32581 + Interview Questions in Mathematics

1.	Find the H.C.F of 16a2b3x4y5, 40 a3b2x3y4 and 24 a5b5x6y4
Answer» Find the H.C.F of $16 a^{2} b^{3} x^{4} y^{5}$ , $40 a^{3} b^{2} x^{3} y^{4}$ and $24 a^{5} b^{5} x^{6} y^{4}$

Discussion

2.	Which of the following equations has x = 3, y = - 4 as solution?
Answer» Which of the following equations has x = 3, y = - 4 as solution?

Discussion

3.	Question 1(vii) Check whether the following are quadratic equations: (vii) (x+2)3=2x(x2−1)
Answer» Question 1(vii) Check whether the following are quadratic equations: (vii) $(x + 2)^{3} = 2 x (x^{2} - 1)$

Discussion

4.	Question 2 (ii) Fill in the blanks: (ii) A line intersecting a circle at two points is called a___.
Answer» Question 2 (ii) Fill in the blanks: (ii) A line intersecting a circle at two points is called a___.

Discussion

5.	Check if (x−2)2+1=2x–3 is a quadratic equation or not. Enter your answer Y/N accordingly in the given space.___
Answer» Check if $(x - 2)^{2} + 1 = 2 x - 3$ is a quadratic equation or not. Enter your answer Y/N accordingly in the given space.___

Discussion

6.	Suppose p denotes the perimeter of a triangle with sides a, b and c and s is the semi perimeter and r is the inradius. If A denotes the area of the triangle, select the statements that are true.
Answer» Suppose p denotes the perimeter of a triangle with sides a, b and c and s is the semi perimeter and r is the inradius. If A denotes the area of the triangle, select the statements that are true.

Discussion

7.	If the sum of first 10 natural numbers is S1 and that of first 10 whole numbers is S2. Then S1−S2 is
Answer» If the sum of first 10 natural numbers is $S_{1}$ and that of first 10 whole numbers is $S_{2} .$ Then $S_{1} - S_{2}$ is

Discussion

8.	Which of the following statements is / are correct statements? 1. Centroid of a triangle is the point of concurrrency of medians 2. Incentre of a triangle is the point of concurrency of perpendicular bisectors of the sides of the triangle 3. Circumcentre of a triangle is the point of concurrency of internal bisectors of the angles of the triangle 4. Orthocentre of a triangle is the point of concurrency of altitudes of the triangle drawn from one vertex to opposite side 5. A triangle can have only one excentre
Answer» Which of the following statements is / are correct statements? 1. Centroid of a triangle is the point of concurrrency of medians 2. Incentre of a triangle is the point of concurrency of perpendicular bisectors of the sides of the triangle 3. Circumcentre of a triangle is the point of concurrency of internal bisectors of the angles of the triangle 4. Orthocentre of a triangle is the point of concurrency of altitudes of the triangle drawn from one vertex to opposite side 5. A triangle can have only one excentre

Discussion

9.	A corn cob shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length as 20 cm. If each 1 sq cm of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob? [4 MARKS]
Answer» A corn cob shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length as 20 cm. If each 1 sq cm of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob? [4 MARKS]

Discussion

10.	The sum of n natural numbers is 5n2+4n. Find its 8th term.
Answer» The sum of n natural numbers is $5 n^{2} + 4 n .$ Find its $8^{t h}$ term.

Discussion

11.	√3,1(√3),13(√3)..... The 19th term of the above sequence is .
Answer» $\sqrt{3}, \frac{1}{(\sqrt{3})}, \frac{1}{3 (\sqrt{3})} . . . . .$ The $19^{th}$ term of the above sequence is .

Discussion

12.	Question 13 Find the sum of first 15 multiples of 8.
Answer» Question 13 Find the sum of first 15 multiples of 8.

Discussion

13.	Locus of a point which is at a distance of 3 cm from the point O in the given diagram is:
Answer» Locus of a point which is at a distance of 3 cm from the point O in the given diagram is:

Discussion

14.	In the given right triangle ABC, right angled at B, the hypotenuse, base and perpendicular are _____________ respectively.
Answer» In the given right triangle ABC, right angled at B, the hypotenuse, base and perpendicular are _____________ respectively.

Discussion

15.	If xacosθ+ybsinθ=1 and xasinθ−ybcosθ=1, then which of the following equations is true ?
Answer» If $\frac{x}{a} c o s θ + \frac{y}{b} s i n θ = 1$ and $\frac{x}{a} s i n θ - \frac{y}{b} c o s θ = 1,$ then which of the following equations is true ?

Discussion

16.	The 16th term of an AP is five times its third term. If its 10th term is 41, then find the sum of its first fifteen terms.
Answer» The $16^{t h}$ term of an AP is five times its third term. If its $10^{t h}$ term is 41, then find the sum of its first fifteen terms.

Discussion

17.	Question 3 A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.
Answer» Question 3 A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

Discussion

18.	Question 4 Prove that through a given point, we can draw only one perpendicular to a given line.
Answer» Question 4 Prove that through a given point, we can draw only one perpendicular to a given line.

Discussion

19.	Find the circumference of the circle, whose area is 144 cm2.
Answer» Find the circumference of the circle, whose area is 144 cm².

Discussion

20.	Question 7 The distribution below gives the weights of 30 students of a class. Find the median weight of the students. Weight (in kg)40−4545−5050−5555−6060−6565−7070−75Number of students 2386632
Answer» Question 7 The distribution below gives the weights of 30 students of a class. Find the median weight of the students. $\begin{matrix} W e i g h t (i n k g) & 40 - 45 & 45 - 50 & 50 - 55 & 55 - 60 & 60 - 65 & 65 - 70 & 70 - 75 N u m b e r o f s t u d e n t s & 2 & 3 & 8 & 6 & 6 & 3 & 2 \end{matrix}$

Discussion

21.	Question 4 (xiii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xiii) √3,√6,√9,√12……
Answer» Question 4 (xiii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xiii) $\sqrt{3}, \sqrt{6}, \sqrt{9}, \sqrt{12} \dots \dots$

Discussion

22.	If the polynomial 6x4+8x3+17x2+21x+7 is divided by another polynomial 3x2+4x+1, the remainder comes out to be ax+b, find a and b. [4 MARKS]
Answer» If the polynomial $6 x^{4} + 8 x^{3} + 17 x^{2} + 21 x + 7$ is divided by another polynomial $3 x^{2} + 4 x + 1$ , the remainder comes out to be $a x + b$ , find a and b. [4 MARKS]

Discussion

23.	Find the probability of getting a multiple of 2 on one die and a multiple of 3 on the other die, if pair of dice are thrown.
Answer» Find the probability of getting a multiple of 2 on one die and a multiple of 3 on the other die, if pair of dice are thrown.

Discussion

24.	If Zeba had been younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. Her actual age now is ___ years.
Answer» If Zeba had been younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. Her actual age now is ___ years.

24.

If Zeba had been younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. Her actual age now is ___ years.

Answer»

If Zeba had been younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. Her actual age now is ___ years.

Discussion

25.	Question 8 Find the area of the shaded field shown in figure.
Answer» Question 8 Find the area of the shaded field shown in figure.

Discussion

26.	Question 9 Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.
Answer» Question 9 Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.

Discussion

27.	The measurements of the lateral surface of a square pyramid are shown in the figure. What are the slant height and the base edge of the pyramid respectively?
Answer» The measurements of the lateral surface of a square pyramid are shown in the figure. What are the slant height and the base edge of the pyramid respectively?

Discussion

28.	In a triangle ABC right angled at B, ∠ACB=θ. If tan θ=34,then find sin θ.
Answer» In a triangle ABC right angled at B, $∠ A C B = θ .$ $If t a n θ = \frac{3}{4}, then find s i n θ$ .

Discussion

29.	In a right angled triangle ABC right angled at B, 5×sinA=3. Find the value of cosC + tanA + cosecC.
Answer» In a right angled triangle ABC right angled at B, $5 \times s i n A = 3$ . Find the value of cosC + tanA + cosecC.

Discussion

30.	If the sides of a triangle measure 72,75 and 21, what is the measure of its inradius
Answer» If the sides of a triangle measure 72,75 and 21, what is the measure of its inradius

Discussion

31.	Find the value of k, if (x −1) is a factor of p(x) in the following case: p(x)=2x2+kx+√2
Answer» Find the value of k, if (x −1) is a factor of p(x) in the following case: $p (x) = {2 x}^{2} + k x + \sqrt{2}$

Discussion

32.	The distance between the points (a cos25∘,0) and (0,a cos65∘) is ___.
Answer» The distance between the points $(a c o s 25^{\circ}, 0)$ and $(0, a c o s 65^{\circ})$ is ___.

Discussion

33.	Write the truth value (T/F) of each of the following statements. (i) Any two similar figures are congruent. (ii) Any two congruent figures are similar. (iii) Two polygons are similar, if their corresponding sides are porportional (iv) Two polygons are similar, if their corresponding angles are porportional (v) Two triangles are similar if their corresponding angles are proportional. (v) Two triangles are similar if their corresponding angles are equal.
Answer» Write the truth value (T/F) of each of the following statements. (i) Any two similar figures are congruent. (ii) Any two congruent figures are similar. (iii) Two polygons are similar, if their corresponding sides are porportional (iv) Two polygons are similar, if their corresponding angles are porportional (v) Two triangles are similar if their corresponding angles are proportional. (v) Two triangles are similar if their corresponding angles are equal.

Discussion

34.	S(n) represents the sum of the first n natural numbers. Sort the following in the decreasing order:
Answer» $S (n)$ represents the sum of the first n natural numbers. Sort the following in the decreasing order:

Discussion

35.	Question 2 If AB = QR, BC+PR and CA = PQ, then (A) ΔABC≅ΔPQR (B) ΔCBA≅ΔPQR (C) ΔBAC≅ΔBCA (D) ΔPQR≅ΔBCA
Answer» Question 2 If AB = QR, BC+PR and CA = PQ, then (A) $Δ A B C ≅ Δ P Q R$ (B) $Δ C B A ≅ Δ P Q R$ (C) $Δ B A C ≅ Δ B C A$ (D) $Δ P Q R ≅ Δ B C A$

Discussion

36.	A coin is tossed 4 times. Match the probability of the different outcomes given below.
Answer» A coin is tossed 4 times. Match the probability of the different outcomes given below.

Discussion

37.	The angles of elevation of the top of a tower from two points on the ground at distances a metres and b metres from the base of the tower and in the same straight line are complemetary. Prove that the height of the tower is √ab metres. [4 MARKS]
Answer» The angles of elevation of the top of a tower from two points on the ground at distances a metres and b metres from the base of the tower and in the same straight line are complemetary. Prove that the height of the tower is $\sqrt{a b}$ metres. [4 MARKS]

Discussion

38.	From a window (h metres high above the ground) of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are θ and ϕ respectively. Find the height of the opposite house.
Answer» From a window (h metres high above the ground) of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are $θ$ and $ϕ$ respectively. Find the height of the opposite house.

Discussion

39.	A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8, if a page is chosen at random?
Answer» A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8, if a page is chosen at random?

Discussion

40.	Which of the following forms can be used to represent any positive even integer? (Note: q > 0)
Answer» Which of the following forms can be used to represent any positive even integer? (Note: q > 0)

Discussion

41.	The line segment AB was divided in the ratio 4:7 by taking 2 rays. The number of arcs to be made on the ray AX is:
Answer» The line segment AB was divided in the ratio 4:7 by taking 2 rays. The number of arcs to be made on the ray AX is:

Discussion

42.	Question 11 (i) State whether the following are true or false. Justify your answer. (i) The value of tan A is always less than 1.
Answer» Question 11 (i) State whether the following are true or false. Justify your answer. (i) The value of tan A is always less than 1.

Discussion

43.	Write the converse and contrapositive of each of the following statements: (i) If n is an even number, then n2 is even. (ii) If two integers a and b are such that a>b, then (a−b) is always a positive integer. (iii) If a ΔABC is right angled at B, then AB2+BC2=AC2. (iv) If ΔABC and ΔDEF are congruent, then they are equiangular. (v) You cannot comprehend geometry if you do not know how to reason deductively. (vi) Something is cold implies that it has low temperature.
Answer» Write the converse and contrapositive of each of the following statements: (i) If n is an even number, then $n^{2}$ is even. (ii) If two integers a and b are such that $a > b,$ then $(a - b)$ is always a positive integer. (iii) If a $Δ A B C$ is right angled at B, then $A B^{2} + B C^{2} = A C^{2} .$ (iv) If $Δ A B C$ and $Δ D E F$ are congruent, then they are equiangular. (v) You cannot comprehend geometry if you do not know how to reason deductively. (vi) Something is cold implies that it has low temperature.

43.

Write the converse and contrapositive of each of the following statements: (i) If n is an even number, then n2 is even. (ii) If two integers a and b are such that a>b, then (a−b) is always a positive integer. (iii) If a ΔABC is right angled at B, then AB2+BC2=AC2. (iv) If ΔABC and ΔDEF are congruent, then they are equiangular. (v) You cannot comprehend geometry if you do not know how to reason deductively. (vi) Something is cold implies that it has low temperature.

Answer»

Write the converse and contrapositive of each of the following statements:

(i) If n is an even number, then $n^{2}$ is even.

(ii) If two integers a and b are such that $a > b,$ then $(a - b)$ is always a positive integer.

(iii) If a $Δ A B C$ is right angled at B, then $A B^{2} + B C^{2} = A C^{2} .$

(iv) If $Δ A B C$ and $Δ D E F$ are congruent, then they are equiangular.

(v) You cannot comprehend geometry if you do not know how to reason deductively.

(vi) Something is cold implies that it has low temperature.

Discussion

44.	Find the highest positive integer by which dividing the numbers 396,436,542 remainders 5,11&15 respectively.
Answer» Find the highest positive integer by which dividing the numbers 396,436,542 remainders 5,11&15 respectively.

Discussion

45.	P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that: I)DP:PL=DC:BL ii)DL:DP =AL:DC
Answer» P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that: I)DP:PL=DC:BL ii)DL:DP =AL:DC

45.

P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that: I)DP:PL=DC:BL ii)DL:DP =AL:DC

Answer»

P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that:

I)DP:PL=DC:BL

ii)DL:DP =AL:DC

Discussion

46.	Median of the data given below will lie in the class
Answer» Median of the data given below will lie in the class

46.

Median of the data given below will lie in the class

Answer»

Median of the data given below will lie in the class

Discussion

47.	In an examination, one mark is awarded for every correct answer, while 1/4 mark is deducted for every wrong answer. A student answered 120 questions and got 20 marks. Which of the following pair of equations would give the result for how many questions did he answered correctly?
Answer» In an examination, one mark is awarded for every correct answer, while 1/4 mark is deducted for every wrong answer. A student answered 120 questions and got 20 marks. Which of the following pair of equations would give the result for how many questions did he answered correctly?

Discussion

48.	The slope of a line segment whose inclination is 135∘ is __
Answer» The slope of a line segment whose inclination is $135^{\circ}$ is __

Discussion

49.	Process in which the blastocyst gets attached to the walls of the uterus
Answer» Process in which the blastocyst gets attached to the walls of the uterus

Discussion

50.	Which of the following is the graphical representation of the line 2x - y = 10?
Answer» Which of the following is the graphical representation of the line 2x - y = 10?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the H.C.F of 16a2b3x4y5, 40 a3b2x3y4 and 24 a5b5x6y4

Which of the following equations has x = 3, y = - 4 as solution?

Question 1(vii) Check whether the following are quadratic equations: (vii) (x+2)3=2x(x2−1)

Question 2 (ii) Fill in the blanks: (ii) A line intersecting a circle at two points is called a___.

Check if (x−2)2+1=2x–3 is a quadratic equation or not. Enter your answer Y/N accordingly in the given space.___

Suppose p denotes the perimeter of a triangle with sides a, b and c and s is the semi perimeter and r is the inradius. If A denotes the area of the triangle, select the statements that are true.

If the sum of first 10 natural numbers is S1 and that of first 10 whole numbers is S2. Then S1−S2 is

A corn cob shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length as 20 cm. If each 1 sq cm of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob? [4 MARKS]

The sum of n natural numbers is 5n2+4n. Find its 8th term.

√3,1(√3),13(√3)..... The 19th term of the above sequence is .

Question 13 Find the sum of first 15 multiples of 8.

Locus of a point which is at a distance of 3 cm from the point O in the given diagram is:

In the given right triangle ABC, right angled at B, the hypotenuse, base and perpendicular are _____________ respectively.

If xacosθ+ybsinθ=1 and xasinθ−ybcosθ=1, then which of the following equations is true ?

The 16th term of an AP is five times its third term. If its 10th term is 41, then find the sum of its first fifteen terms.

Question 3 A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

Question 4 Prove that through a given point, we can draw only one perpendicular to a given line.

Find the circumference of the circle, whose area is 144 cm2.

Question 7 The distribution below gives the weights of 30 students of a class. Find the median weight of the students. Weight (in kg)40−4545−5050−5555−6060−6565−7070−75Number of students 2386632

Question 4 (xiii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xiii) √3,√6,√9,√12……

If the polynomial 6x4+8x3+17x2+21x+7 is divided by another polynomial 3x2+4x+1, the remainder comes out to be ax+b, find a and b. [4 MARKS]

Find the probability of getting a multiple of 2 on one die and a multiple of 3 on the other die, if pair of dice are thrown.

If Zeba had been younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. Her actual age now is ___ years.

Question 8 Find the area of the shaded field shown in figure.

Question 9 Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.

The measurements of the lateral surface of a square pyramid are shown in the figure. What are the slant height and the base edge of the pyramid respectively?

In a triangle ABC right angled at B, ∠ACB=θ. If tan θ=34,then find sin θ.

In a right angled triangle ABC right angled at B, 5×sinA=3. Find the value of cosC + tanA + cosecC.

If the sides of a triangle measure 72,75 and 21, what is the measure of its inradius

Find the value of k, if (x −1) is a factor of p(x) in the following case: p(x)=2x2+kx+√2

The distance between the points (a cos25∘,0) and (0,a cos65∘) is ___.

S(n) represents the sum of the first n natural numbers. Sort the following in the decreasing order:

Question 2 If AB = QR, BC+PR and CA = PQ, then (A) ΔABC≅ΔPQR (B) ΔCBA≅ΔPQR (C) ΔBAC≅ΔBCA (D) ΔPQR≅ΔBCA

A coin is tossed 4 times. Match the probability of the different outcomes given below.

The angles of elevation of the top of a tower from two points on the ground at distances a metres and b metres from the base of the tower and in the same straight line are complemetary. Prove that the height of the tower is √ab metres. [4 MARKS]

From a window (h metres high above the ground) of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are θ and ϕ respectively. Find the height of the opposite house.

A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8, if a page is chosen at random?

Which of the following forms can be used to represent any positive even integer? (Note: q &gt; 0)

The line segment AB was divided in the ratio 4:7 by taking 2 rays. The number of arcs to be made on the ray AX is:

Question 11 (i) State whether the following are true or false. Justify your answer. (i) The value of tan A is always less than 1.

Find the highest positive integer by which dividing the numbers 396,436,542 remainders 5,11&15 respectively.

P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that: I)DP:PL=DC:BL ii)DL:DP =AL:DC

Median of the data given below will lie in the class

In an examination, one mark is awarded for every correct answer, while 1/4 mark is deducted for every wrong answer. A student answered 120 questions and got 20 marks. Which of the following pair of equations would give the result for how many questions did he answered correctly?

The slope of a line segment whose inclination is 135∘ is __

Process in which the blastocyst gets attached to the walls of the uterus

Which of the following is the graphical representation of the line 2x - y = 10?

Which of the following forms can be used to represent any positive even integer? (Note: q > 0)