The value of p2−(q−r)2(p+r)2−q2+q2−(p−r)2(p+q)2−r2+r2−(p−q)2(q+r)2−p2\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2}(p+r)2−q2p2−(q−r)2+(p+q)2−r2q2−(p−r)2+(q+r)2−p2r2−(p−q)2 is

Correct option is A

Given:

$\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2}$

Concept Used:

We can find the value of the expression by letting the values of p, q and r.

Solution:

Putting p = q = r = 1

$\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2}$

$\frac{1^2 - (1 - 1)^2}{(1 + 1)^2 - 1^2} + \frac{1^2 - (1 - 1)^2}{(1 + 1)^2 - 1^2} + \frac{1^2 - (1 - 1)^2}{(1 + 1)^2 - 1^2}$

\frac{1}{3}+\frac{1}{3}+\frac{1}{3}

= 1

Thus, the value of the expression is 1.

Free Tests

Free

Must Attempt

SSC CGL T-I Similar Paper (Held on 12 Sep 2025 S2)

English

100 Questions
200 Marks
60 Mins

English

Free

Must Attempt

SSC CGL T-I GA Section Test 01

English

25 Questions
50 Marks
15 Mins

English

Free

Must Attempt

SSC CGL T-I Full Mock Test 1 (Exam Level)

English

100 Questions
200 Marks
60 Mins

English

The value of $\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2}$ is

1

2

0

3

Correct option is A

Free Tests

SSC CGL T-I Similar Paper (Held on 12 Sep 2025 S2)

SSC CGL T-I GA Section Test 01

SSC CGL T-I Full Mock Test 1 (Exam Level)

Similar Questions

Access ‘SSC CGL Tier I’ Mock Tests with

Access ‘SSC CGL Tier I’ Mock Tests with

Discover Our Other Platforms

The value of p2−(q−r)2(p+r)2−q2+q2−(p−r)2(p+q)2−r2+r2−(p−q)2(q+r)2−p2\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2}(p+r)2−q2p2−(q−r)2​+(p+q)2−r2q2−(p−r)2​+(q+r)2−p2r2−(p−q)2​ is​

1

2

0

3

Correct option is A

Free Tests

SSC CGL T-I Similar Paper (Held on 12 Sep 2025 S2)

SSC CGL T-I GA Section Test 01

SSC CGL T-I Full Mock Test 1 (Exam Level)

Similar Questions

Access ‘SSC CGL Tier I’ Mock Tests with

Access ‘SSC CGL Tier I’ Mock Tests with

The value of $\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2}$ is