Chapter 2

Mathematics

+2 college entrance (after SEE) past exam questions

Past questions and answers

20 questions set from this chapter. Most repeated first.

2026 Set A · 1 mark

The possible number of subsets for a set $P$ is 16 then the set $P$ is (a) $P=\{a,b\}$ (b) $P=\{a,b,c\}$ (c) $P=\{a,b,c,d\}$ (d) $P=\{a,b,c,d,e\}$

Similar questions: If the possible number of subsets (2026 Set B)

Answer

(c) $P=\{a,b,c,d\}$

A set with $n$ elements has $2^n$ subsets. Here $2^n=16=2^4$ , so $n=4$ , and only option (c) has 4 elements.

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2026 Set A · 1 mark

What is the simple interest earned on Rs.4000 at the rate of 10% yearly for 18 months? (a) Rs.300 (b) Rs.400 (c) Rs.500 (d) Rs.600

Similar questions: What is the simple interest earned (2026 Set B)

Answer

(d) Rs.600

$I=\frac{PTR}{100}=\frac{4000\times 1.5\times 10}{100}=\text{Rs }600$

Here 18 months is $1.5$ years.

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2026 Set A · 1 mark

If lines represented by the homogeneous equation $3x^2-5xy-by^2=0$ are orthogonal then (a) $b=3$ (b) $b=15$ (c) $b=-3$ (d) $b=-\frac{25}{12}$

Similar questions: If lines represented by the homogeneous (2026 Set B)

Answer

(a) $b=3$

For $ax^2+2hxy+by^2=0$ the lines are perpendicular when $a+b=0$ (coefficient of $x^2$ plus coefficient of $y^2$ ). Here $3+(-b)=0$ , so $b=3$ .

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2026 Set B · 1 mark

If the possible number of subsets for a set $R$ is 64, then the number of elements in set $R$ is: (a) $4$ (b) $5$ (c) $6$ (d) $8$

Similar questions: The possible number of subsets for (2026 Set A)

Answer

(c) $6$

A set with $n$ elements has $2^n$ subsets, so $2^n = 64 = 2^6$ , giving $n = 6$ .

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2026 Set B · 1 mark

What is the simple interest earned on Rs. 12,000 at the rate of 8% yearly for 9 months? (a) Rs. 960 (b) Rs. 720 (c) Rs. 840 (d) Rs. 600

Similar questions: What is the simple interest earned (2026 Set A)

Answer

(b) Rs. 720

$I = \frac{PTR}{100} = \frac{12000 \times \frac{9}{12} \times 8}{100} = \frac{12000 \times 0.75 \times 8}{100} = \text{Rs. } 720$

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2026 Set B · 1 mark

If lines represented by the homogeneous equation $kx^2+4xy-5y^2=0$ are orthogonal, then: (a) $k=4$ (b) $k=5$ (c) $k=-5$ (d) $k=0$

Similar questions: If lines represented by the homogeneous (2026 Set A)

Answer

(b) $k=5$

For $ax^2+2hxy+by^2=0$ the lines are perpendicular when $a+b=0$ . Here $a=k$ , $b=-5$ , so $k-5=0$ , giving $k=5$ .

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2026 Set A · 1 mark

If $a:b=2:5$ and $a:c=1:4$ . Then $b:c=$ ? (a) $1:10$ (b) $5:8$ (c) $1:5$ (d) $1:2$

Answer

(b) $5:8$

Make $a$ equal in both ratios: $a:b=2:5$ and $a:c=1:4=2:8$ . Then $b:c=5:8$ .

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2026 Set A · 1 mark

The H.C.F. of $a^3-1$ and $a^4+a^2+1$ is (a) $a+1$ (b) $a-1$ (c) $a^2-a+1$ (d) $a^2+a+1$

Answer

(d) $a^2+a+1$

$a^3-1=(a-1)(a^2+a+1)$

$a^4+a^2+1=(a^2+1)^2-a^2=(a^2+a+1)(a^2-a+1)$

The common factor is $a^2+a+1$ .

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2026 Set A · 1 mark

If $x^2+\frac{1}{x^2}=18$ , what is the value of $x-\frac{1}{x}$ ? (a) $4$ (b) $\pm4$ (c) $2$ (d) $\pm2$

Answer

(b) $\pm4$

$\left(x-\frac1x\right)^2=x^2+\frac1{x^2}-2=18-2=16$

So $x-\frac1x=\pm4$ .

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2026 Set A · 1 mark

What is the ratio of circumference to diameter of the circle? (a) $\pi:1$ (b) $2\pi:1$ (c) $\pi:2$ (d) $2:\pi$

Answer

(a) $\pi:1$

Circumference is $C=\pi d$ , so $C:d=\pi:1$ .

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2026 Set A · 1 mark

What is the total surface area of a cubical tank of length of side 10 m? (a) $600\ m^2$ (b) $500\ m^2$ (c) $400\ m^2$ (d) $300\ m^2$

Answer

(a) $600\ m^2$

For a cube, $TSA=6a^2=6\times10^2=600\ m^2$ .

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2026 Set A · 1 mark

If $\bar{X}=150$ , $N=10$ , then the value of $\sum fx$ is (a) $24$ (b) $600$ (c) $1200$ (d) $1500$

Answer

(d) $1500$

$\bar X=\frac{\sum fx}{N}\Rightarrow \sum fx=150\times10=1500$

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2026 Set A · 1 mark

From the normal pack of 52 cards, a card is drawn at random, the probability of getting a king is... (a) $\frac14$ (b) $\frac{1}{26}$ (c) $\frac{1}{13}$ (d) $\frac12$

Answer

(c) $\frac{1}{13}$

There are 4 kings in 52 cards, so $P=\frac4{52}=\frac1{13}$ .

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2026 Set B · 1 mark

If $x:y=3:4$ and $x:z=2:5$ . Then $y:z=$ ? (a) $3:10$ (b) $8:15$ (c) $15:8$ (d) $4:5$

Answer

(b) $8:15$

Make $x$ equal in both ratios: LCM of 3 and 2 is 6, so $x:y = 6:8$ and $x:z = 6:15$ .

Hence $y:z = 8:15$ .

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2026 Set B · 1 mark

The H.C.F. of $x^3-64$ and $x^2-16$ is: (a) $x-4$ (b) $x+4$ (c) $x^2+4x+16$ (d) $(x-4)^2$

Answer

(a) $x-4$

$x^3-64 = (x-4)(x^2+4x+16)$ and $x^2-16 = (x-4)(x+4)$ .

The common factor is $x-4$ , so the H.C.F. is $x-4$ .

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2026 Set B · 1 mark

If $x^2+\frac{1}{x^2}=14$ , what is the positive value of $x-\frac{1}{x}$ ? (a) $3$ (b) $4$ (c) $5$ (d) $16$

Answer

(a) $3$ (nearest option)

$\left(x-\frac{1}{x}\right)^2 = x^2+\frac{1}{x^2}-2 = 14-2 = 12$

So $x-\frac{1}{x} = \sqrt{12} = 2\sqrt{3} \approx 3.46$ . This is not exactly any of the listed options, and $3$ is the closest. (For $x^2+\frac{1}{x^2}=11$ the value would be exactly $3$ .)

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2026 Set B · 1 mark

If the radius of a circle is doubled, the ratio of the new area to the original area is: (a) $2:1$ (b) $4:1$ (c) $1:2$ (d) $8:1$

Answer

(b) $4:1$

Original area $=\pi r^2$ ; new area $=\pi(2r)^2 = 4\pi r^2$ . Ratio $= 4\pi r^2 : \pi r^2 = 4:1$ .

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2026 Set B · 1 mark

What is the total surface area of a cubical tank if its volume is $216\ m^3$ ? (a) $216\ m^2$ (b) $144\ m^2$ (c) $36\ m^2$ (d) $180\ m^2$

Answer

(a) $216\ m^2$

$a^3 = 216 \Rightarrow a = 6$ m.

$\text{TSA} = 6a^2 = 6 \times 36 = 216\ m^2$

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2026 Set B · 1 mark

If $\bar{X}=45$ , $N=20$ , then the value of $\sum fx$ is (a) $450$ (b) $900$ (c) $1000$ (d) $90$

Answer

(b) $900$

$\bar{X} = \frac{\sum fx}{N} \Rightarrow \sum fx = \bar{X}\times N = 45 \times 20 = 900$

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2026 Set B · 1 mark

From a normal pack of 52 cards, the probability of getting a red queen is: (a) $\frac{1}{13}$ (b) $\frac{1}{26}$ (c) $\frac{1}{52}$ (d) $\frac14$

Answer

(b) $\frac{1}{26}$

There are 2 red queens (hearts and diamonds) in 52 cards, so

$P = \frac{2}{52} = \frac{1}{26}$

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Questions from National School of Sciences, Faculty of Management, Entrance Model Question Set A (College-published model question set (30 minutes, 25 marks), 2026) and National School of Sciences, Faculty of Management, Entrance Model Question Set B (College-published model question set (30 minutes, 25 marks), 2026). Answers are written for this site; check them against your class notes.

Past questions and answers

1.The possible number of subsets for a set PPP is 16 then the set PPP is (a) P={a,b}P=\{a,b\}P={a,b} (b) P={a,b,c}P=\{a,b,c\}P={a,b,c} (c) P={a,b,c,d}P=\{a,b,c,d\}P={a,b,c,d} (d) P={a,b,c,d,e}P=\{a,b,c,d,e\}P={a,b,c,d,e}

2.What is the simple interest earned on Rs.4000 at the rate of 10% yearly for 18 months? (a) Rs.300 (b) Rs.400 (c) Rs.500 (d) Rs.600

3.If lines represented by the homogeneous equation 3x2−5xy−by2=03x^2-5xy-by^2=03x2−5xy−by2=0 are orthogonal then (a) b=3b=3b=3 (b) b=15b=15b=15 (c) b=−3b=-3b=−3 (d) b=−2512b=-\frac{25}{12}b=−1225​

4.If the possible number of subsets for a set RRR is 64, then the number of elements in set RRR is: (a) 444 (b) 555 (c) 666 (d) 888

5.What is the simple interest earned on Rs. 12,000 at the rate of 8% yearly for 9 months? (a) Rs. 960 (b) Rs. 720 (c) Rs. 840 (d) Rs. 600

6.If lines represented by the homogeneous equation kx2+4xy−5y2=0kx^2+4xy-5y^2=0kx2+4xy−5y2=0 are orthogonal, then: (a) k=4k=4k=4 (b) k=5k=5k=5 (c) k=−5k=-5k=−5 (d) k=0k=0k=0

7.If a:b=2:5a:b=2:5a:b=2:5 and a:c=1:4a:c=1:4a:c=1:4. Then b:c=b:c=b:c= ? (a) 1:101:101:10 (b) 5:85:85:8 (c) 1:51:51:5 (d) 1:21:21:2

8.The H.C.F. of a3−1a^3-1a3−1 and a4+a2+1a^4+a^2+1a4+a2+1 is (a) a+1a+1a+1 (b) a−1a-1a−1 (c) a2−a+1a^2-a+1a2−a+1 (d) a2+a+1a^2+a+1a2+a+1

9.If x2+1x2=18x^2+\frac{1}{x^2}=18x2+x21​=18, what is the value of x−1xx-\frac{1}{x}x−x1​? (a) 444 (b) ±4\pm4±4 (c) 222 (d) ±2\pm2±2

10.What is the ratio of circumference to diameter of the circle? (a) π:1\pi:1π:1 (b) 2π:12\pi:12π:1 (c) π:2\pi:2π:2 (d) 2:π2:\pi2:π

11.What is the total surface area of a cubical tank of length of side 10 m? (a) 600 m2600\ m^2600 m2 (b) 500 m2500\ m^2500 m2 (c) 400 m2400\ m^2400 m2 (d) 300 m2300\ m^2300 m2

12.If Xˉ=150\bar{X}=150Xˉ=150, N=10N=10N=10, then the value of ∑fx\sum fx∑fx is (a) 242424 (b) 600600600 (c) 120012001200 (d) 150015001500

13.From the normal pack of 52 cards, a card is drawn at random, the probability of getting a king is... (a) 14\frac1441​ (b) 126\frac{1}{26}261​ (c) 113\frac{1}{13}131​ (d) 12\frac1221​

14.If x:y=3:4x:y=3:4x:y=3:4 and x:z=2:5x:z=2:5x:z=2:5. Then y:z=y:z=y:z= ? (a) 3:103:103:10 (b) 8:158:158:15 (c) 15:815:815:8 (d) 4:54:54:5

15.The H.C.F. of x3−64x^3-64x3−64 and x2−16x^2-16x2−16 is: (a) x−4x-4x−4 (b) x+4x+4x+4 (c) x2+4x+16x^2+4x+16x2+4x+16 (d) (x−4)2(x-4)^2(x−4)2

16.If x2+1x2=14x^2+\frac{1}{x^2}=14x2+x21​=14, what is the positive value of x−1xx-\frac{1}{x}x−x1​? (a) 333 (b) 444 (c) 555 (d) 161616

17.If the radius of a circle is doubled, the ratio of the new area to the original area is: (a) 2:12:12:1 (b) 4:14:14:1 (c) 1:21:21:2 (d) 8:18:18:1

18.What is the total surface area of a cubical tank if its volume is 216 m3216\ m^3216 m3? (a) 216 m2216\ m^2216 m2 (b) 144 m2144\ m^2144 m2 (c) 36 m236\ m^236 m2 (d) 180 m2180\ m^2180 m2

19.If Xˉ=45\bar{X}=45Xˉ=45, N=20N=20N=20, then the value of ∑fx\sum fx∑fx is (a) 450450450 (b) 900900900 (c) 100010001000 (d) 909090

20.From a normal pack of 52 cards, the probability of getting a red queen is: (a) 113\frac{1}{13}131​ (b) 126\frac{1}{26}261​ (c) 152\frac{1}{52}521​ (d) 14\frac1441​

The possible number of subsets for a set $P$ is 16 then the set $P$ is (a) $P=\{a,b\}$ (b) $P=\{a,b,c\}$ (c) $P=\{a,b,c,d\}$ (d) $P=\{a,b,c,d,e\}$

What is the simple interest earned on Rs.4000 at the rate of 10% yearly for 18 months? (a) Rs.300 (b) Rs.400 (c) Rs.500 (d) Rs.600

If lines represented by the homogeneous equation $3x^2-5xy-by^2=0$ are orthogonal then (a) $b=3$ (b) $b=15$ (c) $b=-3$ (d) $b=-\frac{25}{12}$

If the possible number of subsets for a set $R$ is 64, then the number of elements in set $R$ is: (a) $4$ (b) $5$ (c) $6$ (d) $8$

What is the simple interest earned on Rs. 12,000 at the rate of 8% yearly for 9 months? (a) Rs. 960 (b) Rs. 720 (c) Rs. 840 (d) Rs. 600

If lines represented by the homogeneous equation $kx^2+4xy-5y^2=0$ are orthogonal, then: (a) $k=4$ (b) $k=5$ (c) $k=-5$ (d) $k=0$

If $a:b=2:5$ and $a:c=1:4$ . Then $b:c=$ ? (a) $1:10$ (b) $5:8$ (c) $1:5$ (d) $1:2$

The H.C.F. of $a^3-1$ and $a^4+a^2+1$ is (a) $a+1$ (b) $a-1$ (c) $a^2-a+1$ (d) $a^2+a+1$

If $x^2+\frac{1}{x^2}=18$ , what is the value of $x-\frac{1}{x}$ ? (a) $4$ (b) $\pm4$ (c) $2$ (d) $\pm2$

What is the ratio of circumference to diameter of the circle? (a) $\pi:1$ (b) $2\pi:1$ (c) $\pi:2$ (d) $2:\pi$

What is the total surface area of a cubical tank of length of side 10 m? (a) $600\ m^2$ (b) $500\ m^2$ (c) $400\ m^2$ (d) $300\ m^2$

If $\bar{X}=150$ , $N=10$ , then the value of $\sum fx$ is (a) $24$ (b) $600$ (c) $1200$ (d) $1500$

From the normal pack of 52 cards, a card is drawn at random, the probability of getting a king is... (a) $\frac14$ (b) $\frac{1}{26}$ (c) $\frac{1}{13}$ (d) $\frac12$

If $x:y=3:4$ and $x:z=2:5$ . Then $y:z=$ ? (a) $3:10$ (b) $8:15$ (c) $15:8$ (d) $4:5$

The H.C.F. of $x^3-64$ and $x^2-16$ is: (a) $x-4$ (b) $x+4$ (c) $x^2+4x+16$ (d) $(x-4)^2$

If $x^2+\frac{1}{x^2}=14$ , what is the positive value of $x-\frac{1}{x}$ ? (a) $3$ (b) $4$ (c) $5$ (d) $16$

If the radius of a circle is doubled, the ratio of the new area to the original area is: (a) $2:1$ (b) $4:1$ (c) $1:2$ (d) $8:1$

What is the total surface area of a cubical tank if its volume is $216\ m^3$ ? (a) $216\ m^2$ (b) $144\ m^2$ (c) $36\ m^2$ (d) $180\ m^2$

If $\bar{X}=45$ , $N=20$ , then the value of $\sum fx$ is (a) $450$ (b) $900$ (c) $1000$ (d) $90$

From a normal pack of 52 cards, the probability of getting a red queen is: (a) $\frac{1}{13}$ (b) $\frac{1}{26}$ (c) $\frac{1}{52}$ (d) $\frac14$