Topic: FPSC PAST PAPERS

Explanation
If the common difference d = 0 d = 0 , the sequence is constant. General formula for an arithmetic sequence:
a n = a + ( n − 1 ) d a_n = a + (n - 1)d For d = 0 d = 0
a n = 3 + ( n − 1 ) × 0 = 3 a_n = 3 + (n - 1) times 0 = 3

So, the 5th number a 5 = 3 a_5 = 3

Explanation
This looks like an arithmetic sequence problem.
If the first term a = 3 a = 3 and last term l = 18 l = 18 , and there are 4 numbers in between , the total terms n = 6 (3 + 4 + 18). The terms:
a 1 = 3 a_1 = 3
a 6 = 18 a_6 = 18
Number of terms n = 6 n = 6 n = 6 Common difference d = 18 − 3 6 − 1 = 15 5 = 3 d = frac{18 - 3}{6 - 1} = frac{15}{5} = 3 d

The 3rd middle number is the 4th term :
a 4 = a 1 + 3 d = 3 + 3 × 3 = 12

Explanation
To solve the equation:
x 2 + 16 = 0 x^2 + 16 = 0 Step 1: Isolate x^2
x 2 = − 16 x^2 = -16 Step 2: Take the square root of both sides
x = ± − 16 x = pm sqrt{-16} Since − 16 sqrt{-16} − 1 involves the square root of a negative number, we use imaginary numbers :
x = ± 4 i x = pm 4i x = ± 4 i

Explanation
DVR stands for Digital Video Recorders They are devices used to record and store video content, as explained by Infiniti Electro-Optics.

Explanation
A non-traditional security threat refers to issues that are not related to traditional military threats like war or invasion. Climate change is considered non-traditional Because it poses a significant threat to Pakistan's stability and security, But it's not a direct military threat like an invasion

Explanation
  Given:

Speed from A to B = 40 km/h

Speed from B to A = 40 km/h + 50% of 40 km/h = 40 + 20 = 60 km/h

Find:
Average speed for the whole journey (both ways).
Formula for average speed when distance is the same but speeds differ:
Average speed = 2 × Speed 1 × Speed 2 Speed 1 + Speed 2 text{Average speed} = frac{2 times text{Speed}_1 times text{Speed}_2}{text{Speed}_1 + text{Speed}_2} ​ ​
Plug in values:
= 2 × 40 × 60 40 + 60 = 4800 100 = 48  km/h = frac{2 times 40 times 60}{40 + 60} = frac{4800}{100} = 48 text{ km/h} = 2 × 40 × 60 ​ 40 + 60 = 4800 /100 = 48  km/h

Explanation
 The formula for the nth term of an arithmetic sequence is aₙ = a₁ + (n - 1)d, where:  aₙ is the nth term of the sequence a₁ is the first term of the sequence n is the term number (e.g., 1st term, 2nd term, etc.) d is the common difference between consecutive terms For example, if the first term (a₁) is 2 and the commo n difference (d) is 3, then the 5th term (a₅) would be calculated as follows:  a₅ = 2 + (5 - 1)3 = 2 + 4 * 3 = 2 + 12 = 14 

Explanation
If the common difference d = 0 d = 0 , the sequence is constant. General formula for an arithmetic sequence:
a n = a + ( n − 1 ) d a_n = a + (n - 1)d For d = 0 d = 0
a n = 3 + ( n − 1 ) × 0 = 3 a_n = 3 + (n - 1) times 0 = 3

So, the 5th number a 5 = 3 a_5 = 3

Explanation
This looks like an arithmetic sequence problem.
If the first term a = 3 a = 3 and last term l = 18 l = 18 , and there are 4 numbers in between , the total terms n = 6 (3 + 4 + 18). The terms:
a 1 = 3 a_1 = 3
a 6 = 18 a_6 = 18
Number of terms n = 6 n = 6 n = 6 Common difference d = 18 − 3 6 − 1 = 15 5 = 3 d = frac{18 - 3}{6 - 1} = frac{15}{5} = 3 d

The 3rd middle number is the 4th term :
a 4 = a 1 + 3 d = 3 + 3 × 3 = 12

Explanation
To solve the equation:
x 2 + 16 = 0 x^2 + 16 = 0 Step 1: Isolate x^2
x 2 = − 16 x^2 = -16 Step 2: Take the square root of both sides
x = ± − 16 x = pm sqrt{-16} Since − 16 sqrt{-16} − 1 involves the square root of a negative number, we use imaginary numbers :
x = ± 4 i x = pm 4i x = ± 4 i

Explanation
DVR stands for Digital Video Recorders They are devices used to record and store video content, as explained by Infiniti Electro-Optics. 

Explanation
The December 2023 ceasefire in Yemen was facilitated by the United Nations. Part of the Yemeni civil war and the Iran –Saudi Arabia proxy conflict Date: 26 March 2015 – ongoing  (10 years and 2 months) Operation Decisive Storm  26 March – 21 April 2015  (3 weeks and 6 days) Operation Restoring Hope  22 April 2015 – present   (10 years, 1 month and 4 days)

Explanation
 The official motto of the Pakistan Army is "Iman, Taqwa, Jihad fi-Sabilillah" Translates to " Faith, Piety, Struggle in the Name of God ". This motto emphasizes the concept of "struggle" (Jihad) in the service of God.  Founded: 14 August 1947 Colours white and green Anniversaries: Defence Day: 6 September

Explanation
 "Who" is used as the subject of a clause referring to people. The clause "who wants a pen" describes "the one" — the person. "Whom" is used for objects of verbs or prepositions. "Whose" shows possession. "Which" refers to things, not people.

Explanation
A non-traditional security threat refers to issues that are not related to traditional military threats like war or invasion. Climate change is considered non-traditional Because it poses a significant threat to Pakistan's stability and security, But it's not a direct military threat like an invasion

Explanation
  Given:

Speed from A to B = 40 km/h

Speed from B to A = 40 km/h + 50% of 40 km/h = 40 + 20 = 60 km/h

Find:
Average speed for the whole journey (both ways).
Formula for average speed when distance is the same but speeds differ:
Average speed = 2 × Speed 1 × Speed 2 Speed 1 + Speed 2 text{Average speed} = frac{2 times text{Speed}_1 times text{Speed}_2}{text{Speed}_1 + text{Speed}_2} ​ ​
Plug in values:
= 2 × 40 × 60 40 + 60 = 4800 100 = 48  km/h = frac{2 times 40 times 60}{40 + 60} = frac{4800}{100} = 48 text{ km/h} = 2 × 40 × 60 ​ 40 + 60 = 4800 /100 = 48  km/h

Explanation
 The formula for the nth term of an arithmetic sequence is aₙ = a₁ + (n - 1)d, where:  aₙ is the nth term of the sequence a₁ is the first term of the sequence n is the term number (e.g., 1st term, 2nd term, etc.) d is the common difference between consecutive terms For example, if the first term (a₁) is 2 and the commo n difference (d) is 3, then the 5th term (a₅) would be calculated as follows:  a₅ = 2 + (5 - 1)3 = 2 + 4 * 3 = 2 + 12 = 14 

Explanation
If the common difference d = 0 d = 0 , the sequence is constant. General formula for an arithmetic sequence:
a n = a + ( n − 1 ) d a_n = a + (n - 1)d For d = 0 d = 0
a n = 3 + ( n − 1 ) × 0 = 3 a_n = 3 + (n - 1) times 0 = 3

So, the 5th number a 5 = 3 a_5 = 3

Explanation
This looks like an arithmetic sequence problem.
If the first term a = 3 a = 3 and last term l = 18 l = 18 , and there are 4 numbers in between , the total terms n = 6 (3 + 4 + 18). The terms:
a 1 = 3 a_1 = 3
a 6 = 18 a_6 = 18
Number of terms n = 6 n = 6 n = 6 Common difference d = 18 − 3 6 − 1 = 15 5 = 3 d = frac{18 - 3}{6 - 1} = frac{15}{5} = 3 d

The 3rd middle number is the 4th term :
a 4 = a 1 + 3 d = 3 + 3 × 3 = 12

Explanation
To solve the equation:
x 2 + 16 = 0 x^2 + 16 = 0 Step 1: Isolate x^2
x 2 = − 16 x^2 = -16 Step 2: Take the square root of both sides
x = ± − 16 x = pm sqrt{-16} Since − 16 sqrt{-16} − 1 involves the square root of a negative number, we use imaginary numbers :
x = ± 4 i x = pm 4i x = ± 4 i

Explanation
DVR stands for Digital Video Recorders They are devices used to record and store video content, as explained by Infiniti Electro-Optics. 

Explanation
The December 2023 ceasefire in Yemen was facilitated by the United Nations. Part of the Yemeni civil war and the Iran –Saudi Arabia proxy conflict Date: 26 March 2015 – ongoing  (10 years and 2 months) Operation Decisive Storm  26 March – 21 April 2015  (3 weeks and 6 days) Operation Restoring Hope  22 April 2015 – present   (10 years, 1 month and 4 days)

Explanation
 The official motto of the Pakistan Army is "Iman, Taqwa, Jihad fi-Sabilillah" Translates to " Faith, Piety, Struggle in the Name of God ". This motto emphasizes the concept of "struggle" (Jihad) in the service of God.  Founded: 14 August 1947 Colours white and green Anniversaries: Defence Day: 6 September

Explanation
 "Who" is used as the subject of a clause referring to people. The clause "who wants a pen" describes "the one" — the person. "Whom" is used for objects of verbs or prepositions. "Whose" shows possession. "Which" refers to things, not people.

Explanation
A non-traditional security threat refers to issues that are not related to traditional military threats like war or invasion. Climate change is considered non-traditional Because it poses a significant threat to Pakistan's stability and security, But it's not a direct military threat like an invasion

Explanation
  Given:

Speed from A to B = 40 km/h

Speed from B to A = 40 km/h + 50% of 40 km/h = 40 + 20 = 60 km/h

Find:
Average speed for the whole journey (both ways).
Formula for average speed when distance is the same but speeds differ:
Average speed = 2 × Speed 1 × Speed 2 Speed 1 + Speed 2 text{Average speed} = frac{2 times text{Speed}_1 times text{Speed}_2}{text{Speed}_1 + text{Speed}_2} ​ ​
Plug in values:
= 2 × 40 × 60 40 + 60 = 4800 100 = 48  km/h = frac{2 times 40 times 60}{40 + 60} = frac{4800}{100} = 48 text{ km/h} = 2 × 40 × 60 ​ 40 + 60 = 4800 /100 = 48  km/h

Explanation
 The formula for the nth term of an arithmetic sequence is aₙ = a₁ + (n - 1)d, where:  aₙ is the nth term of the sequence a₁ is the first term of the sequence n is the term number (e.g., 1st term, 2nd term, etc.) d is the common difference between consecutive terms For example, if the first term (a₁) is 2 and the commo n difference (d) is 3, then the 5th term (a₅) would be calculated as follows:  a₅ = 2 + (5 - 1)3 = 2 + 4 * 3 = 2 + 12 = 14 

Explanation
If the common difference d = 0 d = 0 , the sequence is constant. General formula for an arithmetic sequence:
a n = a + ( n − 1 ) d a_n = a + (n - 1)d For d = 0 d = 0
a n = 3 + ( n − 1 ) × 0 = 3 a_n = 3 + (n - 1) times 0 = 3

So, the 5th number a 5 = 3 a_5 = 3

Explanation
This looks like an arithmetic sequence problem.
If the first term a = 3 a = 3 and last term l = 18 l = 18 , and there are 4 numbers in between , the total terms n = 6 (3 + 4 + 18). The terms:
a 1 = 3 a_1 = 3
a 6 = 18 a_6 = 18
Number of terms n = 6 n = 6 n = 6 Common difference d = 18 − 3 6 − 1 = 15 5 = 3 d = frac{18 - 3}{6 - 1} = frac{15}{5} = 3 d

The 3rd middle number is the 4th term :
a 4 = a 1 + 3 d = 3 + 3 × 3 = 12

Explanation
To solve the equation:
x 2 + 16 = 0 x^2 + 16 = 0 Step 1: Isolate x^2
x 2 = − 16 x^2 = -16 Step 2: Take the square root of both sides
x = ± − 16 x = pm sqrt{-16} Since − 16 sqrt{-16} − 1 involves the square root of a negative number, we use imaginary numbers :
x = ± 4 i x = pm 4i x = ± 4 i

Explanation
DVR stands for Digital Video Recorders They are devices used to record and store video content, as explained by Infiniti Electro-Optics. 

Explanation
The December 2023 ceasefire in Yemen was facilitated by the United Nations. Part of the Yemeni civil war and the Iran –Saudi Arabia proxy conflict Date: 26 March 2015 – ongoing  (10 years and 2 months) Operation Decisive Storm  26 March – 21 April 2015  (3 weeks and 6 days) Operation Restoring Hope  22 April 2015 – present   (10 years, 1 month and 4 days)

Explanation
 The official motto of the Pakistan Army is "Iman, Taqwa, Jihad fi-Sabilillah" Translates to " Faith, Piety, Struggle in the Name of God ". This motto emphasizes the concept of "struggle" (Jihad) in the service of God.  Founded: 14 August 1947 Colours white and green Anniversaries: Defence Day: 6 September

Explanation
 "Who" is used as the subject of a clause referring to people. The clause "who wants a pen" describes "the one" — the person. "Whom" is used for objects of verbs or prepositions. "Whose" shows possession. "Which" refers to things, not people.

Explanation
A non-traditional security threat refers to issues that are not related to traditional military threats like war or invasion. Climate change is considered non-traditional Because it poses a significant threat to Pakistan's stability and security, But it's not a direct military threat like an invasion

Explanation
  Given:

Speed from A to B = 40 km/h

Speed from B to A = 40 km/h + 50% of 40 km/h = 40 + 20 = 60 km/h

Find:
Average speed for the whole journey (both ways).
Formula for average speed when distance is the same but speeds differ:
Average speed = 2 × Speed 1 × Speed 2 Speed 1 + Speed 2 text{Average speed} = frac{2 times text{Speed}_1 times text{Speed}_2}{text{Speed}_1 + text{Speed}_2} ​ ​
Plug in values:
= 2 × 40 × 60 40 + 60 = 4800 100 = 48  km/h = frac{2 times 40 times 60}{40 + 60} = frac{4800}{100} = 48 text{ km/h} = 2 × 40 × 60 ​ 40 + 60 = 4800 /100 = 48  km/h

Explanation
 The formula for the nth term of an arithmetic sequence is aₙ = a₁ + (n - 1)d, where:  aₙ is the nth term of the sequence a₁ is the first term of the sequence n is the term number (e.g., 1st term, 2nd term, etc.) d is the common difference between consecutive terms For example, if the first term (a₁) is 2 and the commo n difference (d) is 3, then the 5th term (a₅) would be calculated as follows:  a₅ = 2 + (5 - 1)3 = 2 + 4 * 3 = 2 + 12 = 14 

Explanation
If the common difference d = 0 d = 0 , the sequence is constant. General formula for an arithmetic sequence:
a n = a + ( n − 1 ) d a_n = a + (n - 1)d For d = 0 d = 0
a n = 3 + ( n − 1 ) × 0 = 3 a_n = 3 + (n - 1) times 0 = 3

So, the 5th number a 5 = 3 a_5 = 3

Explanation
This looks like an arithmetic sequence problem.
If the first term a = 3 a = 3 and last term l = 18 l = 18 , and there are 4 numbers in between , the total terms n = 6 (3 + 4 + 18). The terms:
a 1 = 3 a_1 = 3
a 6 = 18 a_6 = 18
Number of terms n = 6 n = 6 n = 6 Common difference d = 18 − 3 6 − 1 = 15 5 = 3 d = frac{18 - 3}{6 - 1} = frac{15}{5} = 3 d

The 3rd middle number is the 4th term :
a 4 = a 1 + 3 d = 3 + 3 × 3 = 12

Explanation
To solve the equation:
x 2 + 16 = 0 x^2 + 16 = 0 Step 1: Isolate x^2
x 2 = − 16 x^2 = -16 Step 2: Take the square root of both sides
x = ± − 16 x = pm sqrt{-16} Since − 16 sqrt{-16} − 1 involves the square root of a negative number, we use imaginary numbers :
x = ± 4 i x = pm 4i x = ± 4 i

Explanation
DVR stands for Digital Video Recorders They are devices used to record and store video content, as explained by Infiniti Electro-Optics. 

Explanation
The December 2023 ceasefire in Yemen was facilitated by the United Nations. Part of the Yemeni civil war and the Iran –Saudi Arabia proxy conflict Date: 26 March 2015 – ongoing  (10 years and 2 months) Operation Decisive Storm  26 March – 21 April 2015  (3 weeks and 6 days) Operation Restoring Hope  22 April 2015 – present   (10 years, 1 month and 4 days)

Explanation
 The official motto of the Pakistan Army is "Iman, Taqwa, Jihad fi-Sabilillah" Translates to " Faith, Piety, Struggle in the Name of God ". This motto emphasizes the concept of "struggle" (Jihad) in the service of God.  Founded: 14 August 1947 Colours white and green Anniversaries: Defence Day: 6 September

Explanation
 "Who" is used as the subject of a clause referring to people. The clause "who wants a pen" describes "the one" — the person. "Whom" is used for objects of verbs or prepositions. "Whose" shows possession. "Which" refers to things, not people.

Explanation

Explanation
Active Voice : Might have + third form of a verb Passive Voice : Might have been + third form of a verb.

Explanation
Because earthquake gives vowel sound. Earthquake means زلزل ہ

Explanation
This is a sentence of present indefinite tense. Helping Verbs A.V = Do/Does P.V = is/am/are Sell is an irregular verb which means فروخت کرنا Sold is the second form of Sell. Sold is also the third form of Sell.

Explanation
Given sentence is in Past simple tense and it is in active voice, we need to change it into passive voice. Rule : Subject + (was / were) + V3 + Optional Agents.

Explanation
Millennium means ایک ہزار سال کی مدت

Explanation
The sentence is in Past Continuous Tense.  Present Continuous Tense Active Voice : Subject + is/am/are + First of verb + ing + object. Passive Voice : Object + is being/am being/ are being + third form of verb + by + subject.

Explanation

Explanation
The term variance refers to a statistical measurement of the spread between numbers in a data set

Explanation
Average speed,=2×x×yx+y=2×100×150100+150=200×150250=120km/hr

Explanation