32581 + Interview Questions in Mathematics Page 91 InterviewSolution

4501.	9. At a point on a level plane a vertical Tower subtends an angle 'a' (alpha) and a pole of height 'h' meters at the top of the tower subtends an angle 'b' (beta). Show that the height of the tower is "hsin(a) cosec(b)cos(a+b)".
Answer» 9. At a point on a level plane a vertical Tower subtends an angle 'a' (alpha) and a pole of height 'h' meters at the top of the tower subtends an angle 'b' (beta). Show that the height of the tower is "hsin(a) cosec(b)cos(a+b)".

Discussion

4502.	In the XY plane two points A(2,2) and B(7,7) are taken. R is the region in the first quadrant which consists of points C such that triangle ABC is an acute angled triangle. The closest integer to the area of the region R is
Answer» In the XY plane two points A(2,2) and B(7,7) are taken. R is the region in the first quadrant which consists of points C such that triangle ABC is an acute angled triangle. The closest integer to the area of the region R is

Discussion

4503.	A man buys a product for Rs. 648 including sales tax. If the marked price is Rs. 600, then the rate of sales tax is
Answer» A man buys a product for Rs. 648 including sales tax. If the marked price is Rs. 600, then the rate of sales tax is

Discussion

4504.	Write a program to input line(s) of text from the user until enter is pressed. Count the total number of characters in the text (including white spaces), total number of alphabets, total number of digits, total number of special symbols and total number of words in the given text. (Assume that each word is separated by one space).
Answer» Write a program to input line(s) of text from the user until enter is pressed. Count the total number of characters in the text (including white spaces), total number of alphabets, total number of digits, total number of special symbols and total number of words in the given text. (Assume that each word is separated by one space).

Discussion

4505.	Q: If the bisector of two consecutive angle A and B of a quadrilateral ABCD intersect at a point O such that angle C + angle D =K⊾AOD, then find the value of K??
Answer» Q: If the bisector of two consecutive angle A and B of a quadrilateral ABCD intersect at a point O such that angle C + angle D =K⊾AOD, then find the value of K??

Discussion

4506.	Area of square ABCD with A(1,0) and B(4,0) is ___ square units.
Answer» Area of square ABCD with A(1,0) and B(4,0) is ___ square units.

Discussion

4507.	sec^6θ = †an^6θ+ 3 †an^2θ sec^2θ +
Answer» sec^6θ = †an^6θ+ 3 †an^2θ sec^2θ +

Discussion

4508.	ntIf a,b,c are distinct and p(x) is a polynomial in x; which leaves remainder on division by (x-a), (x-b), (x-c) respectively , then the remainder on division of p(x) by (x-a)(x-b)(x-c)isn ntA) x+a+b+cn ntB) a+b+cn ntC) xn ntD) None of thesen
Answer» ntIf a,b,c are distinct and p(x) is a polynomial in x; which leaves remainder on division by (x-a), (x-b), (x-c) respectively , then the remainder on division of p(x) by (x-a)(x-b)(x-c)isn ntA) x+a+b+cn ntB) a+b+cn ntC) xn ntD) None of thesen

Discussion

4509.	If R(5, 6) is the midpoint of the line segment AB joining the points A(6, 5) and B(4, y) then y equals(a) 5 (b) 7 (c) 12 (d) 6
Answer» If R(5, 6) is the midpoint of the line segment AB joining the points A(6, 5) and B(4, y) then y equals (a) 5 (b) 7 (c) 12 (d) 6

Discussion

4510.	For the following arithmetic progressions write the first term a and the common difference d:(i) −5, −1, 3, 7, ...(ii) 15,35,55,75(iii) 0.3, 0.55, 0.80, 1.05, ...(iv) −1.1, −3.1, −5.1, −7.1, ...
Answer» For the following arithmetic progressions write the first term a and the common difference d: (i) −5, −1, 3, 7, ... (ii) $\frac{1}{5}, \frac{3}{5}, \frac{5}{5}, \frac{7}{5}$ (iii) 0.3, 0.55, 0.80, 1.05, ... (iv) −1.1, −3.1, −5.1, −7.1, ...

Discussion

4511.	Form the pair of linear equations for the following problems and find their solution by substitution method.(i) The difference between two numbers is 26 and one number is three times the other. Find them.(ii) The larger of the two supplementary angles exceeds the smaller by 18 degrees. Find them.(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls forRs 1750. Find the cost of each bat and each ball.(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?(v) A fraction becomes 911, if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and denominator it becomes 56. Find the fraction.(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?
Answer» Form the pair of linear equations for the following problems and find their solution by substitution method. (i) The difference between two numbers is 26 and one number is three times the other. Find them. (ii) The larger of the two supplementary angles exceeds the smaller by 18 degrees. Find them. (iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball. (iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km? (v) A fraction becomes $\frac{9}{11}$ , if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and denominator it becomes $\frac{5}{6}$ . Find the fraction. (vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?

Discussion

4512.	Find lateral shift Δ in cm?
Answer» Find lateral shift $Δ$ in $cm$ ?

Discussion

4513.	Find the ratio compounded of the duplicate ratio of 5 : 6, the reciprocal ratio of 25 : 42 and the sub-triplicate ratio of 216 : 343.
Answer» Find the ratio compounded of the duplicate ratio of 5 : 6, the reciprocal ratio of 25 : 42 and the sub-triplicate ratio of 216 : 343.

Discussion

4514.	The value of sin18∘cos72∘ is ______.
Answer» The value of $\frac{s i n 18^{\circ}}{c o s 72^{\circ}}$ is ______.

Discussion

4515.	Show that in a trapezium the line joining the midpoint of non-parallel sides is parallel to the parallel sides.
Answer» Show that in a trapezium the line joining the midpoint of non-parallel sides is parallel to the parallel sides.

Discussion

4516.	46. If the common difference of AP is 3, Find the value of a17-a12.
Answer» 46. If the common difference of AP is 3, Find the value of a17-a12.

Discussion

4517.	Solve 5x+1+52−x=53+1 [4 MARKS]
Answer» Solve $5^{x + 1} + 5^{2 - x} = 5^{3} + 1$ [4 MARKS]

Discussion

4518.	Consider the Boolean expression:f(A,B,C,D)=(A+B+C+¯D)(A+¯B+¯C+D)(A+B+¯C+¯D)(¯A+¯B+¯C+¯D)(¯A+¯B+¯C+D)Then, the function f(A,B,C,D) can be expressed as
Answer» Consider the Boolean expression: $f (A, B, C, D) = (A + B + C + ¯ D) (A + ¯ B + ¯ C + D) (A + B + ¯ C + ¯ D) (¯ A + ¯ B + ¯ C + ¯ D) (¯ A + ¯ B + ¯ C + D)$ Then, the function $f (A, B, C, D)$ can be expressed as

Discussion

4519.	The coordinate of the mid-point of the line segment joining the points (2,1) and (1,-3) is ____.
Answer» The coordinate of the mid-point of the line segment joining the points (2,1) and (1,-3) is ____.

Discussion

4520.	The radii of two spheres s1 and s2 are in the ratio 4 : 3. If s1 and s2 are melted and converted into a new sphere, then the ratio of volumes of sphere s1 and the new sphere is
Answer» The radii of two spheres s1 and s2 are in the ratio 4 : 3. If s1 and s2 are melted and converted into a new sphere, then the ratio of volumes of sphere s1 and the new sphere is

Discussion

4521.	In △ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -
Answer» In $△$ ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -

4521.

In △ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -

Answer»

In $△$ ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -

Discussion

4522.	56. A right circular cylinder just encloses a sphere of radius r. Find: (1) surface area of the sphere, (2) curved surface area of the cylinder, (3) ratio of the areas obtained in (1) & (2).
Answer» 56. A right circular cylinder just encloses a sphere of radius r. Find: (1) surface area of the sphere, (2) curved surface area of the cylinder, (3) ratio of the areas obtained in (1) & (2).

Discussion

4523.	Fill in the blanks:(i) The common point of a tangent and the circle is called ..........(ii) A circle may have .............. parallel tangents.(iii) A tangent to a circle intersects in it ............ point(s).(iv) A line intersecting a circle in two points is called a ...........(v) The angle between tangent at a point on a circle and the radius through the point is ........
Answer» Fill in the blanks: (i) The common point of a tangent and the circle is called .......... (ii) A circle may have .............. parallel tangents. (iii) A tangent to a circle intersects in it ............ point(s). (iv) A line intersecting a circle in two points is called a ........... (v) The angle between tangent at a point on a circle and the radius through the point is ........

Discussion

4524.	In the given figure, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.
Answer» In the given figure, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.

Discussion

4525.	Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. What is Rohan's present age?
Answer» Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. What is Rohan's present age?

Discussion

4526.	Find the probability of getting an even number on the die and tail on the coin, if a die and a coin both are tossed simultaneously.
Answer» Find the probability of getting an even number on the die and tail on the coin, if a die and a coin both are tossed simultaneously.

Discussion

4527.	If 'x' is the common number in the following two Pythagorean triplets (6, x, 10) and (x, 15, 17), then find the value of (x2 - 1 ).
Answer» If 'x' is the common number in the following two Pythagorean triplets (6, x, 10) and (x, 15, 17), then find the value of ( $x^{2}$ - 1 ).

Discussion

4528.	Find a cubic polynomial with sum of zeroes , product of its zeroes taken two at a time and product of zeroes as : 5,-3 and -7 respectively . Also find the value of its zeroes.
Answer» Find a cubic polynomial with sum of zeroes , product of its zeroes taken two at a time and product of zeroes as : 5,-3 and -7 respectively . Also find the value of its zeroes.

Discussion

4529.	The difference of number of even and odd factors of 10478160 is
Answer» The difference of number of even and odd factors of 10478160 is

Discussion

4530.	If f(x) = x ^ 4 + a * x ^ 3 + b * x ^ 2 + cx + d is a polynomial such that f(1) = 5, f(2) = 10 , f(3) = 15, f(4) = 20 , then the value of f(5) + f * (- 5) is
Answer» If f(x) = x ^ 4 + a * x ^ 3 + b * x ^ 2 + cx + d is a polynomial such that f(1) = 5, f(2) = 10 , f(3) = 15, f(4) = 20 , then the value of f(5) + f * (- 5) is

Discussion

4531.	61. The dimeter of a sphere is decrease by 20% by what percent does its curved sunface area decrease
Answer» 61. The dimeter of a sphere is decrease by 20% by what percent does its curved sunface area decrease

Discussion

4532.	Question 5In the figure, BA \|\| ED and BC \|\| EF. Show that ∠ABC=∠DEF.
Answer» Question 5 In the figure, BA \|\| ED and BC \|\| EF. Show that $∠ A B C = ∠ D E F$ .

Discussion

4533.	The reflection of a point (x,y) in the x axis is
Answer» The reflection of a point (x,y) in the x axis is

Discussion

4534.	The HCF of 100 and 101 is .(a) 1(b) 7(c) 37(d) None of these
Answer» The HCF of 100 and 101 is . (a) 1 (b) 7 (c) 37 (d) None of these

Discussion

4535.	Arrange these numbers in ascending order √2,616,313
Answer» Arrange these numbers in ascending order $\sqrt{2}, 6^{\frac{1}{6}}, 3^{\frac{1}{3}}$

Discussion

4536.	Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60∘. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.
Answer» Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is $60^{\circ}$ . Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

Discussion

4537.	A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area. [4 MARKS]
Answer» A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area. [4 MARKS]

Discussion

4538.	Find all the zeroes of the polynomial f(x) = x^4 -3x^3 +6x-4, if two of its zeroes are √2 and -√2
Answer» Find all the zeroes of the polynomial f(x) = x^4 -3x^3 +6x-4, if two of its zeroes are √2 and -√2

Discussion

4539.	Draw a circle of radius 3.5 cm. Mark s point P outside the circle at a distance of 6 cm from the centre, construct two tangents from P to the given circle. Measure and write down the length of one tangent. [3 MARKS]
Answer» Draw a circle of radius 3.5 cm. Mark s point P outside the circle at a distance of 6 cm from the centre, construct two tangents from P to the given circle. Measure and write down the length of one tangent. [3 MARKS]

Discussion

4540.	If sum of n term is equal to n and sum of n term is equal to m Find the sum of (m+n).
Answer» If sum of n term is equal to n and sum of n term is equal to m Find the sum of (m+n).

4540.

If sum of n term is equal to n and sum of n term is equal to m Find the sum of (m+n).

Answer»

If sum of n term is equal to n and sum of n term is equal to m

Find the sum of (m+n).

Discussion

4541.	Write a pair of irrational numbers whose sum is rational.
Answer» Write a pair of irrational numbers whose sum is rational.

Discussion

4542.	Fifteen identical spheres are made by melting a solid cylinder of radius 10 cm and height 5.4 cm, the diameter of each sphere is _________.
Answer» Fifteen identical spheres are made by melting a solid cylinder of radius 10 cm and height 5.4 cm, the diameter of each sphere is _________.

Discussion

4543.	Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) :2y − x = 96y − 3x = 21
Answer» Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) : 2y − x = 9 6y − 3x = 21

Discussion

4544.	Find the quadratic polynomial whose sum of its zeroes (roots) is −85 and the product of the zeroes (roots) is 75.
Answer» Find the quadratic polynomial whose sum of its zeroes (roots) is $- \frac{8}{5}$ and the product of the zeroes (roots) is $\frac{7}{5}$ .

Discussion

4545.	19. Two coins are tossed simultaneously. The Probability of getting at most two heads is
Answer» 19. Two coins are tossed simultaneously. The Probability of getting at most two heads is

Discussion

4546.	Solvethe linear equation
Answer» Solve the linear equation

Discussion

4547.	In the given figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is
Answer» In the given figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is

Discussion

4548.	The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are(a) (2, 0, 0) (b) (0, 5, 0)(c) (0, 0, 7)(d) (0, 5, 7)
Answer» The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are (a) (2, 0, 0) (b) (0, 5, 0) (c) (0, 0, 7) (d) (0, 5, 7)

Discussion

4549.	In the given figure, the sides AB , BC and CA of triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then length of BC is(a) 11 cm (b) 10 cm (c) 14 cm (d) 15 cm [CBSE 2012]
Answer» In the given figure, the sides AB , BC and CA of triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then length of BC is (a) 11 cm (b) 10 cm (c) 14 cm (d) 15 cm [CBSE 2012]

Discussion

4550.	In the arithmetic sequence got by adding to itself repeatedly, does the number 10 occur anywhere? What about 11?
Answer» In the arithmetic sequence got by adding to itself repeatedly, does the number 10 occur anywhere? What about 11?

Discussion

Explore topic-wise InterviewSolutions in .

9. At a point on a level plane a vertical Tower subtends an angle 'a' (alpha) and a pole of height 'h' meters at the top of the tower subtends an angle 'b' (beta). Show that the height of the tower is "hsin(a) cosec(b)cos(a+b)".

In the XY plane two points A(2,2) and B(7,7) are taken. R is the region in the first quadrant which consists of points C such that triangle ABC is an acute angled triangle. The closest integer to the area of the region R is

A man buys a product for Rs. 648 including sales tax. If the marked price is Rs. 600, then the rate of sales tax is

Q: If the bisector of two consecutive angle A and B of a quadrilateral ABCD intersect at a point O such that angle C + angle D =K⊾AOD, then find the value of K??

Area of square ABCD with A(1,0) and B(4,0) is ___ square units.

sec^6θ = †an^6θ+ 3 †an^2θ sec^2θ +

ntIf a,b,c are distinct and p(x) is a polynomial in x; which leaves remainder on division by (x-a), (x-b), (x-c) respectively , then the remainder on division of p(x) by (x-a)(x-b)(x-c)isn ntA) x+a+b+cn ntB) a+b+cn ntC) xn ntD) None of thesen

If R(5, 6) is the midpoint of the line segment AB joining the points A(6, 5) and B(4, y) then y equals(a) 5 (b) 7 (c) 12 (d) 6

For the following arithmetic progressions write the first term a and the common difference d:(i) −5, −1, 3, 7, ...(ii) 15,35,55,75(iii) 0.3, 0.55, 0.80, 1.05, ...(iv) −1.1, −3.1, −5.1, −7.1, ...

Find lateral shift Δ in cm?

Find the ratio compounded of the duplicate ratio of 5 : 6, the reciprocal ratio of 25 : 42 and the sub-triplicate ratio of 216 : 343.

The value of sin18∘cos72∘ is ______.

Show that in a trapezium the line joining the midpoint of non-parallel sides is parallel to the parallel sides.

46. If the common difference of AP is 3, Find the value of a17-a12.

Solve 5x+1+52−x=53+1 [4 MARKS]

Consider the Boolean expression:f(A,B,C,D)=(A+B+C+¯D)(A+¯B+¯C+D)(A+B+¯C+¯D)(¯A+¯B+¯C+¯D)(¯A+¯B+¯C+D)Then, the function f(A,B,C,D) can be expressed as

The coordinate of the mid-point of the line segment joining the points (2,1) and (1,-3) is ____.

The radii of two spheres s1 and s2 are in the ratio 4 : 3. If s1 and s2 are melted and converted into a new sphere, then the ratio of volumes of sphere s1 and the new sphere is

In △ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -

56. A right circular cylinder just encloses a sphere of radius r. Find: (1) surface area of the sphere, (2) curved surface area of the cylinder, (3) ratio of the areas obtained in (1) & (2).

In the given figure, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.

Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. What is Rohan's present age?

Find the probability of getting an even number on the die and tail on the coin, if a die and a coin both are tossed simultaneously.

If 'x' is the common number in the following two Pythagorean triplets (6, x, 10) and (x, 15, 17), then find the value of (x2 - 1 ).

Find a cubic polynomial with sum of zeroes , product of its zeroes taken two at a time and product of zeroes as : 5,-3 and -7 respectively . Also find the value of its zeroes.

The difference of number of even and odd factors of 10478160 is

If f(x) = x ^ 4 + a * x ^ 3 + b * x ^ 2 + cx + d is a polynomial such that f(1) = 5, f(2) = 10 , f(3) = 15, f(4) = 20 , then the value of f(5) + f * (- 5) is

61. The dimeter of a sphere is decrease by 20% by what percent does its curved sunface area decrease

Question 5In the figure, BA || ED and BC || EF. Show that ∠ABC=∠DEF.

The reflection of a point (x,y) in the x axis is

The HCF of 100 and 101 is .(a) 1(b) 7(c) 37(d) None of these

Arrange these numbers in ascending order √2,616,313

Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60∘. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area. [4 MARKS]

Find all the zeroes of the polynomial f(x) = x^4 -3x^3 +6x-4, if two of its zeroes are √2 and -√2

Draw a circle of radius 3.5 cm. Mark s point P outside the circle at a distance of 6 cm from the centre, construct two tangents from P to the given circle. Measure and write down the length of one tangent. [3 MARKS]

If sum of​​​​​ n term is equal to​​​​​ n and sum of​​​​​ n term is equal to m Find the sum of (m+n).

Write a pair of irrational numbers whose sum is rational.

Fifteen identical spheres are made by melting a solid cylinder of radius 10 cm and height 5.4 cm, the diameter of each sphere is _________.

Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) :2y − x = 96y − 3x = 21

Find the quadratic polynomial whose sum of its zeroes (roots) is −85 and the product of the zeroes (roots) is 75.

19. Two coins are tossed simultaneously. The Probability of getting at most two heads is

Solvethe linear equation

In the given figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is

The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are(a) (2, 0, 0) (b) (0, 5, 0)(c) (0, 0, 7)(d) (0, 5, 7)

In the given figure, the sides AB , BC and CA of triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then length of BC is(a) 11 cm (b) 10 cm (c) 14 cm (d) 15 cm [CBSE 2012]

In the arithmetic sequence got by adding to itself repeatedly, does the number 10 occur anywhere? What about 11?

If sum of n term is equal to n and sum of n term is equal to m Find the sum of (m+n).