32581 + Interview Questions in Mathematics

1.	A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find the length and breadth of the rectangular park.
Answer» A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find the length and breadth of the rectangular park.

Discussion

2.	A chord AB of a circle is equal to the radius of the circle. The angle subtended by the chord at a point on the major arc and minor arc are respectively _____.
Answer» A chord AB of a circle is equal to the radius of the circle. The angle subtended by the chord at a point on the major arc and minor arc are respectively _____.

Discussion

3.	Find the common difference of the given AP: 34,1,114.........
Answer» Find the common difference of the given AP: $\frac{3}{4}, 1, 1 \frac{1}{4}$ .........

Discussion

4.	Question 3 If tan (A + B) = √3 and tan (A - B) = 1√3; 0∘<A+B≤90∘;A>B, find A and B.
Answer» Question 3 If tan (A + B) = $\sqrt{3}$ and tan (A - B) = $\frac{1}{\sqrt{3}}$ ; $0^{\circ} < A + B \leq 90^{\circ}; A > B$ , find A and B.

Discussion

5.	Which term of the GP 1, 2, 4, 8,.... is 512?
Answer» Which term of the GP 1, 2, 4, 8,.... is 512?

Discussion

6.	A restaurant POQR is being constructed in the middle of a circular lake. The circle, which has its center at O is touching the mid-points of the boundary ABCD as shown in the figure. AB=CD and AD=BC. If BC=8 cm, then the area of AQOP is
Answer» A restaurant POQR is being constructed in the middle of a circular lake. The circle, which has its center at O is touching the mid-points of the boundary ABCD as shown in the figure. AB=CD and AD=BC. If BC=8 cm, then the area of AQOP is

Discussion

7.	Which of the following is incorrect?
Answer» Which of the following is incorrect?

Discussion

8.	Question 2 (i) On comparing the ratios a1a2 , b1b2 and c1c2 , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident. 5x - 4y + 8 = 0 7x + 6y - 9 = 0
Answer» Question 2 (i) On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident. 5x - 4y + 8 = 0 7x + 6y - 9 = 0

Discussion

9.	D,E,F are the mid- point of the sides BC , CA and AB respectively of a Δ Determine the ratio of the areas of ΔDEF and ΔABC. [3 MARKS]
Answer» D,E,F are the mid- point of the sides BC , CA and AB respectively of a $Δ$ Determine the ratio of the areas of $Δ D E F$ and $Δ A B C$ . [3 MARKS]

Discussion

10.	The cost of fencing a circular field at the rate of Rs 25 permetre is Rs 5500. The field is to be ploughed at the rate of 50 paise per m^2. Find the cost of ploughin the field. [Take π = \frac{22}{7}]
Answer» The cost of fencing a circular field at the rate of Rs 25 permetre is Rs 5500. The field is to be ploughed at the rate of 50 paise per m^2. Find the cost of ploughin the field. [Take $π$ = \frac{22}{7}]

Discussion

11.	Solve the following quadratic equation by factorization. 5+x5−x−5−x5+x=334;x≠5,−5
Answer» Solve the following quadratic equation by factorization. $\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3 \frac{3}{4}; x \neq 5, - 5$

Discussion

12.	The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall, to what height does its tip reach?
Answer» The foot of a ladder is $6 m$ away from a wall and its top reaches a window $8 m$ above the ground. If the ladder is shifted in such a way that its foot is $8 m$ away from the wall, to what height does its tip reach?

Discussion

13.	Question 20 The Picture interprets (a) 14÷3 (b) 3×14 (c) 34×3 (d) 3÷14
Answer» Question 20 The Picture interprets (a) $\frac{1}{4} \div 3$ (b) $3 \times \frac{1}{4}$ (c) $\frac{3}{4} \times 3$ (d) $3 \div \frac{1}{4}$

13.

Question 20 The Picture interprets (a) 14÷3 (b) 3×14 (c) 34×3 (d) 3÷14

Answer»

Question 20

The Picture

interprets

(a) $\frac{1}{4} \div 3$
(b) $3 \times \frac{1}{4}$
(c) $\frac{3}{4} \times 3$
(d) $3 \div \frac{1}{4}$

Discussion

14.	The difference of two natural numbers is 3 and the difference of their reciprocals is 328
Answer» The difference of two natural numbers is 3 and the difference of their reciprocals is $\frac{3}{28}$

Discussion

15.	In the centre of a rectangular lawn of dimensions 50m×40m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184m2. Find the length and breadth of the pond.
Answer» In the centre of a rectangular lawn of dimensions $50 m \times 40 m,$ a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be $1184 m^{2} .$ Find the length and breadth of the pond.

Discussion

16.	In Fig. 8.64, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at M. Prove that PL+LM=PN+MN.
Answer» In Fig. 8.64, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at M. Prove that PL+LM=PN+MN.

16.

In Fig. 8.64, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at M. Prove that PL+LM=PN+MN.

Answer»

In Fig. 8.64, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at M. Prove that PL+LM=PN+MN.

Discussion

17.	Write the median clas of the following distribution: Class0−1010−2020−3030−4040−5050−6060−70Frequency448101284
Answer» Write the median clas of the following distribution: $\begin{matrix} C l a s s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 F r e q u e n c y & 4 & 4 & 8 & 10 & 12 & 8 & 4 \end{matrix}$

17.

Write the median clas of the following distribution: Class0−1010−2020−3030−4040−5050−6060−70Frequency448101284

Answer»

Write the median clas of the following distribution:

$\begin{matrix} C l a s s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 F r e q u e n c y & 4 & 4 & 8 & 10 & 12 & 8 & 4 \end{matrix}$

Discussion

18.	A farmer has 70 m of fencing, with which he encloses three sides of a rectangular sheep pen; the fourth side being a wall. If the area of the pen is 600 sq. m, find the length of its shorter side.
Answer» A farmer has 70 m of fencing, with which he encloses three sides of a rectangular sheep pen; the fourth side being a wall. If the area of the pen is 600 sq. m, find the length of its shorter side.

Discussion

19.	One of the two digit number is three times the other digit.When we interchange the digits of this two digit number and add the result ing number to the original number,you get 88.What is the original number
Answer» One of the two digit number is three times the other digit.When we interchange the digits of this two digit number and add the result ing number to the original number,you get 88.What is the original number

Discussion

20.	Find the area of the region bounded by y=√x and y=x.
Answer» Find the area of the region bounded by $y = \sqrt{x} a n d y = x .$

Discussion

21.	Let A=[1234] and B=[abcd] are two matrices such that AB = BA and c≠0, then value of a−d3b−c is :
Answer» Let $A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$ and $B = [\begin{matrix} a & b c & d \end{matrix}]$ are two matrices such that AB = BA and $c \neq 0$ , then value of $\frac{a - d}{3 b - c}$ is :

Discussion

22.	Solve the following pair of linear equations. (a−b)x+(a+b)y=a2−2ab−b2 (a+b)(x+y)=a2+b2
Answer» Solve the following pair of linear equations. (a−b)x+(a+b)y=a²−2ab−b² (a+b)(x+y)=a²+b²

22.

Solve the following pair of linear equations. (a−b)x+(a+b)y=a2−2ab−b2 (a+b)(x+y)=a2+b2

Answer»

Solve the following pair of linear equations.
(a−b)x+(a+b)y=a²−2ab−b²

(a+b)(x+y)=a²+b²

Discussion

23.	In the given figure: ∠A+∠B+∠C+∠D+∠E is equal to:
Answer» In the given figure: $∠ A + ∠ B + ∠ C + ∠ D + ∠ E$ is equal to:

23.

In the given figure: ∠A+∠B+∠C+∠D+∠E is equal to:

Answer»

In the given figure: $∠ A + ∠ B + ∠ C + ∠ D + ∠ E$ is equal to:

Discussion

24.	If the sum of the first n terms of an AP is 4n-n², what is the first term (S1)? What is the second term?
Answer» If the sum of the first n terms of an AP is 4n-n², what is the first term (S₁)? What is the second term?

Discussion

25.	A shopkeeper buys a camera at a discount of 20% from a wholesaler. The printed price of the camera is Rs. 1600 and the rate of sales tax is 6%. The shopkeeper sells it to a buyer at the printed price and charges tax at the same rate. Find: (i) The price paid by the shopkeeper. (ii) The VAT (Value Added Tax) paid by the shopkeeper.
Answer» A shopkeeper buys a camera at a discount of 20% from a wholesaler. The printed price of the camera is Rs. 1600 and the rate of sales tax is 6%. The shopkeeper sells it to a buyer at the printed price and charges tax at the same rate. Find: (i) The price paid by the shopkeeper. (ii) The VAT (Value Added Tax) paid by the shopkeeper.

25.

A shopkeeper buys a camera at a discount of 20% from a wholesaler. The printed price of the camera is Rs. 1600 and the rate of sales tax is 6%. The shopkeeper sells it to a buyer at the printed price and charges tax at the same rate. Find: (i) The price paid by the shopkeeper. (ii) The VAT (Value Added Tax) paid by the shopkeeper.

Answer»

A shopkeeper buys a camera at a discount of 20% from a wholesaler. The printed price of the camera is Rs. 1600 and the rate of sales tax is 6%. The shopkeeper sells it to a buyer at the printed price and charges tax at the same rate. Find:

(i) The price paid by the shopkeeper.

(ii) The VAT (Value Added Tax) paid by the shopkeeper.

Discussion

26.	Seven times a two digit number is equal to four times the number obtained by reversing the order of the digit. If the sum of the digit is 9, fin the number
Answer» Seven times a two digit number is equal to four times the number obtained by reversing the order of the digit. If the sum of the digit is 9, fin the number

Discussion

27.	If the secant AB and a tangent at the point T of a circle intersect at a point P otside the circle then, PA×PB=.
Answer» If the secant AB and a tangent at the point T of a circle intersect at a point P otside the circle then, $P A \times P B =$ .

Discussion

28.	Find the HCF of the positive integers 180, 252 and 324 with the help of division algorithm.
Answer» Find the HCF of the positive integers 180, 252 and 324 with the help of division algorithm.

Discussion

29.	Banks provide a high rate of interest on which one of the following accounts?
Answer» Banks provide a high rate of interest on which one of the following accounts?

Discussion

30.	the difference of the square of two number is 180 the square of the smaller number is 8 times the larger number find the two numbers
Answer» the difference of the square of two number is 180 the square of the smaller number is 8 times the larger number find the two numbers

Discussion

31.	from a rectangular sheet of paper abcd with ab=40 and ad = 28 a semi circle prtion with bc as diameter is cut of . fint the area of remaining part
Answer» from a rectangular sheet of paper abcd with ab=40 and ad = 28 a semi circle prtion with bc as diameter is cut of . fint the area of remaining part

Discussion

32.	If A+B=[242353],A−B=[000−1−31], then find A and B
Answer» If A+B= $[\begin{matrix} 2 & 4 & 2 3 & 5 & 3 \end{matrix}], A - B = [\begin{matrix} 0 & 0 & 0 - 1 & - 3 & 1 \end{matrix}]$ , then find A and B

Discussion

33.	In the given figure, ABC is a triangle, DE is parallel to BC and ADDB=32 (i) Determine the ratios ADAB and DEBC. (ii) Prove that ΔDEF is similar to ΔCBF Hence, find EFFB. (iii) What is the ratio of the areas of ΔDFEandΔBFC? [4 MARKS]
Answer» In the given figure, ABC is a triangle, DE is parallel to BC and $\frac{A D}{D B} = \frac{3}{2}$ (i) Determine the ratios $\frac{A D}{A B} a n d \frac{D E}{B C} .$ (ii) Prove that $Δ D E F$ is similar to $Δ C B F$ Hence, find $\frac{E F}{F B}$ . (iii) What is the ratio of the areas of $Δ D F E a n d Δ B F C$ ? [4 MARKS]

Discussion

34.	3x^2+11x+6=0
Answer» 3x^2+11x+6=0

Discussion

35.	When the polynomial f(x) = 4x3 + 8x2 + 8x + 7 is divided by the polynomial g(x) = 2x2 - x + 1, the quotient and the remainder are
Answer» When the polynomial f(x) = 4x³ + 8x² + 8x + 7 is divided by the polynomial g(x) = 2x² - x + 1, the quotient and the remainder are

Discussion

36.	Complete the sentence. Indirect Mirabelle screamed that her purse was missing. Robert calmly asked her if she checked under the table. Direct Mirabelle: (a)______________________ Robert: (b) ______________________
Answer» Complete the sentence. Indirect Mirabelle screamed that her purse was missing. Robert calmly asked her if she checked under the table. Direct Mirabelle: (a)______________________ Robert: (b) ______________________

36.

Complete the sentence. Indirect Mirabelle screamed that her purse was missing. Robert calmly asked her if she checked under the table. Direct Mirabelle: (a) Robert: (b)

Answer»

Complete the sentence.

Indirect

Mirabelle screamed that her purse was missing. Robert calmly asked her if she checked under the table.

Direct

Mirabelle: (a)______________________

Robert: (b) ______________________

Discussion

37.	Number of tangents, that can be drawn to a circle, parallel to a given chord is
Answer» Number of tangents, that can be drawn to a circle, parallel to a given chord is

Discussion

38.	A tower stands vertically on the ground from a point on the ground which is 25 m away from the foot of tower if the height of tower is 25√5 metres find the angle of elevation.
Answer» A tower stands vertically on the ground from a point on the ground which is 25 m away from the foot of tower if the height of tower is 25√5 metres find the angle of elevation.

Discussion

39.	If cosec A = √10, then tan A is
Answer» If cosec A = √10, then tan A is

Discussion

40.	In the following, determine whether the given quadratic equation has real roots and if so, find the roots. [3 MARKS] 6x2+x−2=0
Answer» In the following, determine whether the given quadratic equation has real roots and if so, find the roots. [3 MARKS] $6 x^{2} + x - 2 = 0$

Discussion

41.	If the roots of 3mx2 - 2mx + (m - 2) = 0 are equal, then the value of 'm' will be
Answer» If the roots of 3mx² - 2mx + (m - 2) = 0 are equal, then the value of 'm' will be

Discussion

42.	In ∆ABC, AD is bisector of ∠A and AD meets BC at D. If AB = 5cm, BD = 2cm, CD = 3cm. Then AC is equal to.
Answer» In ∆ABC, AD is bisector of ∠A and AD meets BC at D. If AB = 5cm, BD = 2cm, CD = 3cm. Then AC is equal to.

Discussion

43.	If H and h be the heights of two cylinders, then the ratio of curved surface areas of two cylinders with equal radii is
Answer» If H and h be the heights of two cylinders, then the ratio of curved surface areas of two cylinders with equal radii is

Discussion

44.	Write the condition, when given quadratic equation has real and distinct roots
Answer» Write the condition, when given quadratic equation has real and distinct roots

Discussion

45.	Which is the adjacent side to the angle θ?
Answer» Which is the adjacent side to the angle $θ$ ?

45.

Which is the adjacent side to the angle θ?

Answer»

Which is the adjacent side to the angle $θ$ ?

Discussion

46.	Find the value of and , if ( – 2) & ( + 3) are both factors of the expression 3 + 2 + – 12.
Answer» Find the value of and , if ( – 2) & ( + 3) are both factors of the expression ³ + ² + – 12.

46.

Find the value of and , if ( – 2) & ( + 3) are both factors of the expression 3 + 2 + – 12.

Answer»

Find the value of and , if ( – 2) & ( + 3) are both factors of the expression

³ + ² + – 12.

Discussion

47.	In the method to find the roots of the quadratic equation 3x2- 2√6 x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The values of a and d are
Answer» In the method to find the roots of the quadratic equation 3 $x^{2}$ - 2 $\sqrt{6}$ x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The values of a and d are

Discussion

48.	In the figure, PM is a tangent to the circle and PA = AM. Find PA.PB = ?
Answer» In the figure, PM is a tangent to the circle and PA = AM. Find PA.PB = ?

48.

In the figure, PM is a tangent to the circle and PA = AM. Find PA.PB = ?

Answer»

In the figure, PM is a tangent to the circle and PA = AM. Find PA.PB = ?

Discussion

49.	In a factory 56% of the workers like oranges and 69% likes apples. Then the maximum percentage of people who can like both is ___ .
Answer» In a factory 56% of the workers like oranges and 69% likes apples. Then the maximum percentage of people who can like both is ___ .

Discussion

50.	Let S1,S2,S3−−−−−−−−Sn denotes the sum of 1, 2, 3 ----n terms of an A.P, having first term a. If SkxSx k ≠ 1, is independent of x, then S1+S2+S3−−−−−−−−Sn =
Answer» Let $S_{1}, S_{2}, S_{3} - - - - - - - - S_{n}$ denotes the sum of 1, 2, 3 ----n terms of an A.P, having first term a. If $\frac{S_{k x}}{S_{x}}$ k $\neq$ 1, is independent of x, then $S_{1} + S_{2} + S_{3} - - - - - - - - S_{n}$ =

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A chord AB of a circle is equal to the radius of the circle. The angle subtended by the chord at a point on the major arc and minor arc are respectively _____.

Find the common difference of the given AP: 34,1,114.........

Question 3 If tan (A + B) = √3 and tan (A - B) = 1√3; 0∘&lt;A+B≤90∘;A&gt;B, find A and B.

Which term of the GP 1, 2, 4, 8,.... is 512?

A restaurant POQR is being constructed in the middle of a circular lake. The circle, which has its center at O is touching the mid-points of the boundary ABCD as shown in the figure. AB=CD and AD=BC. If BC=8 cm, then the area of AQOP is

Which of the following is incorrect?

Question 2 (i) On comparing the ratios a1a2 , b1b2 and c1c2 , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident. 5x - 4y + 8 = 0 7x + 6y - 9 = 0

D,E,F are the mid- point of the sides BC , CA and AB respectively of a Δ Determine the ratio of the areas of ΔDEF and ΔABC. [3 MARKS]

The cost of fencing a circular field at the rate of Rs 25 permetre is Rs 5500. The field is to be ploughed at the rate of 50 paise per m^2. Find the cost of ploughin the field. [Take π = \frac{22}{7}]

Solve the following quadratic equation by factorization. 5+x5−x−5−x5+x=334;x≠5,−5

The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall, to what height does its tip reach?

Question 20 The Picture interprets (a) 14÷3 (b) 3×14 (c) 34×3 (d) 3÷14

The difference of two natural numbers is 3 and the difference of their reciprocals is 328

In the centre of a rectangular lawn of dimensions 50m×40m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184m2. Find the length and breadth of the pond.

In Fig. 8.64, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at M. Prove that PL+LM=PN+MN.

Write the median clas of the following distribution: Class0−1010−2020−3030−4040−5050−6060−70Frequency448101284

A farmer has 70 m of fencing, with which he encloses three sides of a rectangular sheep pen; the fourth side being a wall. If the area of the pen is 600 sq. m, find the length of its shorter side.

One of the two digit number is three times the other digit.When we interchange the digits of this two digit number and add the result ing number to the original number,you get 88.What is the original number

Find the area of the region bounded by y=√x and y=x.

Let A=[1234] and B=[abcd] are two matrices such that AB = BA and c≠0, then value of a−d3b−c is :

Solve the following pair of linear equations. (a−b)x+(a+b)y=a2−2ab−b2 (a+b)(x+y)=a2+b2

In the given figure: ∠A+∠B+∠C+∠D+∠E is equal to:

If the sum of the first n terms of an AP is 4n-n², what is the first term (S​​​​​​1​​​​​)? What is the second term?

Seven times a two digit number is equal to four times the number obtained by reversing the order of the digit. If the sum of the digit is 9, fin the number

If the secant AB and a tangent at the point T of a circle intersect at a point P otside the circle then, PA×PB=.

Find the HCF of the positive integers 180, 252 and 324 with the help of division algorithm.

Banks provide a high rate of interest on which one of the following accounts?

the difference of the square of two number is 180 the square of the smaller number is 8 times the larger number find the two numbers

from a rectangular sheet of paper abcd with ab=40 and ad = 28 a semi circle prtion with bc as diameter is cut of . fint the area of remaining part

If A+B=[242353],A−B=[000−1−31], then find A and B

In the given figure, ABC is a triangle, DE is parallel to BC and ADDB=32 (i) Determine the ratios ADAB and DEBC. (ii) Prove that ΔDEF is similar to ΔCBF Hence, find EFFB. (iii) What is the ratio of the areas of ΔDFEandΔBFC? [4 MARKS]

3x^2+11x+6=0

When the polynomial f(x) = 4x3 + 8x2 + 8x + 7 is divided by the polynomial g(x) = 2x2 - x + 1, the quotient and the remainder are

Complete the sentence. Indirect Mirabelle screamed that her purse was missing. Robert calmly asked her if she checked under the table. Direct Mirabelle: (a)______________________ Robert: (b) ______________________

Number of tangents, that can be drawn to a circle, parallel to a given chord is

A tower stands vertically on the ground from a point on the ground which is 25 m away from the foot of tower if the height of tower is 25√5 metres find the angle of elevation.

If cosec A = √10, then tan A is

In the following, determine whether the given quadratic equation has real roots and if so, find the roots. [3 MARKS] 6x2+x−2=0

If the roots of 3mx2 - 2mx + (m - 2) = 0 are equal, then the value of 'm' will be

In ∆ABC, AD is bisector of ∠A and AD meets BC at D. If AB = 5cm, BD = 2cm, CD = 3cm. Then AC is equal to.

If H and h be the heights of two cylinders, then the ratio of curved surface areas of two cylinders with equal radii is

Write the condition, when given quadratic equation has real and distinct roots

Which is the adjacent side to the angle θ?

Find the value of and , if ( – 2) &amp; ( + 3) are both factors of the expression 3 + 2 + – 12.

In the method to find the roots of the quadratic equation 3x2- 2√6 x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The values of a and d are

In the figure, PM is a tangent to the circle and PA = AM. Find PA.PB = ?

In a factory 56% of the workers like oranges and 69% likes apples. Then the maximum percentage of people who can like both is ___ .

Let S1,S2,S3−−−−−−−−Sn denotes the sum of 1, 2, 3 ----n terms of an A.P, having first term a. If SkxSx k ≠ 1, is independent of x, then S1+S2+S3−−−−−−−−Sn =

Question 3 If tan (A + B) = √3 and tan (A - B) = 1√3; 0∘<A+B≤90∘;A>B, find A and B.

If the sum of the first n terms of an AP is 4n-n², what is the first term (S1)? What is the second term?

Complete the sentence. Indirect Mirabelle screamed that her purse was missing. Robert calmly asked her if she checked under the table. Direct Mirabelle: (a) Robert: (b)

Find the value of and , if ( – 2) & ( + 3) are both factors of the expression 3 + 2 + – 12.