always less than their product.

Q.

Solve:$5x-\frac{1}{3}(x+1)=6(x+\frac{1}{30})$

Q. Find three consecutive whole numbers whose sum is more than $45$ but less than $54$.

Q.

Simplify $(x^3-3x^2-x)(x^2-3x+1)$

Q. A father's present age is seven years less than $30$ times of what his son's age was $20$ years ago. Also, the father's present age is $31$ years more than his won's present age. Find the sum of their present ages in years.

Q.

If $\frac{5x}{3}–4=\frac{2x}{5}$, then the numerical value of $2x–7$ is

1. $\frac{19}{13}$

2. $\frac{-13}{19}$

3. $0$

4. $\frac{13}{19}$

Q. This section contains 1 Matrix Match type question, which has 2 Columns (Column I and Column II). Column I has four entries (A), (B), (C) and (D), Column II has four entries (P), (Q), (R) and (S). Match the entries in Column I with the entries in Column II. Each entry in Column I may match with one or more entries in Column II.
इस खण्ड में 1 मैट्रिक्स मिलान प्रकार का प्रश्न है, जिसमें 2 कॉलम (कॉलम I तथा कॉलम II) हैं। कॉलम I में चार प्रविष्टियाँ (A), (B), (C) तथा (D) हैं, कॉलम II में चार प्रविष्टियाँ (P), (Q), (R) तथा (S) हैं। कॉलम I में दी गयी प्रविष्टियों का मिलान कॉलम II में दी गयी प्रविष्टियों के साथ कीजिए। कॉलम I में दी गयी प्रत्येक प्रविष्टि का मिलान कॉलम II में दी गयी एक या अधिक प्रविष्टियों के साथ हो सकता है।

Match the Columns and choose the appropriate answer

कॉलमों का मिलान करें और सही उत्तर चुनें

	Column-I कॉलम-I		Column-II कॉलम-II
(A)	Complete solution set of the inequality $\frac{(x^2-5x+6)}{(x^2-6x)}⩽0$ is असमिका $\frac{(x^2-5x+6)}{(x^2-6x)}⩽0$ का सम्पूर्ण हल समुच्चय है	(P)	x ∈ [1, 3) ∪ [4, ∞)
(B)	Complete solution set of the inequality (x2 + 3x)(x2 – 3x + 2) ≤ 0 is असमिका (x2 + 3x)(x2 – 3x + 2) ≤ 0 का सम्पूर्ण हल समुच्चय है	(Q)	x ∈ (0, 2] ∪ [3, 6)
(C)	Complete solution set of the inequality $\frac{x^2-5x+4}{x-3}⩾0$ is असमिका $\frac{x^2-5x+4}{x-3}⩾0$ का सम्पूर्ण हल समुच्चय है	(R)	x ∈ [–3, 0] ∪ [1, 2]
(D)	Complete solution set of the inequality $\frac{x^2-4}{x-3}⩾0$ is असमिका $\frac{x^2-4}{x-3}⩾0$ का सम्पूर्ण हल समुच्चय है	(S)	x ∈ [–2, 2] ∪ (3, ∞)

1. A-Q, B-R, C-P, D-S
2. A-R, B-Q, C-P, D-S
3. A-S, B-R, C-P, D-Q
4. A-S, B-P, C-R, D-Q

Q.

If x<25 and y>25 are two inequalities, then:

1. y = 0

2. x = 0

3. x < y

4. x > y

Q. Solve the following inequation:
$-2(p+3)>5,p\epsilon I$

Q. Solve the following inequation:
$2x-3<x+2,x\epsilon N$

Q. Solve the following inequation:
$4>3x-11,x\epsilon N$

Q.

Solve the following equation

$\frac{5}{2}x=10$.

Q. Disprove, by finding a suitable counter example, the statement $x^2>y^2$ for all $x>y$.

Q. $\frac{9}{4}\times 3\frac{4}{5}÷5\frac{2}{11}=$ $1\frac{x}{20}$. Find x.