24740 + Interview Questions in Mathematics

1.	Identify constant, linear, quadratic, cubic and quartic polynomials from the following. (i) −7+x (ii) 6y (iii) −z3 (iv) 1−y−y3 (v) x−x3+x4 (vi) 1+x+x2 (viii) −6x2 (viii) −13 (ix) −p
Answer» Identify constant, linear, quadratic, cubic and quartic polynomials from the following. (i) $- 7 + x$ (ii) $6 y$ (iii) $- z^{3}$ (iv) $1 - y - y^{3}$ (v) $x - x^{3} + x^{4}$ (vi) $1 + x + x^{2}$ (viii) $- 6 x^{2}$ (viii) $- 13$ (ix) $- p$

1.

Identify constant, linear, quadratic, cubic and quartic polynomials from the following. (i) −7+x (ii) 6y (iii) −z3 (iv) 1−y−y3 (v) x−x3+x4 (vi) 1+x+x2 (viii) −6x2 (viii) −13 (ix) −p

Answer»

Identify constant, linear, quadratic, cubic and quartic polynomials from the following.

(i) $- 7 + x$

(ii) $6 y$

(iii) $- z^{3}$

(iv) $1 - y - y^{3}$

(v) $x - x^{3} + x^{4}$

(vi) $1 + x + x^{2}$

(viii) $- 6 x^{2}$

(viii) $- 13$

(ix) $- p$

Discussion

2.	The perimeter and area of a sector are 18 and 20cm^2 resp. Then find length of arc?
Answer» The perimeter and area of a sector are 18 and 20cm^2 resp. Then find length of arc?

Discussion

3.	The difference between the compound interest and the simple interest accured on an amount of ₹18000 in 2 years was ₹405. Find the rate of interest per annum?
Answer» The difference between the compound interest and the simple interest accured on an amount of ₹18000 in 2 years was ₹405. Find the rate of interest per annum?

Discussion

4.	The points scored by a Volleyball team in a series of matches are as follows:17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28Find the median of the scores.12
Answer» The points scored by a Volleyball team in a series of matches are as follows: 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28 Find the median of the scores. 12

Discussion

5.	what is the sign of c if the parobola or the graph of the polynomial does not cut the y axis
Answer» what is the sign of c if the parobola or the graph of the polynomial does not cut the y axis

Discussion

6.	Question 5 (iv) In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that: (iv) ar(BFE) = ar(AFD)
Answer» Question 5 (iv) In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that: (iv) ar(BFE) = ar(AFD)

Discussion

7.	cos1∘ × cos2∘ × cos3∘ ×……..× cos180∘ is equal to _________ .
Answer» cos $1^{\circ}$ $\times$ cos $2^{\circ}$ $\times$ cos $3^{\circ}$ $\times$ …….. $\times$ cos $180^{\circ}$ is equal to _________ .

Discussion

8.	Match the volume of the cone of radius 'r' cm, height 'h' cm and slant height 'l' cm in each case .
Answer» Match the volume of the cone of radius 'r' cm, height 'h' cm and slant height 'l' cm in each case .

Discussion

9.	The volume of a cube is 2744 cm3. Its surface area is __________.
Answer» The volume of a cube is 2744 cm³. Its surface area is __________.

Discussion

10.	Metal M1 and M2 crystallise in body centred cubic lattice and face centred cubic lattice respectively. Density of both metal lattice is same if a1 = 0.5a2 (a = edge length of particular unit cell). The ratio of molar mass of metal M2 to that of M1 is
Answer» Metal $M_{1}$ and $M_{2}$ crystallise in body centred cubic lattice and face centred cubic lattice respectively. Density of both metal lattice is same if $a_{1}$ = 0.5 $a_{2}$ (a = edge length of particular unit cell). The ratio of molar mass of metal $M_{2}$ to that of $M_{1}$ is

Discussion

11.	If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that1V=2S 1a+1b+1c
Answer» If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that $\frac{1}{V} = \frac{2}{S} (\frac{1}{a} + \frac{1}{b} + \frac{1}{c})$

Discussion

12.	Question 7Which of the following figures satisfy the following property? -Has two pairs of congruent adjacent sides.
Answer» Question 7 Which of the following figures satisfy the following property? -Has two pairs of congruent adjacent sides.

Discussion

13.	Factorise:x2+2x-24
Answer» Factorise: $x^{2} + \sqrt{2} x - 24$

Discussion

14.	Question 1 (iii)ABCD is a quadrilateral in which P, Q,R and S are mid-points of the sides AB, BC, CD and DA ( see the given figure). AC is a diagonal. Show that:PQRS is a parallelogram
Answer» Question 1 (iii) ABCD is a quadrilateral in which P, Q,R and S are mid-points of the sides AB, BC, CD and DA ( see the given figure). AC is a diagonal. Show that: PQRS is a parallelogram

Discussion

15.	Find the sum of the squares of the following: √3√2+1,√3√2−1,√2√3
Answer» Find the sum of the squares of the following: $\frac{\sqrt{3}}{\sqrt{2} + 1}, \frac{\sqrt{3}}{\sqrt{2} - 1}, \frac{\sqrt{2}}{\sqrt{3}}$

Discussion

16.	In the given figure, D is the mid-point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that :(i) b2=p2+ax+a24(ii) c2=p2-ax+a24(iii) b2+c2=2p2+a22
Answer» In the given figure, D is the mid-point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that : (i) $b^{2} = p^{2} + a x + \frac{a^{2}}{4}$ (ii) $c^{2} = p^{2} - a x + \frac{a^{2}}{4}$ (iii) $b^{2} + c^{2} = 2 p^{2} + \frac{a^{2}}{2}$

Discussion

17.	If the operation ⊕ is defined by a⊕ b=a2+b2 for all real numbers ‘a’ and ‘b’, then (2⊕3)⊕4=
Answer» If the operation $\oplus$ is defined by $a \oplus b = a^{2} + b^{2}$ for all real numbers ‘a’ and ‘b’, then $(2 \oplus 3) \oplus 4 =$

Discussion

18.	Question 86 (vi) Using suitable identities, evaluate the following: (995)2
Answer» Question 86 (vi) Using suitable identities, evaluate the following: $(995)^{2}$

18.

Question 86 (vi) Using suitable identities, evaluate the following: (995)2

Answer»

Question 86 (vi)

Using suitable identities, evaluate the following:

$(995)^{2}$

Discussion

19.	Question 161Find the values of x and y in the following parallelogram.
Answer» Question 161 Find the values of x and y in the following parallelogram.

Discussion

20.	Factorize a3x3−3a2bx2+3ab2x−b3
Answer» Factorize $a^{3} x^{3} - 3 a^{2} b x^{2} + 3 a b^{2} x - b^{3}$

Discussion

21.	If the linear equation y=7x−4 is written in standard form, the standard form being ax+by+c=0, then what are the possible value of a,b,c?
Answer» If the linear equation $y = 7 x - 4$ is written in standard form, the standard form being $a x + b y + c = 0,$ then what are the possible value of $a, b, c$ ?

Discussion

22.	The number of rectangles of any size, excluding the squares from a rectangle of size 8 x 7
Answer» The number of rectangles of any size, excluding the squares from a rectangle of size 8 x 7

Discussion

23.	The argument of the complex number -1+i31+icos θ+i sinθ is ____________.
Answer» The argument of the complex number $(- 1 + i \sqrt{3}) (1 + i) (\cos θ + i \sin θ)$ is ____________.

Discussion

24.	On a particular day, the rainfall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is
Answer» On a particular day, the rainfall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is

Discussion

25.	Sameera spent 90% of her income and donated 3% for socially useful causes. If she left with Rs. 1750 at the end of the month, what was her actual income ?
Answer» Sameera spent 90% of her income and donated 3% for socially useful causes. If she left with Rs. 1750 at the end of the month, what was her actual income ?

Discussion

26.	Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11.
Answer» Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11.

Discussion

27.	Bisector AD of ∠BAC of ΔABC passes through the centre O of the circumcircle of ΔABC. Prove that AB = AC. [2 MARKS]
Answer» Bisector AD of $∠ B A C$ of $Δ A B C$ passes through the centre O of the circumcircle of $Δ A B C$ . Prove that AB = AC. [2 MARKS]

27.

Bisector AD of ∠BAC of ΔABC passes through the centre O of the circumcircle of ΔABC. Prove that AB = AC. [2 MARKS]

Answer»

Bisector AD of $∠ B A C$ of $Δ A B C$ passes through the centre O of the circumcircle of $Δ A B C$ . Prove that AB = AC. [2 MARKS]

Discussion

28.	How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?
Answer» How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?

Discussion

29.	If x=2 and y=3, what is the value of xx+yy ?
Answer» If x=2 and y=3, what is the value of $x^{x}$ + $y^{y}$ ?

Discussion

30.	In the figure given below, the radius of the circle is 84 cm. The angle in the sector is 60∘. What is the area of the minor segment APB?
Answer» In the figure given below, the radius of the circle is 84 cm. The angle in the sector is $60^{\circ}$ . What is the area of the minor segment APB?

Discussion

31.	Events E1, E2, E3 are the possible events of an experiment and their probabilities are recorded. Mark the possible correct answer
Answer» Events $E_{1}, E_{2}, E_{3}$ are the possible events of an experiment and their probabilities are recorded. Mark the possible correct answer

Discussion

32.	If tan θ=12, find the value of cosec2 θ-sec2 θcosec2 θ+cot2 θ.
Answer» If $\tan θ = \frac{1}{\sqrt{2}}$ , find the value of $\frac{{cosec}^{2} θ - \sec^{2} θ}{{cosec}^{2} θ + \cot^{2} θ}$ .

Discussion

33.	4[1 – sin2θ] [1 + tan2θ]
Answer» 4[1 – $s i n^{2} θ$ ] [1 + $t a n^{2} θ$ ]

Discussion

34.	In the adjoining figure, ABCD is a square. A line segment CX cuts AB at X and the diagonal BD at O such that ∠COD=80∘ and ∠OXA=x∘. Find the value of x.
Answer» In the adjoining figure, ABCD is a square. A line segment CX cuts AB at X and the diagonal BD at O such that $∠ C O D = 80^{\circ}$ and $∠ O X A = x^{\circ}$ . Find the value of x.

34.

In the adjoining figure, ABCD is a square. A line segment CX cuts AB at X and the diagonal BD at O such that ∠COD=80∘ and ∠OXA=x∘. Find the value of x.

Answer»

In the adjoining figure, ABCD is a square. A line segment CX cuts AB at X and the diagonal BD at O such that $∠ C O D = 80^{\circ}$ and $∠ O X A = x^{\circ}$ . Find the value of x.

Discussion

35.	The dimension of force is:
Answer» The dimension of force is:

Discussion

36.	The graph of the linear equation 2x+3y=6 cuts the y-axis at the point ___.
Answer» The graph of the linear equation $2 x + 3 y = 6$ cuts the y-axis at the point ___.

Discussion

37.	Question 31(ii) An integer is chosen between 0 and 100. What is the probability that it is not divisible by 7?
Answer» Question 31(ii) An integer is chosen between 0 and 100. What is the probability that it is not divisible by 7?

Discussion

38.	Which of the following are five irrational numbers between 2√5 and 3√3
Answer» Which of the following are five irrational numbers between $2 \sqrt{5}$ and $3 \sqrt{3}$

38.

Which of the following are five irrational numbers between 2√5 and 3√3

Answer»

Which of the following are five irrational numbers between $2 \sqrt{5}$

and $3 \sqrt{3}$

Discussion

39.	If x varies directly with y, and x1 = 15, y1 = 16, x2 = 25, then find the value of y2.
Answer» $If x varies directly with y,$ $a n d x_{1} = \frac{1}{5}, y_{1} = \frac{1}{6}, x_{2} = \frac{2}{5}, then find the value of y_{2} .$

Discussion

40.	Factorise: (ax+by)2+(bx−ay)2
Answer» Factorise: $(a x + b y)^{2} + (b x - a y)^{2}$

Discussion

41.	Explain remainder theorem.
Answer» Explain remainder theorem.

Discussion

42.	Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each.(i) (ii) (iii) (iv) (v)
Answer» Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each. (i) (ii) (iii) (iv) (v)

42.

Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each.(i) (ii) (iii) (iv) (v)

Answer»

Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each.

(i)

(ii)

(iii)

(iv)

(v)

Discussion

43.	Define mean?
Answer» Define mean?

Discussion

44.	If the graph 2x−3y+6=0 intersects the x-axis at A, then find the coordinates of A.
Answer» If the graph $2 x - 3 y + 6 = 0$ intersects the x-axis at A, then find the coordinates of A.

Discussion

45.	Match the polynomials with their respective factors.
Answer» Match the polynomials with their respective factors.

Discussion

46.	In the adjoining figure, OPQR is a square. A circle drawn with centre O cuts the square in X and Y. Prove that QX = QY.
Answer» In the adjoining figure, OPQR is a square. A circle drawn with centre O cuts the square in X and Y. Prove that QX = QY.

46.

In the adjoining figure, OPQR is a square. A circle drawn with centre O cuts the square in X and Y. Prove that QX = QY.

Answer»

In the adjoining figure, OPQR is a square. A circle drawn with centre O cuts the square in X and Y. Prove that QX = QY.

Discussion

47.	In figure, ∠ACD=120∘ and ∠APB=100∘ ,(i) find x and y. (ii) If ∠BAC=2.5y, find ∠ABC.
Answer» In figure, $∠ A C D = 120^{\circ}$ and $∠ A P B = 100^{\circ}$ , (i) find x and y. (ii) If $∠ B A C = 2.5 y,$ find $∠ A B C$ .

47.

In figure, ∠ACD=120∘ and ∠APB=100∘ ,(i) find x and y. (ii) If ∠BAC=2.5y, find ∠ABC.

Answer»

In figure, $∠ A C D = 120^{\circ}$ and $∠ A P B = 100^{\circ}$ ,

(i) find x and y.

(ii) If $∠ B A C = 2.5 y,$ find $∠ A B C$ .

Discussion

48.	10. Let AB cuts of intercept of 7units and 7/3units on positive sides of axes . Find the number of integral values of map that x-coordinate of the point of intersection of lines mx+y=3and AB is also an integer.
Answer» 10. Let AB cuts of intercept of 7units and 7/3units on positive sides of axes . Find the number of integral values of map that x-coordinate of the point of intersection of lines mx+y=3and AB is also an integer.

Discussion

49.	A die is rolled once. Then the probability of getting a 7 is
Answer» A die is rolled once. Then the probability of getting a 7 is

Discussion

50.	In figure,∠AOB =35∘, find the reflex ∠ AOB.
Answer» In figure, $∠$ AOB = $35^{\circ}$ , find the reflex $∠$ AOB.

50.

In figure,∠AOB =35∘, find the reflex ∠ AOB.

Answer»

In figure, $∠$ AOB = $35^{\circ}$ , find the reflex $∠$ AOB.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Identify constant, linear, quadratic, cubic and quartic polynomials from the following. (i) −7+x (ii) 6y (iii) −z3 (iv) 1−y−y3 (v) x−x3+x4 (vi) 1+x+x2 (viii) −6x2 (viii) −13 (ix) −p

The perimeter and area of a sector are 18 and 20cm^2 resp. Then find length of arc?

The difference between the compound interest and the simple interest accured on an amount of ₹18000 in 2 years was ₹405. Find the rate of interest per annum?

The points scored by a Volleyball team in a series of matches are as follows:17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28Find the median of the scores.12

what is the sign of c if the parobola or the graph of the polynomial does not cut the y axis

Question 5 (iv) In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that: (iv) ar(BFE) = ar(AFD)

cos1∘ × cos2∘ × cos3∘ ×……..× cos180∘ is equal to _________ .

Match the volume of the cone of radius 'r' cm, height 'h' cm and slant height 'l' cm in each case .

The volume of a cube is 2744 cm3. Its surface area is __________.

Metal M1 and M2 crystallise in body centred cubic lattice and face centred cubic lattice respectively. Density of both metal lattice is same if a1 = 0.5a2 (a = edge length of particular unit cell). The ratio of molar mass of metal M2 to that of M1 is

If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that1V=2S 1a+1b+1c

Question 7Which of the following figures satisfy the following property? -Has two pairs of congruent adjacent sides.

Factorise:x2+2x-24

Question 1 (iii)ABCD is a quadrilateral in which P, Q,R and S are mid-points of the sides AB, BC, CD and DA ( see the given figure). AC is a diagonal. Show that:PQRS is a parallelogram

Find the sum of the squares of the following: √3√2+1,√3√2−1,√2√3

In the given figure, D is the mid-point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that :(i) b2=p2+ax+a24(ii) c2=p2-ax+a24(iii) b2+c2=2p2+a22

If the operation ⊕ is defined by a⊕ b=a2+b2 for all real numbers ‘a’ and ‘b’, then (2⊕3)⊕4=

Question 86 (vi) Using suitable identities, evaluate the following: (995)2

Question 161Find the values of x and y in the following parallelogram.

Factorize a3x3−3a2bx2+3ab2x−b3

If the linear equation y=7x−4 is written in standard form, the standard form being ax+by+c=0, then what are the possible value of a,b,c?

The number of rectangles of any size, excluding the squares from a rectangle of size 8 x 7

The argument of the complex number -1+i31+icos θ+i sinθ is ____________.

On a particular day, the rainfall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is

Sameera spent 90% of her income and donated 3% for socially useful causes. If she left with Rs. 1750 at the end of the month, what was her actual income ?

Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11.

Bisector AD of ∠BAC of ΔABC passes through the centre O of the circumcircle of ΔABC. Prove that AB = AC. [2 MARKS]

How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?

If x=2 and y=3, what is the value of xx+yy ?

In the figure given below, the radius of the circle is 84 cm. The angle in the sector is 60∘​. What is the area of the minor segment APB?

Events E1, E2, E3 are the possible events of an experiment and their probabilities are recorded. Mark the possible correct answer

If tan θ=12, find the value of cosec2 θ-sec2 θcosec2 θ+cot2 θ.

4[1 – sin2θ] [1 + tan2θ]

In the adjoining figure, ABCD is a square. A line segment CX cuts AB at X and the diagonal BD at O such that ∠COD=80∘ and ∠OXA=x∘. Find the value of x.

The dimension of force is:

The graph of the linear equation 2x+3y=6 cuts the y-axis at the point ___.

Question 31(ii) An integer is chosen between 0 and 100. What is the probability that it is not divisible by 7?

Which of the following are five irrational numbers between 2√5 and 3√3

If x varies directly with y, and x1 = 15, y1 = 16, x2 = 25, then find the value of y2.

Factorise: (ax+by)2+(bx−ay)2

Explain remainder theorem.

Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each.(i) (ii) (iii) (iv) (v)

Define mean?

If the graph 2x−3y+6=0 intersects the x-axis at A, then find the coordinates of A.

Match the polynomials with their respective factors.

In the adjoining figure, OPQR is a square. A circle drawn with centre O cuts the square in X and Y. Prove that QX = QY.

In figure, ∠ACD=120∘ and ∠APB=100∘ ,(i) find x and y. (ii) If ∠BAC=2.5y, find ∠ABC.

10. Let AB cuts of intercept of 7units and 7/3units on positive sides of axes . Find the number of integral values of map that x-coordinate of the point of intersection of lines mx+y=3and AB is also an integer.

A die is rolled once. Then the probability of getting a 7 is

In figure,∠AOB =35∘, find the reflex ∠ AOB.

In the figure given below, the radius of the circle is 84 cm. The angle in the sector is 60∘. What is the area of the minor segment APB?