32581 + Interview Questions in Mathematics

1.	In the given figure, A is the centre of the circle. ∠ABC = 45° and AC = 72cm. Find the area of segment BXC.
Answer» In the given figure, A is the centre of the circle. $∠$ ABC = 45^°and AC = 7 $\sqrt{2}$ cm. Find the area of segment BXC.

Discussion

2.	In the given figure, chords AB and CD when extended meet at P. If AB = 4 cm, BP = 6 cm, DP = 5 cm, then find the value of CD.
Answer» In the given figure, chords AB and CD when extended meet at P. If AB = 4 cm, BP = 6 cm, DP = 5 cm, then find the value of CD.

Discussion

3.	If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay. [4 MARKS]
Answer» If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay. [4 MARKS]

Discussion

4.	The present age of a woman is 3 years more than three times the of her daughter.Three years hence,the woman's age will be 10 years more than twice the age of her daughter.Find their present ages.
Answer» The present age of a woman is 3 years more than three times the of her daughter.Three years hence,the woman's age will be 10 years more than twice the age of her daughter.Find their present ages.

Discussion

5.	From a point 30 m away from the foot of a tower, if the angle of elevation of the top of the tower is 45°, then the height of the tower is ___m.
Answer» From a point 30 m away from the foot of a tower, if the angle of elevation of the top of the tower is 45°, then the height of the tower is ___m.

5.

From a point 30 m away from the foot of a tower, if the angle of elevation of the top of the tower is 45°, then the height of the tower is ___m.

Answer»

From a point 30 m away from the foot of a tower, if the angle of elevation of the top of the tower is 45°, then the height of the tower is ___m.

Discussion

6.	In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.( Assume that three consecutive terms in A.P. are a – d , a , a + d .)
Answer» In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms. ( Assume that three consecutive terms in A.P. are a – d , a , a + d .)

Discussion

7.	Using Euclid’s division algorithm, find the HCF of (i) 405 and 2520 (ii) 504 and 1188 (iii) 960 and 1575
Answer» Using Euclid’s division algorithm, find the HCF of (i) 405 and 2520 (ii) 504 and 1188 (iii) 960 and 1575

7.

Using Euclid’s division algorithm, find the HCF of (i) 405 and 2520 (ii) 504 and 1188 (iii) 960 and 1575

Answer»

Using Euclid’s division algorithm, find the HCF of

(i) 405 and 2520 (ii) 504 and 1188 (iii) 960 and 1575

Discussion

8.	x ∝ y and x ∝ 1z. if y = 4, z = 5 , then x = 2. Now, if y = 20 and z = 25 ,then x =
Answer» x ∝ y and x ∝ $\frac{1}{z}$ . if y = 4, z = 5 , then x = 2. Now, if y = 20 and z = 25 ,then x =

Discussion

9.	SRCC Ltd. has issued on 1st April, 2017, 20,000, 12% Debentures of ₹ 100 each redeemable by draw of lots as under:During the year ended on 31st March, 2018 : 15%During the year ended on 31st March, 2019 : 25%During the year ended on 31st March, 2020 : 15%During the year ended on 31st March, 2021 : 25%During the year ended on 31st March, 2022 : 20%How much minimum investment should be made by SRCC Ltd. as per Companies Act, 2013 before redemption of debentures? When should it be made?
Answer» SRCC Ltd. has issued on 1st April, 2017, 20,000, 12% Debentures of ₹ 100 each redeemable by draw of lots as under: During the year ended on 31st March, 2018 : 15% During the year ended on 31st March, 2019 : 25% During the year ended on 31st March, 2020 : 15% During the year ended on 31st March, 2021 : 25% During the year ended on 31st March, 2022 : 20% How much minimum investment should be made by SRCC Ltd. as per Companies Act, 2013 before redemption of debentures? When should it be made?

Discussion

10.	ABC is a right triangle right angle at B such that BC = 6 cm and AB = 8 cm. The radius of its in-circle is
Answer» ABC is a right triangle right angle at B such that BC = 6 cm and AB = 8 cm. The radius of its in-circle is

10.

ABC is a right triangle right angle at B such that BC = 6 cm and AB = 8 cm. The radius of its in-circle is

Answer»

ABC is a right triangle right angle at B such that BC = 6 cm and AB = 8 cm. The radius of its in-circle is

Discussion

11.	The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the orginal cone, determine at what height above the base the section in made.
Answer» The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the orginal cone, determine at what height above the base the section in made.

Discussion

12.	If an equal number of largest possible squares are removed from this rectangular sheet of paper, what fraction of the paper will be left unused?
Answer» If an equal number of largest possible squares are removed from this rectangular sheet of paper, what fraction of the paper will be left unused?

Discussion

13.	137.If ab/ a + b = 2, ac/ a + c = 5, bc/ b + c = 9 then find a + b + c
Answer» 137.If ab/ a + b = 2, ac/ a + c = 5, bc/ b + c = 9 then find a + b + c

Discussion

14.	Question 3The angle of elevation of the top of a tower from a certain point is 30∘. If the observer moves 20m towards the tower, the angle of elevation of the top increases by 15∘. Find the height of the tower.
Answer» Question 3 The angle of elevation of the top of a tower from a certain point is $30^{\circ}$ . If the observer moves 20m towards the tower, the angle of elevation of the top increases by $15^{\circ}$ . Find the height of the tower.

Discussion

15.	The length of the arc of a sector of angle θ° of a circle of radius r is ___________.
Answer» The length of the arc of a sector of angle θ° of a circle of radius r is ___________.

Discussion

16.	The component of vector i+j in the direction of 3i+4j is
Answer» The component of vector i+j in the direction of 3i+4j is

Discussion

17.	The probability that a marksman will hit a target is given as 15. Then the probability that he hits at least once in 10 shots is
Answer» The probability that a marksman will hit a target is given as $\frac{1}{5} .$ Then the probability that he hits at least once in $10$ shots is

Discussion

18.	Question 5Factorise:(i) 4x2+9y2+16z2+12xy−24yz−16xz(ii) 2x2+y2+8z2−2√2xy+4√2yz−8xz
Answer» Question 5 Factorise: $(i) 4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z (i i) 2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 x z$

Discussion

19.	A single die is rolled. Find the probability of the sum of the five visible faces being greater than or equal to 19.
Answer» A single die is rolled. Find the probability of the sum of the five visible faces being greater than or equal to 19.

Discussion

20.	If ABC is an isosceles triangle and D is a point of BC such that AD ⊥ BC, then(a) AB2 − AD2 = BD.DC(b) AB2 − AD2 = BD2 − DC2(c) AB2 + AD2 = BD.DC(d) AB2 + AD2 = BD2 − DC2
Answer» If ABC is an isosceles triangle and D is a point of BC such that AD ⊥ BC, then (a) AB² − AD² = BD.DC (b) AB² − AD² = BD² − DC² (c) AB² + AD² = BD.DC (d) AB² + AD² = BD² − DC²

Discussion

21.	How many two-digit numbers are divisible by 6? [CBSE 2011]
Answer» How many two-digit numbers are divisible by 6? [CBSE 2011]

Discussion

22.	Manish Ltd. issued ₹ 40,00,000; 8% Debentures of ₹ 100 each on 1st April, 2017. The terms of issue stated that the debentures are to be redeemed at a premium of 5% on 30th June, 2019. The company decided to transfer ₹ 10,00,000 out of profits to Debentures Redemption Reserve on 31st March, 2018 and ₹ 10,00,000 on 31st March, 2019.Pass Journal entries regarding the issue and redemption of debentures, DRR and Investment without providing for the interest or loss on issue of debentures.
Answer» Manish Ltd. issued ₹ 40,00,000; 8% Debentures of ₹ 100 each on 1st April, 2017. The terms of issue stated that the debentures are to be redeemed at a premium of 5% on 30th June, 2019. The company decided to transfer ₹ 10,00,000 out of profits to Debentures Redemption Reserve on 31st March, 2018 and ₹ 10,00,000 on 31st March, 2019. Pass Journal entries regarding the issue and redemption of debentures, DRR and Investment without providing for the interest or loss on issue of debentures.

Discussion

23.	what is the dis†an ce between the octahedral void present on edge and the octahedral void present on centre in fc
Answer» what is the dis†an ce between the octahedral void present on edge and the octahedral void present on centre in fc

Discussion

24.	Solve 5x−2>3 and represent the solution set on the number line
Answer» Solve $\frac{5}{x - 2} > 3$ and represent the solution set on the number line

Discussion

25.	Volume of a sphere, V is increasing at a constant rate At the moment when volume of is V0, the rate of change of radius is
Answer» Volume of a sphere, V is increasing at a constant rate At the moment when volume of is V0, the rate of change of radius is

Discussion

26.	For some integer m, every integer is of the form (a) m (b) m + 1 (c) 2m (d) 2m+ 1
Answer» For some integer m, every integer is of the form (a) m (b) m + 1 (c) 2m (d) 2m+ 1

Discussion

27.	What is the distance between the points (0,4) and (-3,0)?
Answer» What is the distance between the points (0,4) and (-3,0)?

Discussion

28.	48. 2 (sin 45 raise to the power 4-cos cube 60)+(tan square 30cot square 45) is equal to ?
Answer» 48. 2 (sin 45 raise to the power 4-cos cube 60)+(tan square 30cot square 45) is equal to ?

Discussion

29.	a=(sinx-2)² b=(cosy-3)²Find amax+bmin
Answer» a=(sinx-2)² b=(cosy-3)² Find amax+bmin

Discussion

30.	Solve each of the following equations by using the method of completing the square:x2-6x+3=0
Answer» Solve each of the following equations by using the method of completing the square: $x^{2} - 6 x + 3 = 0$

Discussion

31.	Mr. Bijoy purchased 100 shares in a company at Rs 150 each. The company issues one bonus share for every two shares held by him. When the price of the shares fell to Rs 120 he sold the shares. Find his percentage gain.
Answer» Mr. Bijoy purchased 100 shares in a company at Rs 150 each. The company issues one bonus share for every two shares held by him. When the price of the shares fell to Rs 120 he sold the shares. Find his percentage gain.

Discussion

32.	If 4x – 8 ≤ 12, then the maximum value of x is ________.
Answer» If 4x – 8 $\leq$ 12, then the maximum value of x is ________.

Discussion

33.	Find the value of k for which each of the following system of equations have no solution :cx + 2y = 312x + cy = 6
Answer» Find the value of k for which each of the following system of equations have no solution : cx + 2y = 3 12x + cy = 6

Discussion

34.	If cot θ=13, show that 1-cos2 θ2-sin2 θ=35.
Answer» If $\cot θ = \frac{1}{\sqrt{3}}$ , show that $\frac{1 - \cos^{2} θ}{2 - \sin^{2} θ} = \frac{3}{5}$ .

Discussion

35.	The greatest angle of a triangle is equal to the sum of other two angles. The smallest angle is 7/13 of the greatest angle. Find all angles.
Answer» The greatest angle of a triangle is equal to the sum of other two angles. The smallest angle is 7/13 of the greatest angle. Find all angles.

Discussion

36.	Two corresponding sides of similar triangles are 3.6 cm and 2.4 cm, respectively. If the area of the bigger triangle is 45 sq. cm. Find the area of the smaller triangle.
Answer» Two corresponding sides of similar triangles are 3.6 cm and 2.4 cm, respectively. If the area of the bigger triangle is 45 sq. cm. Find the area of the smaller triangle.

Discussion

37.	Which of the following is a root of the equation x2 - 3√3 x + 6 = 0?
Answer» Which of the following is a root of the equation x² - 3√3 x + 6 = 0?

Discussion

38.	If the HCF of 408 and 1032 is expressible in the form 1032 m−408×5, find m.
Answer» If the HCF of 408 and 1032 is expressible in the form 1032 $m - 408 \times 5,$ find m.

Discussion

39.	Figure 2.23 show the graph of the polynomial f(x) = ax2 + bx + c for which(a) a < 0, b > 0 and c > 0(b) a < 0, b < 0 and c > 0(c) a < 0, b < 0 and c < 0(d) a > 0, b > 0 and c < 0
Answer» Figure 2.23 show the graph of the polynomial f(x) = ax² + bx + c for which (a) a < 0, b > 0 and c > 0 (b) a < 0, b < 0 and c > 0 (c) a < 0, b < 0 and c < 0 (d) a > 0, b > 0 and c < 0

Discussion

40.	When a die was rolled 60 times, the following was observed. [4 MARKS] Outcome 123456Frequency 910121379 (i) Which number had an experimental probability that matched the theoretical probability? (ii) How many numbers had an experimental probability that was less than that which would have been predicted by theoretical probability?
Answer» When a die was rolled 60 times, the following was observed. [4 MARKS] $\begin{matrix} Outcome & 1 & 2 & 3 & 4 & 5 & 6 Frequency & 9 & 10 & 12 & 13 & 7 & 9 \end{matrix}$ (i) Which number had an experimental probability that matched the theoretical probability? (ii) How many numbers had an experimental probability that was less than that which would have been predicted by theoretical probability?

40.

When a die was rolled 60 times, the following was observed. [4 MARKS] Outcome 123456Frequency 910121379 (i) Which number had an experimental probability that matched the theoretical probability? (ii) How many numbers had an experimental probability that was less than that which would have been predicted by theoretical probability?

Answer»

When a die was rolled 60 times, the following was observed. [4 MARKS]

$\begin{matrix} Outcome & 1 & 2 & 3 & 4 & 5 & 6 Frequency & 9 & 10 & 12 & 13 & 7 & 9 \end{matrix}$

(i) Which number had an experimental probability that matched the theoretical probability?

(ii) How many numbers had an experimental probability that was less than that which would have been predicted by theoretical probability?

Discussion

41.	In the given figure, ▢ABCD is a parallelogram. It circumscribes the circle with cnetre T. Point E, F, G, H are touching points. If AE = 4.5, EB = 5.5, find AD.
Answer» In the given figure, ▢ABCD is a parallelogram. It circumscribes the circle with cnetre T. Point E, F, G, H are touching points. If AE = 4.5, EB = 5.5, find AD.

Discussion

42.	Factorise : 3a2−1−2a
Answer» Factorise : $3 a^{2} - 1 - 2 a$

42.

Factorise : 3a2−1−2a

Answer»

Factorise :

$3 a^{2} - 1 - 2 a$

Discussion

43.	A bag contains tickets numbered 11, 12, 13, ..., 30. A ticket is taken out from the bag at random. Find the probability that the number on the drawn ticket (i) is a multiple of 7 (ii) is greater than 15 and a multiple of 5.
Answer» A bag contains tickets numbered 11, 12, 13, ..., 30. A ticket is taken out from the bag at random. Find the probability that the number on the drawn ticket (i) is a multiple of 7 (ii) is greater than 15 and a multiple of 5.

Discussion

44.	Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
Answer» Two poles of heights $6 m$ and $11 m$ stand on a plane ground. If the distance between their feet is $12 m$ , find the distance between their tops.

Discussion

45.	If lines L1:x2=y−2−1=z−11 and L2:x−1α=y+22+α=z−1 are coplanar, then the line L2 passes through point(s)
Answer» If lines $L_{1} : \frac{x}{2} = \frac{y - 2}{- 1} = \frac{z - 1}{1}$ and $L_{2} : \frac{x - 1}{α} = \frac{y + 2}{2 + α} = \frac{z}{- 1}$ are coplanar, then the line $L_{2}$ passes through point(s)

Discussion

46.	The values of k for which the quadratic equation 16x2+4kx+9=0 has real and equal roots are(a) 6, -16(b) 36, −36(c) 6, −6(d) 34, -34
Answer» The values of k for which the quadratic equation $16 x^{2} + 4 k x + 9 = 0$ has real and equal roots are (a) $6, - \frac{1}{6}$ (b) 36, −36 (c) 6, −6 (d) $\frac{3}{4}, - \frac{3}{4}$

Discussion

47.	From a point on a bridge across a river the angles of depression of the banks on opposite side of the river are 30° and 45° respectively. If bridge is at the height of 30 m from the banks, find the width of the river.
Answer» From a point on a bridge across a river the angles of depression of the banks on opposite side of the river are 30° and 45° respectively. If bridge is at the height of 30 m from the banks, find the width of the river.

Discussion

48.	If a = 0, what is the degree of the equation ax2 + bx + c = 0
Answer» If a = 0, what is the degree of the equation a $x^{2}$ + bx + c = 0

Discussion

49.	Two rectangular boxes have the same height and length, but different widths as shown in the figure.If the difference in the volumes of the boxes is 360 cm3, then what is the height of the boxes?
Answer» Two rectangular boxes have the same height and length, but different widths as shown in the figure. If the difference in the volumes of the boxes is 360 cm $^{3}$ , then what is the height of the boxes?

Discussion

50.	Find the value of x if x2−4(x\|+3=0
Answer» Find the value of x if $x^{2} - 4 (x \| + 3 = 0$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In the given figure, A is the centre of the circle. ∠ABC = 45° and AC = 72cm. Find the area of segment BXC.

In the given figure, chords AB and CD when extended meet at P. If AB = 4 cm, BP = 6 cm, DP = 5 cm, then find the value of CD.

If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay. [4 MARKS]

The present age of a woman is 3 years more than three times the of her daughter.Three years hence,the woman's age will be 10 years more than twice the age of her daughter.Find their present ages.

From a point 30 m away from the foot of a tower, if the angle of elevation of the top of the tower is 45°, then the height of the tower is ___m.

In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.( Assume that three consecutive terms in A.P. are a – d , a , a + d .)

Using Euclid’s division algorithm, find the HCF of (i) 405 and 2520 (ii) 504 and 1188 (iii) 960 and 1575

x ∝ y and x ∝ 1z. if y = 4, z = 5 , then x = 2. Now, if y = 20 and z = 25 ,then x =

ABC is a right triangle right angle at B such that BC = 6 cm and AB = 8 cm. The radius of its in-circle is

The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the orginal cone, determine at what height above the base the section in made.

If an equal number of largest possible squares are removed from this rectangular sheet of paper, what fraction of the paper will be left unused?

137.If ab/ a + b = 2, ac/ a + c = 5, bc/ b + c = 9 then find a + b + c

Question 3The angle of elevation of the top of a tower from a certain point is 30∘. If the observer moves 20m towards the tower, the angle of elevation of the top increases by 15∘. Find the height of the tower.

The length of the arc of a sector of angle θ° of a circle of radius r is ___________.

The component of vector i+j in the direction of 3i+4j is

The probability that a marksman will hit a target is given as 15. Then the probability that he hits at least once in 10 shots is

Question 5Factorise:(i) 4x2+9y2+16z2+12xy−24yz−16xz(ii) 2x2+y2+8z2−2√2xy+4√2yz−8xz

A single die is rolled. Find the probability of the sum of the five visible faces being greater than or equal to 19.

If ABC is an isosceles triangle and D is a point of BC such that AD ⊥ BC, then(a) AB2 − AD2 = BD.DC(b) AB2 − AD2 = BD2 − DC2(c) AB2 + AD2 = BD.DC(d) AB2 + AD2 = BD2 − DC2

How many two-digit numbers are divisible by 6? [CBSE 2011]

what is the dis†an ce between the octahedral void present on edge and the octahedral void present on centre in fc

Solve 5x−2&gt;3 and represent the solution set on the number line

Volume of a sphere, V is increasing at a constant rate At the moment when volume of is V0, the rate of change of radius is

For some integer m, every integer is of the form (a) m (b) m + 1 (c) 2m (d) 2m+ 1

What is the distance between the points (0,4) and (-3,0)?

48. 2 (sin 45 raise to the power 4-cos cube 60)+(tan square 30cot square 45) is equal to ?

a=(sinx-2)² b=(cosy-3)²Find amax+bmin

Solve each of the following equations by using the method of completing the square:x2-6x+3=0

Mr. Bijoy purchased 100 shares in a company at Rs 150 each. The company issues one bonus share for every two shares held by him. When the price of the shares fell to Rs 120 he sold the shares. Find his percentage gain.

If 4x – 8 ≤ 12, then the maximum value of x is ________.

Find the value of k for which each of the following system of equations have no solution :cx + 2y = 312x + cy = 6

If cot θ=13, show that 1-cos2 θ2-sin2 θ=35.

The greatest angle of a triangle is equal to the sum of other two angles. The smallest angle is 7/13 of the greatest angle. Find all angles.

Two corresponding sides of similar triangles are 3.6 cm and 2.4 cm, respectively. If the area of the bigger triangle is 45 sq. cm. Find the area of the smaller triangle.

Which of the following is a root of the equation x2 - 3√3 x + 6 = 0?

If the HCF of 408 and 1032 is expressible in the form 1032 m−408×5, find m.

Figure 2.23 show the graph of the polynomial f(x) = ax2 + bx + c for which(a) a < 0, b > 0 and c > 0(b) a < 0, b < 0 and c > 0(c) a < 0, b < 0 and c < 0(d) a > 0, b > 0 and c < 0

In the given figure, ▢ABCD is a parallelogram. It circumscribes the circle with cnetre T. Point E, F, G, H are touching points. If AE = 4.5, EB = 5.5, find AD.

Factorise : 3a2−1−2a

A bag contains tickets numbered 11, 12, 13, ..., 30. A ticket is taken out from the bag at random. Find the probability that the number on the drawn ticket (i) is a multiple of 7 (ii) is greater than 15 and a multiple of 5.

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

If lines L1:x2=y−2−1=z−11 and L2:x−1α=y+22+α=z−1 are coplanar, then the line L2 passes through point(s)

The values of k for which the quadratic equation 16x2+4kx+9=0 has real and equal roots are(a) 6, -16(b) 36, −36(c) 6, −6(d) 34, -34

From a point on a bridge across a river the angles of depression of the banks on opposite side of the river are 30° and 45° respectively. If bridge is at the height of 30 m from the banks, find the width of the river.

If a = 0, what is the degree of the equation ax2 + bx + c = 0

Two rectangular boxes have the same height and length, but different widths as shown in the figure.If the difference in the volumes of the boxes is 360 cm3, then what is the height of the boxes?

Find the value of x if x2−4(x|+3=0

Solve 5x−2>3 and represent the solution set on the number line