32581 + Interview Questions in Mathematics

1.	The diameters of two cones are equal and their slant heights are in the ratio 5 : 4. If the curved surface area of the smaller cone is 200 cm2, then the curved surface area of the bigger cone is _________.
Answer» The diameters of two cones are equal and their slant heights are in the ratio 5 : 4. If the curved surface area of the smaller cone is 200 cm², then the curved surface area of the bigger cone is _________.

Discussion

2.	The students of a school decided to beautify the school on the annual day by fixing colourful on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 meter. The flags are stored at the position of the middle most flag. Ruchi was given the responsiblity of palcing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
Answer» The students of a school decided to beautify the school on the annual day by fixing colourful on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 meter. The flags are stored at the position of the middle most flag. Ruchi was given the responsiblity of palcing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

Discussion

3.	If A and B are two events, the probability that at least one of them occurs is (a) P(A) + P(B) – 2 P(A ∩ B) (b) P(A) + P(B) – P(A ∩ B)(c) P(A) + P(B) + P(A ∩ B) (d) P(A) + P(B) + 2P(A ∩ B)
Answer» If A and B are two events, the probability that at least one of them occurs is (a) P(A) + P(B) – 2 P(A ∩ B) (b) P(A) + P(B) – P(A ∩ B) (c) P(A) + P(B) + P(A ∩ B) (d) P(A) + P(B) + 2P(A ∩ B)

Discussion

4.	Solve for x using the quadratic formula. Write your answer correct to two significant figures: (x−1)2−3x+4=0
Answer» Solve for x using the quadratic formula. Write your answer correct to two significant figures: $(x - 1)^{2} - 3 x + 4 = 0$

4.

Solve for x using the quadratic formula. Write your answer correct to two significant figures: (x−1)2−3x+4=0

Answer»

Solve for x using the quadratic formula. Write your answer correct to two significant figures:

$(x - 1)^{2} - 3 x + 4 = 0$

Discussion

5.	Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Answer» Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.

Discussion

6.	If the total of the numbers written in each line (a row or a column) in the given square is 150, fill the empty blocks using all the numbers from 46 to 54.
Answer» If the total of the numbers written in each line (a row or a column) in the given square is 150, fill the empty blocks using all the numbers from 46 to 54.

Discussion

7.	If the slope(m) and a point (x1,y1) of a line are known, the equation of line is given by
Answer» If the slope(m) and a point (x1,y1) of a line are known, the equation of line is given by

Discussion

8.	A circle of diameter 6cm was drawn. From a point outside the circle the length of the tangent drawn to the circle was found out to be 4cm. The distance between the point and the centre of the circle is
Answer» A circle of diameter 6cm was drawn. From a point outside the circle the length of the tangent drawn to the circle was found out to be 4cm. The distance between the point and the centre of the circle is

Discussion

9.	Find the three rational numbers between 1/4 and 1/2
Answer» Find the three rational numbers between 1/4 and 1/2

Discussion

10.	{1(sec2θ−cos2θ)+1(cosec2θ−sin2θ)}(sin2θcos2θ)=1−sin2θcos2θ2+sin2θcos2θ
Answer» ${\frac{1}{(s e c^{2} θ - c o s^{2} θ)} + \frac{1}{(c o s e c^{2} θ - s i n^{2} θ)}} (s i n^{2} θ c o s^{2} θ) = \frac{1 - s i n^{2} θ c o s^{2} θ}{2 + s i n^{2} θ c o s^{2} θ}$

Discussion

11.	Find the value of x if the line passing through (x,−3) and (-5, 1) is parallel to the line joining (7, -1) and (0, 3).
Answer» Find the value of $x$ if the line passing through $(x, - 3)$ and (-5, 1) is parallel to the line joining (7, -1) and (0, 3).

Discussion

12.	Mary bought a video game as the birthday gift to Sam. Sam likes stamp collection and hence, Mary wants to cover the video game gift box with square shaped stamps, each of side 2 cm. If the gift box has length, breadth and height as 8 cm, 6 cm and 2 cm respectively, then how many stamps she has to collect so as to cover the entire gift box?
Answer» Mary bought a video game as the birthday gift to Sam. Sam likes stamp collection and hence, Mary wants to cover the video game gift box with square shaped stamps, each of side 2 cm. If the gift box has length, breadth and height as 8 cm, 6 cm and 2 cm respectively, then how many stamps she has to collect so as to cover the entire gift box?

Discussion

13.	Question 1 (i)State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:
Answer» Question 1 (i) State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

Discussion

14.	Find the sum of first five odd whole numbers
Answer» Find the sum of first five odd whole numbers

Discussion

15.	Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42 cm. [3 MARKS]
Answer» Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42 cm. [3 MARKS]

Discussion

16.	A red and blue cardboard discus of radii 4.5 cm and 2 cm are fixed to a straight string of length 10 cm; as shown in the figure. What is the radius of another disc, which touches the circular discs at P and Q.
Answer» A red and blue cardboard discus of radii 4.5 cm and 2 cm are fixed to a straight string of length 10 cm; as shown in the figure. What is the radius of another disc, which touches the circular discs at P and Q.

16.

A red and blue cardboard discus of radii 4.5 cm and 2 cm are fixed to a straight string of length 10 cm; as shown in the figure. What is the radius of another disc, which touches the circular discs at P and Q.

Answer»

A red and blue cardboard discus of radii 4.5 cm and 2 cm are fixed to a straight string of length 10 cm; as shown in the figure. What is the radius of another disc, which touches the circular discs at P and Q.

Discussion

17.	In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis ?
Answer» In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis ?

Discussion

18.	Area of the base of a right circular cylinder is 154 sq. cm and height is 10 cm. Calculate the volume of the cylinder.
Answer» Area of the base of a right circular cylinder is 154 sq. cm and height is 10 cm. Calculate the volume of the cylinder.

18.

Area of the base of a right circular cylinder is 154 sq. cm and height is 10 cm. Calculate the volume of the cylinder.

Answer»

Area of the base of a right circular cylinder is 154 sq. cm and height is 10 cm. Calculate the volume of the cylinder.

Discussion

19.	A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If, water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Answer» A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If, water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Discussion

20.	In the middle of a rectangular field measuring 30 m × 20 m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.
Answer» In the middle of a rectangular field measuring 30 m × 20 m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.

Discussion

21.	ABC and BDE are two equilateral triangles such that D is the mid point of BC.Find the areas of triangles ABC and BDE
Answer» ABC and BDE are two equilateral triangles such that D is the mid point of BC.Find the areas of triangles ABC and BDE

Discussion

22.	A ladder 15 metres long just reaches the top of a vertical wall . If the ladder makes an angle of 600 with the wall, find the height of the wall .
Answer» A ladder 15 metres long just reaches the top of a vertical wall . If the ladder makes an angle of 60⁰ with the wall, find the height of the wall .

Discussion

23.	Hanif bought one box of 50 apples for Rs 400. He sold all the apples at the rate of Rs 10 each. Was there a profit or a loss? What was its percentage?
Answer» Hanif bought one box of 50 apples for Rs 400. He sold all the apples at the rate of Rs 10 each. Was there a profit or a loss? What was its percentage?

Discussion

24.	Show that : tan²A-tan²B=sin²A-sin²B/cos²A.cos²B
Answer» Show that : tan²A-tan²B=sin²A-sin²B/cos²A.cos²B

Discussion

25.	If 18, a, b, −3 are in A.P., the a + b =(a) 19(b) 7(c) 11(d) 15
Answer» If 18, a, b, −3 are in A.P., the a + b = (a) 19 (b) 7 (c) 11 (d) 15

Discussion

26.	The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b)(a) a + b + c(b) abc(c) (a + b + c)2(d) 0
Answer» The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b) (a) a + b + c (b) abc (c) (a + b + c)² (d) 0

Discussion

27.	Incircle touches the __ of a polygon
Answer» Incircle touches the __ of a polygon

Discussion

28.	For the equation y = 3x - 7, if y = 0, then what is the value of x?
Answer» For the equation y = 3x - 7, if y = 0, then what is the value of x?

Discussion

29.	A circus tent is in the shape fo a cylinder surmounted by a conical top of same diameter.If their common diameter is 56 m, the height of the cylindrical part is 6m and the total height of the tent above the ground is 27m,find the area of the canvas used in making the tent.
Answer» A circus tent is in the shape fo a cylinder surmounted by a conical top of same diameter.If their common diameter is 56 m, the height of the cylindrical part is 6m and the total height of the tent above the ground is 27m,find the area of the canvas used in making the tent.

Discussion

30.	If (1-b) is a root of the quadratic equation x2+bx+(1−b)=0, then find the roots of the equation.
Answer» If (1-b) is a root of the quadratic equation $x^{2} + b x + (1 - b) = 0$ , then find the roots of the equation.

Discussion

31.	If α and β are the zeros of the quadratic polynomial p(x) = 4x2 − 5x − 1, find the value of α2β + αβ2.
Answer» If α and β are the zeros of the quadratic polynomial p(x) = 4x² − 5x − 1, find the value of α²β + αβ².

Discussion

32.	9 sec2 A − 9 tan2 A is equal to(a) 1(b) 9(c) 8(d) 0
Answer» 9 sec² A − 9 tan² A is equal to (a) 1 (b) 9 (c) 8 (d) 0

Discussion

33.	Find the sum of the first 15 multiples of 8.
Answer» Find the sum of the first 15 multiples of 8.

Discussion

34.	In the given figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC aresemicircles. [CBSE 2012]
Answer» In the given figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles. [CBSE 2012]

Discussion

35.	If the three lines y=m1x+c1,y=m2x+c2 and y=m3x+c3 are concurrent then show that, m1(c2−c3)+m2(c3−c1)+m3(c1−c2)=0
Answer» If the three lines $y = m_{1} x + c_{1}, y = m_{2} x + c_{2}$ and $y = m_{3} x + c_{3}$ are concurrent then show that, $m_{1} (c_{2} - c_{3}) + m_{2} (c_{3} - c_{1}) + m_{3} (c_{1} - c_{2}) = 0$

35.

If the three lines y=m1x+c1,y=m2x+c2 and y=m3x+c3 are concurrent then show that, m1(c2−c3)+m2(c3−c1)+m3(c1−c2)=0

Answer»

If the three lines $y = m_{1} x + c_{1}, y = m_{2} x + c_{2}$ and $y = m_{3} x + c_{3}$ are concurrent then show that,

$m_{1} (c_{2} - c_{3}) + m_{2} (c_{3} - c_{1}) + m_{3} (c_{1} - c_{2}) = 0$

Discussion

36.	Mark the correct alternatives in each of the following:The modulus of an integer x is 9, then(a) x = 9 only (b) x = −9 only (c) x = ± 9 (d) None of these
Answer» Mark the correct alternatives in each of the following: The modulus of an integer x is 9, then (a) x = 9 only (b) x = −9 only (c) x = ± 9 (d) None of these

36.

Mark the correct alternatives in each of the following:The modulus of an integer x is 9, then(a) x = 9 only (b) x = −9 only (c) x = ± 9 (d) None of these

Answer»

Mark the correct alternatives in each of the following:
The modulus of an integer x is 9, then
(a) x = 9 only

(b) x = −9 only

(c) x = ± 9

(d) None of these

Discussion

37.	Find the cardial number of the relation,R = {x:x∈N and 3≤x<7}.4
Answer» Find the cardial number of the relation, R = { $x : x \in N a n d 3 \leq x < 7$ }. 4

Discussion

38.	In right-angled triangle ABC is which ∠C = 90°, if D is the mid-point of BC, prove that AB2 = 4 AD2 − 3AC2.
Answer» In right-angled triangle ABC is which ∠C = 90°, if D is the mid-point of BC, prove that AB² = 4 AD² − 3AC².

Discussion

39.	In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.
Answer» In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.

39.

In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.

Answer»

In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.

Discussion

40.	A rectangular park 35 m long and 18 m wide to be covered with grass,leaving 2.5m uncovered all around it.Find the area to be laid with grass.
Answer» A rectangular park 35 m long and 18 m wide to be covered with grass,leaving 2.5m uncovered all around it.Find the area to be laid with grass.

Discussion

41.	Question 4 (iv) Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Answer» Question 4 (iv) Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Discussion

42.	In a cricket match of India and Pakistan, what is the probability that India would win the toss?
Answer» In a cricket match of India and Pakistan, what is the probability that India would win the toss?

Discussion

43.	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

44.	find the value of K if the quadratic equation ;(K-2)x^2+2(2 k-3)x+(5 K-6)=0
Answer» find the value of K if the quadratic equation ;(K-2)x^2+2(2 k-3)x+(5 K-6)=0

Discussion

45.	In the given figure, circle with centre M touches the circle with centre N at point T. Radius RM touches the smaller circle at S. Radii of circles are 9 cm and 2.5 cm. Find the answers to the following questions hence find the ratio MS:SR.(1) Find the length of segment MT(2) Find the length of seg MN(3) Find the measure of ∠NSM.
Answer» In the given figure, circle with centre M touches the circle with centre N at point T. Radius RM touches the smaller circle at S. Radii of circles are 9 cm and 2.5 cm. Find the answers to the following questions hence find the ratio MS:SR. (1) Find the length of segment MT (2) Find the length of seg MN (3) Find the measure of ∠NSM.

Discussion

46.	For a pair of equations that are consistent in nature, the lines are ________.
Answer» For a pair of equations that are consistent in nature, the lines are ________.

Discussion

47.	Which of the following pairs of sets are disjoint?(i) {1,2,3,4} and {x:x is a natural number and 4≤x≤6}(ii) {a,e,i,o,u} and {c,d,e,f}(iii) {x:x is an even integer} and {x:x is an odd integer}
Answer» Which of the following pairs of sets are disjoint? $(i) {1, 2, 3, 4} and {x : x is a natural number and 4 \leq x \leq 6}$ $(i i) {a, e, i, o, u} and {c, d, e, f}$ $(i i i) {x : x is an even integer} and {x : x is an odd integer}$

Discussion

48.	Solve each of the following systems of equations by the method of cross-multiplication: a2x−b2y=0 a2bx+b2ay=a+b,x,y≠0
Answer» Solve each of the following systems of equations by the method of cross-multiplication: $\frac{a^{2}}{x} - \frac{b^{2}}{y} = 0$ $\frac{a^{2} b}{x} + \frac{b^{2} a}{y} = a + b, x, y \neq 0$

48.

Solve each of the following systems of equations by the method of cross-multiplication: a2x−b2y=0 a2bx+b2ay=a+b,x,y≠0

Answer»

Solve each of the following systems of equations by the method of cross-multiplication:

$\frac{a^{2}}{x} - \frac{b^{2}}{y} = 0$

$\frac{a^{2} b}{x} + \frac{b^{2} a}{y} = a + b, x, y \neq 0$

Discussion

49.	Question 15 (ii)Five cards – ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?
Answer» Question 15 (ii) Five cards – ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

Discussion

50.	Nikhil expressed the quadratic equation x2+10x+16=0 in the form x2+px+qx+16=0 such that the product of p and q is 16. Choose the correct values of p and q.
Answer» Nikhil expressed the quadratic equation $x^{2} + 10 x + 16 = 0$ in the form $x^{2} + p x + q x + 16 = 0$ such that the product of $p$ and $q$ is $16.$ Choose the correct values of $p$ and $q .$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The diameters of two cones are equal and their slant heights are in the ratio 5 : 4. If the curved surface area of the smaller cone is 200 cm2, then the curved surface area of the bigger cone is _________.

If A and B are two events, the probability that at least one of them occurs is (a) P(A) + P(B) – 2 P(A ∩ B) (b) P(A) + P(B) – P(A ∩ B)(c) P(A) + P(B) + P(A ∩ B) (d) P(A) + P(B) + 2P(A ∩ B)

Solve for x using the quadratic formula. Write your answer correct to two significant figures: (x−1)2−3x+4=0

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.

If the total of the numbers written in each line (a row or a column) in the given square is 150, fill the empty blocks using all the numbers from 46 to 54.

If the slope(m) and a point (x1,y1) of a line are known, the equation of line is given by

A circle of diameter 6cm was drawn. From a point outside the circle the length of the tangent drawn to the circle was found out to be 4cm. The distance between the point and the centre of the circle is

Find the three rational numbers between 1/4 and 1/2

{1(sec2θ−cos2θ)+1(cosec2θ−sin2θ)}(sin2θcos2θ)=1−sin2θcos2θ2+sin2θcos2θ

Find the value of x if the line passing through (x,−3) and (-5, 1) is parallel to the line joining (7, -1) and (0, 3).

Question 1 (i)State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

Find the sum of first five odd whole numbers

Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42 cm. [3 MARKS]

A red and blue cardboard discus of radii 4.5 cm and 2 cm are fixed to a straight string of length 10 cm; as shown in the figure. What is the radius of another disc, which touches the circular discs at P and Q.

In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis ?

Area of the base of a right circular cylinder is 154 sq. cm and height is 10 cm. Calculate the volume of the cylinder.

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If, water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

In the middle of a rectangular field measuring 30 m × 20 m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.

ABC and BDE are two equilateral triangles such that D is the mid point of BC.Find the areas of triangles ABC and BDE

A ladder 15 metres long just reaches the top of a vertical wall . If the ladder makes an angle of 600 with the wall, find the height of the wall .

Hanif bought one box of 50 apples for Rs 400. He sold all the apples at the rate of Rs 10 each. Was there a profit or a loss? What was its percentage?

Show that : tan²A-tan²B=sin²A-sin²B/cos²A.cos²B

If 18, a, b, −3 are in A.P., the a + b =(a) 19(b) 7(c) 11(d) 15

The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b)(a) a + b + c(b) abc(c) (a + b + c)2(d) 0

Incircle touches the __ of a polygon

For the equation y = 3x - 7, if y = 0, then what is the value of x?

A circus tent is in the shape fo a cylinder surmounted by a conical top of same diameter.If their common diameter is 56 m, the height of the cylindrical part is 6m and the total height of the tent above the ground is 27m,find the area of the canvas used in making the tent.

If (1-b) is a root of the quadratic equation x2+bx+(1−b)=0, then find the roots of the equation.

If α and β are the zeros of the quadratic polynomial p(x) = 4x2 − 5x − 1, find the value of α2β + αβ2.

9 sec2 A − 9 tan2 A is equal to(a) 1(b) 9(c) 8(d) 0

Find the sum of the first 15 multiples of 8.

In the given figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC aresemicircles. [CBSE 2012]

If the three lines y=m1x+c1,y=m2x+c2 and y=m3x+c3 are concurrent then show that, m1(c2−c3)+m2(c3−c1)+m3(c1−c2)=0

Mark the correct alternatives in each of the following:The modulus of an integer x is 9, then(a) x = 9 only (b) x = −9 only (c) x = ± 9 (d) None of these

Find the cardial number of the relation,R = {x:x∈N and 3≤x&lt;7}.4

In right-angled triangle ABC is which ∠C = 90°, if D is the mid-point of BC, prove that AB2 = 4 AD2 − 3AC2.

In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.

A rectangular park 35 m long and 18 m wide to be covered with grass,leaving 2.5m uncovered all around it.Find the area to be laid with grass.

In a cricket match of India and Pakistan, what is the probability that India would win the toss?

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

find the value of K if the quadratic equation ;(K-2)x^2+2(2 k-3)x+(5 K-6)=0

For a pair of equations that are consistent in nature, the lines are ________.

Which of the following pairs of sets are disjoint?(i) {1,2,3,4} and {x:x is a natural number and 4≤x≤6}(ii) {a,e,i,o,u} and {c,d,e,f}(iii) {x:x is an even integer} and {x:x is an odd integer}

Solve each of the following systems of equations by the method of cross-multiplication: a2x−b2y=0 a2bx+b2ay=a+b,x,y≠0

Question 15 (ii)Five cards – ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

Nikhil expressed the quadratic equation x2+10x+16=0 in the form x2+px+qx+16=0 such that the product of p and q is 16. Choose the correct values of p and q.

Find the cardial number of the relation,R = {x:x∈N and 3≤x<7}.4