32581 + Interview Questions in Mathematics

1.	If (x + 1) is a factor of x2 - 3ax + 3a - 7, then the value of a is:
Answer» If (x + 1) is a factor of x² - 3ax + 3a - 7, then the value of a is:

Discussion

2.	If three consecutive vertices of a parallelogram ABCD areA(1, -2), B(3,6) and C(5,10), find its fourth vertex D.
Answer» If three consecutive vertices of a parallelogram ABCD areA(1, -2), B(3,6) and C(5,10), find its fourth vertex D.

Discussion

3.	Consider the following distribution of SO2 concentration in the air(in ppm = parts per million) in 30 localities. We wish to find the mean SO2 concentration using step assumed mean method.Fill the following table. Determine the assumed mean(a) and proceed. Class IntervalFrequency(fi)Class mark(xi)di=xi−a0−1004050−200D......0.00−0.0440.02−0.080.04−0.0890.06A.........0.08−0.1290.10B........0.12−0.1620.140.040.16−0.2040.18C........0.20−0.2420.220.12Total∑fi=30 The value of A, B and C respectively are:
Answer» Consider the following distribution of $S O_{2}$ concentration in the air(in ppm = parts per million) in 30 localities. We wish to find the mean SO₂ concentration using step assumed mean method.Fill the following table. Determine the assumed mean(a) and proceed. $\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y (f_{i}) & C l a s s m a r k (x_{i}) & d_{i} = x_{i} - a 0 - 100 & 40 & 50 & - 200 & D . . . . . . 0.00 - 0.04 & 4 & 0.02 & - 0.08 0.04 - 0.08 & 9 & 0.06 & A . . . . . . . . . 0.08 - 0.12 & 9 & 0.10 & B . . . . . . . . 0.12 - 0.16 & 2 & 0.14 & 0.04 0.16 - 0.20 & 4 & 0.18 & C . . . . . . . . 0.20 - 0.24 & 2 & 0.22 & 0.12 T o t a l & \sum f_{i} = 30 \end{matrix}$ The value of A, B and C respectively are:

3.

Consider the following distribution of SO2 concentration in the air(in ppm = parts per million) in 30 localities. We wish to find the mean SO2 concentration using step assumed mean method.Fill the following table. Determine the assumed mean(a) and proceed. Class IntervalFrequency(fi)Class mark(xi)di=xi−a0−1004050−200D......0.00−0.0440.02−0.080.04−0.0890.06A.........0.08−0.1290.10B........0.12−0.1620.140.040.16−0.2040.18C........0.20−0.2420.220.12Total∑fi=30 The value of A, B and C respectively are:

Answer»

Consider the following distribution of $S O_{2}$ concentration in the air(in ppm = parts per million) in 30 localities. We wish to find the mean SO₂ concentration using step assumed mean method.Fill the following table. Determine the assumed mean(a) and proceed.

$\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y (f_{i}) & C l a s s m a r k (x_{i}) & d_{i} = x_{i} - a 0 - 100 & 40 & 50 & - 200 & D . . . . . . 0.00 - 0.04 & 4 & 0.02 & - 0.08 0.04 - 0.08 & 9 & 0.06 & A . . . . . . . . . 0.08 - 0.12 & 9 & 0.10 & B . . . . . . . . 0.12 - 0.16 & 2 & 0.14 & 0.04 0.16 - 0.20 & 4 & 0.18 & C . . . . . . . . 0.20 - 0.24 & 2 & 0.22 & 0.12 T o t a l & \sum f_{i} = 30 \end{matrix}$

The value of A, B and C respectively are:

Discussion

4.	Which of the following have a non terminating decimal expansion?
Answer» Which of the following have a non terminating decimal expansion?

Discussion

5.	Why is a first degree polynomial in two variables ax + by + c = 0, called a linear equation?
Answer» Why is a first degree polynomial in two variables ax + by + c = 0, called a linear equation?

Discussion

6.	If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference.2
Answer» If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference. 2

Discussion

7.	Find the value of sin 50ocos 40o+cosec 40osec 50o−4 cos 50o cosec 40o.
Answer» Find the value of $\frac{s i n 50^{o}}{c o s 40^{o}} + \frac{c o s e c 40^{o}}{s e c 50^{o}} - 4$ cos $50^{o}$ cosec $40^{o}$ .

Discussion

8.	In the given figure PQ is a diameter of a circle with centre O and PT is a tangent at P. QT meets the circle at R. If ∠POR = 72∘, find ∠PTR.
Answer» In the given figure PQ is a diameter of a circle with centre O and PT is a tangent at P. QT meets the circle at R. If ∠POR = $72^{\circ}$ , find $∠$ PTR.

8.

In the given figure PQ is a diameter of a circle with centre O and PT is a tangent at P. QT meets the circle at R. If ∠POR = 72∘, find ∠PTR.

Answer»

In the given figure PQ is a diameter of a circle with centre O and PT is a tangent at P. QT meets the circle at R. If ∠POR = $72^{\circ}$ , find $∠$ PTR.

Discussion

9.	The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?
Answer» The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?

Discussion

10.	In the given figure, common tangents AB and CD to the two circles with centres O1 and O2 intersect at E. Prove that AB=CD.
Answer» In the given figure, common tangents $A B$ and $C D$ to the two circles with centres $O_{1}$ and $O_{2}$ intersect at $E .$ Prove that $A B = C D .$

10.

In the given figure, common tangents AB and CD to the two circles with centres O1 and O2 intersect at E. Prove that AB=CD.

Answer»

In the given figure, common tangents $A B$ and $C D$ to the two circles with centres $O_{1}$ and $O_{2}$ intersect at $E .$ Prove that $A B = C D .$

Discussion

11.	A particle moves on a circular arc of radius r, the distance covered by particle when it travels from A to B on the arc subtending an angle 60∘ at centre of circular path.
Answer» A particle moves on a circular arc of radius $r$ , the distance covered by particle when it travels from $A$ to $B$ on the arc subtending an angle $60^{\circ}$ at centre of circular path.

Discussion

12.	Assume that boy and girl babies are equally likely. If a couple have three children, find the probability that at least one is a boy. (Give the answer up to 3 decimal places)
Answer» Assume that boy and girl babies are equally likely. If a couple have three children, find the probability that at least one is a boy. (Give the answer up to 3 decimal places)

Discussion

13.	ΔABC∼ΔDEF and their areas are respectively 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.
Answer» $Δ A B C \sim Δ D E F$ and their areas are respectively 64 $c m^{2}$ and 121 $c m^{2}$ . If EF = 15.4 cm, find BC.

Discussion

14.	M (c, -1) is a point equidistant from the points A(1, 3) and B(-5, -5). Find the value of c.
Answer» M (c, -1) is a point equidistant from the points A(1, 3) and B(-5, -5). Find the value of c.

Discussion

15.	The probability of selecting a vowel from the word CHOCOLATE is .
Answer» The probability of selecting a vowel from the word CHOCOLATE is .

Discussion

16.	Two cars start from the opposite places of a main road , 150 km apart . First car runs for 25 km and takes a right turn and then runs 15 km . It then turns left and then runs for another 25 km and then takes the direction back to reach the main road . In the mean time , due to minor breakdown , the other car has run only 35 km along the main road . What should be the distance between the two cars at this point ?
Answer» Two cars start from the opposite places of a main road , 150 km apart . First car runs for 25 km and takes a right turn and then runs 15 km . It then turns left and then runs for another 25 km and then takes the direction back to reach the main road . In the mean time , due to minor breakdown , the other car has run only 35 km along the main road . What should be the distance between the two cars at this point ?

Discussion

17.	Mode is defined as the
Answer» Mode is defined as the

Discussion

18.	Question 9 ABCD is a trapezium in which AB \|\| DC and its diagonals intersect each other at the point O. Show that AOBO=CODO.
Answer» Question 9 ABCD is a trapezium in which AB \|\| DC and its diagonals intersect each other at the point O. Show that $\frac{A O}{B O} = \frac{C O}{D O}$ .

Discussion

19.	Which of the following operations can convert the expression (x2+8x√3) into a perfect square?
Answer» $Which of the following operations can$ $convert the expression (x^{2} + \frac{8 x}{\sqrt{3}})$ $into a perfect square?$

Discussion

20.	Find the volume of a structure of dimensions 10×10×10.
Answer» Find the volume of a structure of dimensions $10 \times 10 \times 10$ .

Discussion

21.	Divide the polynomial 3x4−4x3−3x−1 by x-1 and then find the remainder.
Answer» Divide the polynomial $3 x^{4} - 4 x^{3} - 3 x - 1$ by x-1 and then find the remainder.

Discussion

22.	Question 2 (ii) E and F are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether EF \|\| QR. (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
Answer» Question 2 (ii) E and F are points on the sides PQ and PR respectively of a $Δ P Q R$ . For the following case, state whether EF \|\| QR. (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm

Discussion

23.	If tan 2A = cot (A - 18∘), where 2A is an acute angle, find the value of A.
Answer» If tan 2A = cot (A - $18^{\circ}$ ), where 2A is an acute angle, find the value of A.

Discussion

24.	If a + b + c = 0, then the value of a2bc+b2ac+c2ab is :
Answer» If a + b + c = 0, then the value of $\frac{a^{2}}{b c} + \frac{b^{2}}{a c} + \frac{c^{2}}{a b}$ is :

Discussion

25.	Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : 29343
Answer» Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{29}{343}$

Discussion

26.	Question 28 A quadrilateral has three acute angles. If each measures 80∘, then the measure of the fourth angle is : a) 150∘ b) 120∘ c) 105∘ d) 140∘
Answer» Question 28 A quadrilateral has three acute angles. If each measures $80^{\circ}$ , then the measure of the fourth angle is : a) $150^{\circ}$ b) $120^{\circ}$ c) $105^{\circ}$ d) $140^{\circ}$

Discussion

27.	Every even positive integer is of the form (a) ___ and every positive odd integer is of the form (b) ___. (x is any positive integer)
Answer» Every even positive integer is of the form (a) ___ and every positive odd integer is of the form (b) ___. (x is any positive integer)

Discussion

28.	ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm. Three circles are drawn touching each other with the vertices as their centres. Find the sum of the radii of the three circles.
Answer» ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm. Three circles are drawn touching each other with the vertices as their centres. Find the sum of the radii of the three circles.

Discussion

29.	Three arithmetic terms are inserted between two number a and b. The resulting sequence is a/an ___.
Answer» Three arithmetic terms are inserted between two number a and b. The resulting sequence is a/an ___.

Discussion

30.	Which among the following represents the total surface area of a right circular cylinder?
Answer» Which among the following represents the total surface area of a right circular cylinder?

Discussion

31.	A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per m2 . (Note that the base of the tent will not be covered with canvas). [3 MARKS]
Answer» A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per $m^{2}$ . (Note that the base of the tent will not be covered with canvas). [3 MARKS]

Discussion

32.	Question 7 (iii) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The amount of money in the account of Varun at the end of every year when Rs. 1000 is deposited at simple interest of 10% per annum.
Answer» Question 7 (iii) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The amount of money in the account of Varun at the end of every year when Rs. 1000 is deposited at simple interest of $10 %$ per annum.

Discussion

33.	If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
Answer» If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

Discussion

34.	Which term of the AP 18, 23, 28, 33, ……. is 98?
Answer» Which term of the AP 18, 23, 28, 33, ……. is 98?

Discussion

35.	In a lucky draw, Rs 9,000 were divided equally among a certain number of people. Had there been 20 more people, each would have got Rs 160 less. Find the original number of people.
Answer» In a lucky draw, Rs 9,000 were divided equally among a certain number of people. Had there been 20 more people, each would have got Rs 160 less. Find the original number of people.

Discussion

36.	If α is the complementary angle of θ, then sin θ = _________ .
Answer» If α is the complementary angle of θ, then sin $θ$ = _________ .

Discussion

37.	Which of the following is a polynomial
Answer» Which of the following is a polynomial

Discussion

38.	If D, E, F are respectively the mid-points of the sides BC, CA, and AB of △ABC, and the area of △ ABC is 24 cm2, then find the area of △ DEF.
Answer» If D, E, F are respectively the mid-points of the sides BC, CA, and AB of $△$ ABC, and the area of $△$ ABC is 24 $c m^{2}$ , then find the area of $△$ DEF.

Discussion

39.	A test tube has radius 2.1 cm and height 16.1 cm. Volume of the test tube is .
Answer» A test tube has radius 2.1 cm and height 16.1 cm. Volume of the test tube is .

Discussion

40.	Find the 60th term of the A.P. 8, 10, 12....if it has a total of 60 terms and hence find the sum of it last 10 terms.
Answer» Find the $60^{t h}$ term of the A.P. 8, 10, 12....if it has a total of 60 terms and hence find the sum of it last 10 terms.

Discussion

41.	Find the values of k for which the system of equations has , 1) unique solution 2) no solution. kx - y = 2. 6x - 2y = 3. Is there a value for which the system has infinitely many solutions?
Answer» Find the values of k for which the system of equations has , 1) unique solution 2) no solution. kx - y = 2. 6x - 2y = 3. Is there a value for which the system has infinitely many solutions?

Discussion

42.	The graph of y = p(x) is given. The number of zeroes of y = p(x) is___.
Answer» The graph of y = p(x) is given. The number of zeroes of y = p(x) is___.

Discussion

43.	A road roller was used for levelling a road of width 2 m. It was observed that, the road roller required 25 complete revolutions to level the entire road. If the radius and the length of the roller is 7 m and 2 m respectively, then length of the road is ____. [Take π = 3.14].
Answer» A road roller was used for levelling a road of width 2 m. It was observed that, the road roller required 25 complete revolutions to level the entire road. If the radius and the length of the roller is 7 m and 2 m respectively, then length of the road is ____. [Take $π$ = 3.14].

Discussion

44.	How can the numbers 6n Where n is a natural number end with digit 5 give reasons
Answer» How can the numbers 6ⁿ Where n is a natural number end with digit 5 give reasons

Discussion

45.	Can we have any n € N, for which 7^n ends with the digit zero?
Answer» Can we have any n € N, for which 7^n ends with the digit zero?

Discussion

46.	Find the number which exceeds its positive square root by 20.
Answer» Find the number which exceeds its positive square root by 20.

Discussion

47.	Sir/Ma'am, The question asked by you in equations of motion the answer ellaborated gives an equation (D/5)1/2 + D/340=180. Kindly please guide me how to solve the equation furture i.e., how will I remove the root.
Answer» Sir/Ma'am, The question asked by you in equations of motion the answer ellaborated gives an equation (D/5)^1/2 + D/340=180. Kindly please guide me how to solve the equation furture i.e., how will I remove the root.

47.

Sir/Ma'am, The question asked by you in equations of motion the answer ellaborated gives an equation (D/5)1/2 + D/340=180. Kindly please guide me how to solve the equation furture i.e., how will I remove the root.

Answer»

Sir/Ma'am,

The question asked by you in equations of motion the answer ellaborated gives an equation (D/5)^1/2 + D/340=180.

Kindly please guide me how to solve the equation furture i.e., how will I remove the root.

Discussion

48.	Show that the sum of a A.P. whose first term is 'a', the second term is 'b' and the last term is 'c', is equal to (a+c)(b+c-2a)/2(b-a)
Answer» Show that the sum of a A.P. whose first term is 'a', the second term is 'b' and the last term is 'c', is equal to (a+c)(b+c-2a)/2(b-a)

Discussion

49.	Complete the equation by filling the given blank. (1−sinθ+cosθ)2 = ___(1+cosθ)(1−sinθ). ___
Answer» Complete the equation by filling the given blank. $(1 - s i n θ + c o s θ)^{2}$ = ___ $(1 + c o s θ) (1 - s i n θ)$ . ___

49.

Complete the equation by filling the given blank. (1−sinθ+cosθ)2 = _(1+cosθ)(1−sinθ). _

Answer»

Complete the equation by filling the given blank.

$(1 - s i n θ + c o s θ)^{2}$ = ___ $(1 + c o s θ) (1 - s i n θ)$ .

___

Discussion

50.	if the point A[x,2] , B[-3-4] and C[7-5] are collinear,then find the value of ?
Answer» if the point A[x,2] , B[-3-4] and C[7-5] are collinear,then find the value of ?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If (x + 1) is a factor of x2 - 3ax + 3a - 7, then the value of a is:

If three consecutive vertices of a parallelogram ABCD areA(1, -2), B(3,6) and C(5,10), find its fourth vertex D.

Which of the following have a non terminating decimal expansion?

Why is a first degree polynomial in two variables ax + by + c = 0, called a linear equation?

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference.2

Find the value of sin 50ocos 40o+cosec 40osec 50o−4 cos 50o cosec 40o.

In the given figure PQ is a diameter of a circle with centre O and PT is a tangent at P. QT meets the circle at R. If ∠POR = 72∘, find ∠PTR.

The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?

In the given figure, common tangents AB and CD to the two circles with centres O1 and O2 intersect at E. Prove that AB=CD.

A particle moves on a circular arc of radius r, the distance covered by particle when it travels from A to B on the arc subtending an angle 60∘ at centre of circular path.

Assume that boy and girl babies are equally likely. If a couple have three children, find the probability that at least one is a boy. (Give the answer up to 3 decimal places)

ΔABC∼ΔDEF and their areas are respectively 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.

M (c, -1) is a point equidistant from the points A(1, 3) and B(-5, -5). Find the value of c.

The probability of selecting a vowel from the word CHOCOLATE is .

Mode is defined as the

Question 9 ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AOBO=CODO.

Which of the following operations can convert the expression (x2+8x√3) into a perfect square?

Find the volume of a structure of dimensions 10×10×10.

Divide the polynomial 3x4−4x3−3x−1 by x-1 and then find the remainder.

Question 2 (ii) E and F are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether EF || QR. (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm

If tan 2A = cot (A - 18∘), where 2A is an acute angle, find the value of A.

If a + b + c = 0, then the value of a2bc+b2ac+c2ab is :

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : 29343

Question 28 A quadrilateral has three acute angles. If each measures 80∘, then the measure of the fourth angle is : a) 150∘ b) 120∘ c) 105∘ d) 140∘

Every even positive integer is of the form (a) ___ and every positive odd integer is of the form (b) ___. (x is any positive integer)

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm. Three circles are drawn touching each other with the vertices as their centres. Find the sum of the radii of the three circles.

Three arithmetic terms are inserted between two number a and b. The resulting sequence is a/an ___.

Which among the following represents the total surface area of a right circular cylinder?

Question 7 (iii) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The amount of money in the account of Varun at the end of every year when Rs. 1000 is deposited at simple interest of 10% per annum.

If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

Which term of the AP 18, 23, 28, 33, ……. is 98?

In a lucky draw, Rs 9,000 were divided equally among a certain number of people. Had there been 20 more people, each would have got Rs 160 less. Find the original number of people.

If α is the complementary angle of θ, then sin θ = _________ .

Which of the following is a polynomial

If D, E, F are respectively the mid-points of the sides BC, CA, and AB of △ABC, and the area of △ ABC is 24 cm2, then find the area of △ DEF.

A test tube has radius 2.1 cm and height 16.1 cm. Volume of the test tube is .

Find the 60th term of the A.P. 8, 10, 12....if it has a total of 60 terms and hence find the sum of it last 10 terms.

Find the values of k for which the system of equations has , 1) unique solution 2) no solution. kx - y = 2. 6x - 2y = 3. Is there a value for which the system has infinitely many solutions?

The graph of y = p(x) is given. The number of zeroes of y = p(x)​ is___.

A road roller was used for levelling a road of width 2 m. It was observed that, the road roller required 25 complete revolutions to level the entire road. If the radius and the length of the roller is 7 m and 2 m respectively, then length of the road is ____. [Take π = 3.14].

How can the numbers 6n Where n is a natural number end with digit 5 give reasons

Can we have any n € N, for which 7^n ends with the digit zero?

Find the number which exceeds its positive square root by 20.

Sir/Ma'am, The question asked by you in equations of motion the answer ellaborated gives an equation (D/5)1/2 + D/340=180. Kindly please guide me how to solve the equation furture i.e., how will I remove the root.

Show that the sum of a A.P. whose first term is 'a', the second term is 'b' and the last term is 'c', is equal to (a+c)(b+c-2a)/2(b-a)

Complete the equation by filling the given blank. (1−sinθ+cosθ)2 = ___(1+cosθ)(1−sinθ). ___

if the point A[x,2] , B[-3-4] and C[7-5] are collinear,then find the value of ?

Every even positive integer is of the form (a) _ and every positive odd integer is of the form (b) _. (x is any positive integer)

The graph of y = p(x) is given. The number of zeroes of y = p(x) is___.

Complete the equation by filling the given blank. (1−sinθ+cosθ)2 = _(1+cosθ)(1−sinθ). _