32581 + Interview Questions in Mathematics

1.	what is a curvillinear trapezoid?
Answer» what is a curvillinear trapezoid?

Discussion

2.	Find a point on x + y = 10 where the Y coordinate is 1.5 times the X coordinate. [2 MARKS]
Answer» Find a point on x + y = 10 where the Y coordinate is 1.5 times the X coordinate. [2 MARKS]

Discussion

3.	→V=2^i+^j−^k and →W=^i+3^k. If →U is a unit vector, then the maximum value of the scalar triple product [→U →V →W] is
Answer» $\to V = 2^i +^j -^k$ and $\to W =^i + 3^k$ . If $\to U$ is a unit vector, then the maximum value of the scalar triple product $[\to U \to V \to W]$ is

Discussion

4.	Question 2 (iv)Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.1, 1
Answer» Question 2 (iv) Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 1, 1

4.

Question 2 (iv)Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.1, 1

Answer»

Question 2 (iv)

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

1, 1

Discussion

5.	If sin θ=32then cosec θ+cot θ=?(a) 2+3(b) 23(c) 2(d) 3
Answer» If $\sin θ = \frac{\sqrt{3}}{2} then (cosec θ + \cot θ) = ?$ (a) $(2 + \sqrt{3})$ (b) $2 \sqrt{3}$ (c) $\sqrt{2}$ (d) $\sqrt{3}$

Discussion

6.	A number is chosen at random from the number –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less then or equal to 1?
Answer» A number is chosen at random from the number –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less then or equal to 1?

Discussion

7.	Solve the following quadratic equations by factorization:3x2-26x+2=0
Answer» Solve the following quadratic equations by factorization: $3 x^{2} - 2 \sqrt{6} x + 2 = 0$

Discussion

8.	Find the distance between P(x1,y1) and Q(x2,y2) when :(i) PQ is parallel to the y− axis.(ii) PQ is parallel to the x− axis.
Answer» Find the distance between $P (x_{1}, y_{1})$ and $Q (x_{2}, y_{2})$ when : $(i) P Q$ is parallel to the $y -$ axis. $(i i) P Q$ is parallel to the $x -$ axis.

Discussion

9.	The radius and height of a cone are in the ratio 4: 3. The area of the base is 154 cm2. The area of the curved surface of cone is ___
Answer» The radius and height of a cone are in the ratio 4: 3. The area of the base is 154 cm². The area of the curved surface of cone is ___

Discussion

10.	Proof of sine law
Answer» Proof of sine law

Discussion

11.	In the given figure, PQ and PR are two tangents to a circle with centre O. If ∠QPR = 46º, then ∠QOR is(a) 67º (b) 134º (c) 44º (d) 46º [CBSE 2014]
Answer» In the given figure, PQ and PR are two tangents to a circle with centre O. If $∠$ QPR = 46º, then $∠$ QOR is (a) 67º (b) 134º (c) 44º (d) 46º [CBSE 2014]

Discussion

12.	Two circles of same radii r and centres O and O' touch each other at P as shown in Fig. 10.91. If O O' is produced to meet the cirele C (O', r) at A and AT is a tangent to the circle C (O,r) such that O'Q ⊥ AT. Then AO : AO' = (a) 3/2(b) 2(c) 3(d) 1/4
Answer» Two circles of same radii r and centres O and O' touch each other at P as shown in Fig. 10.91. If O O' is produced to meet the cirele C (O', r) at A and AT is a tangent to the circle C (O,r) such that O'Q $⊥$ AT. Then AO : AO' = (a) 3/2 (b) 2 (c) 3 (d) 1/4

Discussion

13.	Find the equation of a line with x intercept = 5 and passing through the point (4, –7).
Answer» Find the equation of a line with x intercept = 5 and passing through the point (4, –7).

Discussion

14.	A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kilometres away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is
Answer» A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kilometres away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is

Discussion

15.	\|2x+1\|-2\|x-2\|=5
Answer» \|2x+1\|-2\|x-2\|=5

Discussion

16.	two men on either side of a temple 75 M high have angles of elevation as 45 degree each.The distance between them is
Answer» two men on either side of a temple 75 M high have angles of elevation as 45 degree each.The distance between them is

Discussion

17.	In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides Ab, BC, CD and AD at P, Q, R and S respectively.If the radius of the circle is 10 cm, BC = 38 cm, PB = 27 cm and AD ⊥ CD then the length of CD is [CBSE 2013](a) 11 cm(b) 15 cm(c) 20 cm(d) 21 cm
Answer» In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides Ab, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is 10 cm, BC = 38 cm, PB = 27 cm and AD ⊥ CD then the length of CD is [CBSE 2013] (a) 11 cm (b) 15 cm (c) 20 cm (d) 21 cm

Discussion

18.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula: 2x2+5√3x+6=0
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $2 x^{2} + 5 \sqrt{3} x + 6 = 0$

Discussion

19.	If a hollow copper pipe of inner diameter 6cm and outer diameter 10cm is melted and changed into a solid right circular cylinder of the same height as that of the pipe,then the diameter of the solid cylinder is
Answer» If a hollow copper pipe of inner diameter 6cm and outer diameter 10cm is melted and changed into a solid right circular cylinder of the same height as that of the pipe,then the diameter of the solid cylinder is

Discussion

20.	The nth term of an AP is (3n + 5). Find its common difference.
Answer» The nth term of an AP is (3n + 5). Find its common difference.

Discussion

21.	if m and n are zeros of the quadratic polynomial f(x)= x^2-p(x+1)-c, show that (m+1)(n+1)=1-c
Answer» if m and n are zeros of the quadratic polynomial f(x)= x^2-p(x+1)-c, show that (m+1)(n+1)=1-c

Discussion

22.	Question 2 (ii)Show that : cos38∘cos52∘−sin38∘sin52∘=0
Answer» Question 2 (ii) Show that : $c o s 38^{\circ} c o s 52^{\circ} - s i n 38^{\circ} s i n 52^{\circ} = 0$

Discussion

23.	How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius 8 cm.
Answer» How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius 8 cm.

Discussion

24.	Solve the following quadratic equations by factorization:x2-2+1x+2=0
Answer» Solve the following quadratic equations by factorization: $x^{2} - (\sqrt{2} + 1) x + \sqrt{2} = 0$

Discussion

25.	If angle A and angle B are acute angels such that sin A = sin B than prove that A = B
Answer» If angle A and angle B are acute angels such that sin A = sin B than prove that A = B

Discussion

26.	Form the pair of linear equations in the following problems, and find their solution graphically: 5 pencil and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and a pen.
Answer» Form the pair of linear equations in the following problems, and find their solution graphically: 5 pencil and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and a pen.

26.

Form the pair of linear equations in the following problems, and find their solution graphically: 5 pencil and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and a pen.

Answer»

Form the pair of linear equations in the following problems, and find their solution graphically:

5 pencil and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and a pen.

Discussion

27.	Find the polynomial from the given information. Quotient =x3+2x Divisor =x2+12x Remainder =5
Answer» $Find the polynomial from the given information.$ $Quotient = x^{3} + 2 x$ $Divisor = x^{2} + \frac{1}{2} x$ $Remainder = 5$

Discussion

28.

Krishna and Arjun are partners in a firm . They share profits in the ratio of 4 : 1 . They decided to dissolve the firm on 31st March, 2018 at which date their Balance Sheet stood as: Liabilities Amount (₹) Assets Amount (₹) Bank Loan 1,500 Trademarks 1,200 Creditors for Goods 8,000 Machinery 12,000 Bills Payable 500 Furniture 400 Capital A/cs: Stock 6,000 Krishna 16,000 Debtors 9,000 Arjun 6,000 22,000 Less: Provision for Bad Debts 400 8,600 Cash at Bank 2,800 Advertisement Suspense 1,000 32,000 32,000 The realisation shows the following results:(a) Goodwill was sold for ₹ 1,000.(b) Debtors were realised at book value less 10%.(c) Trademarks were realised for ₹ 800.(d) Machinery and Stock-in-Trade were taken over by Krishna for ₹ 14,400 and ₹ 3,600 respectively.(e) An unrecorded asset estimated at ₹ 500 was sold for ₹ 200.(f) Creditors for goods were settled at a discount of ₹ 80 . The expenses on realisation were ₹ 800.Prepare Realisation Account, Partners' Capital Accounts and Bank Account.

Answer» Krishna and Arjun are partners in a firm . They share profits in the ratio of 4 : 1 . They decided to dissolve the firm on 31st March, 2018 at which date their Balance Sheet stood as:

Liabilities		Amount (₹)	Assets		Amount (₹)
Bank Loan		1,500	Trademarks		1,200
Creditors for Goods		8,000	Machinery		12,000
Bills Payable		500	Furniture		400
Capital A/cs:			Stock		6,000
Krishna	16,000		Debtors	9,000
Arjun	6,000	22,000	Less: Provision for Bad Debts	400	8,600
			Cash at Bank		2,800
			Advertisement Suspense		1,000

		32,000			32,000

The realisation shows the following results:

(a) Goodwill was sold for ₹ 1,000.

(b) Debtors were realised at book value less 10%.

(c) Trademarks were realised for ₹ 800.

(d) Machinery and Stock-in-Trade were taken over by Krishna for ₹ 14,400 and ₹ 3,600 respectively.

(e) An unrecorded asset estimated at ₹ 500 was sold for ₹ 200.

(f) Creditors for goods were settled at a discount of ₹ 80 . The expenses on realisation were ₹ 800.

Prepare Realisation Account, Partners' Capital Accounts and Bank Account.

Discussion

29.	Krish works in a mall and gets paid ₹70 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks
Answer» Krish works in a mall and gets paid ₹70 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks

Discussion

30.	24. A sum of 700 is to be used to give 7 cash prizes to students of a school for their overall academic performance . If each prize is 20 less than is preceeding prize
Answer» 24. A sum of 700 is to be used to give 7 cash prizes to students of a school for their overall academic performance . If each prize is 20 less than is preceeding prize

Discussion

31.	'Surya Electronics' purchased an AC having taxable value of ₹35000 and sold it to a consumer for ₹40000 (taxable value). Rate of GST is 18%. Find the GST payable by Surya Electronics.
Answer» 'Surya Electronics' purchased an AC having taxable value of ₹ $35000$ and sold it to a consumer for ₹ $40000$ (taxable value). Rate of GST is $18 %$ . Find the GST payable by Surya Electronics.

Discussion

32.	Find the area of the dotted portion if the dimensions are as specified in the figure. r = l4.
Answer» Find the area of the dotted portion if the dimensions are as specified in the figure. r = $\frac{l}{4}$ .

32.

Find the area of the dotted portion if the dimensions are as specified in the figure. r = l4.

Answer»

Find the area of the dotted portion if the dimensions are as specified in the figure. r = $\frac{l}{4}$ .

Discussion

33.	In the given figure, AOB is a diameter of the circle and C, D , E are any three points to semi circle then ∠ACD + ∠BED = _______
Answer» In the given figure, AOB is a diameter of the circle and C, D , E are any three points to semi circle then ∠ACD + ∠BED = _______

Discussion

34.	A person recorded the speed (in km/hr) of 10 motorists as 48, 52, 57, 55, 45, 39, 61, 49, 51 and 43. The average speed of the motorists is
Answer» A person recorded the speed (in km/hr) of 10 motorists as 48, 52, 57, 55, 45, 39, 61, 49, 51 and 43. The average speed of the motorists is

Discussion

35.	Find the single discount equivalent to two successive discount 50% and 60%
Answer» Find the single discount equivalent to two successive discount 50% and 60%

Discussion

36.	Calculate the area of shaded portion
Answer» Calculate the area of shaded portion

Discussion

37.	The expression a3+b3+c3−3abc can be expressed as a product of two expressions. What is the product?
Answer» The expression $a^{3} + b^{3} + c^{3} - 3 a b c$ can be expressed as a product of two expressions. What is the product?

Discussion

38.	ABCD is a quadrilateral in which the bisectors of angle-A and angle-C meet DC produced at Y and BA produced at X, respectively. Prove that angle-X+angle-Y=1/2(angle-A+angle-C)
Answer» ABCD is a quadrilateral in which the bisectors of angle-A and angle-C meet DC produced at Y and BA produced at X, respectively. Prove that angle-X+angle-Y=1/2(angle-A+angle-C)

Discussion

39.	Four points A (6, 3), B (-3, 5), C (4, -2) and D (x, 3x) are given in such a way that △DBC△ABC=12,find x.
Answer» Four points A (6, 3), B (-3, 5), C (4, -2) and D (x, 3x) are given in such a way that $\frac{△ D B C}{△ A B C} = \frac{1}{2},$ find x.

Discussion

40.	Evaluate: sec29∘cosec61∘ + 2cot8∘cot17∘cot45∘cot73∘cot82∘
Answer» Evaluate: $\frac{s e c 29^{\circ}}{c o s e c 61^{\circ}}$ + $2 c o t 8^{\circ} c o t 17^{\circ} c o t 45^{\circ} c o t 73^{\circ} c o t 82^{\circ}$

Discussion

41.	Reduce x2−25x2+10x+25 into its simpest form.
Answer» Reduce $\frac{x^{2} - 25}{x^{2} + 10 x + 25}$ into its simpest form.

Discussion

42.	Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla (a game in which you throw a rig on the items kept in the stall, and if the ring covers any object completely you get it). The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride cost Rs 3, and play Hoopla costs Rs 4. If she spent Rs in the fair, represent this situation algebraically and graphically.
Answer» Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla (a game in which you throw a rig on the items kept in the stall, and if the ring covers any object completely you get it). The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride cost Rs 3, and play Hoopla costs Rs 4. If she spent Rs in the fair, represent this situation algebraically and graphically.

Discussion

43.	If alpha , beta and gamma are zeroes of the polynomial x^3 + ax + b , then the value of alpha ^3 + beta^3 + gamma^3 is ___
Answer» If alpha , beta and gamma are zeroes of the polynomial x^3 + ax + b , then the value of alpha ^3 + beta^3 + gamma^3 is ___

Discussion

44.	Question 5 Cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m×16 m. Find the area of the field in which the cow can graze.
Answer» Question 5 Cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions $20 m \times 16 m$ . Find the area of the field in which the cow can graze.

Discussion

45.	Two numbers are selected at random from the numbers 1, 2, . .. . . n. The probability that the difference between the first and second is not less than m (where 0 < m < n), is
Answer» Two numbers are selected at random from the numbers 1, 2, . .. . . n. The probability that the difference between the first and second is not less than m (where 0 < m < n), is

Discussion

46.	The locus of the mid points of the chords of the circle x2+y2+2x−2y−2=0 which makes an angle of 90° at the centre is
Answer» The locus of the mid points of the chords of the circle $x^{2} + y^{2} + 2 x - 2 y - 2 = 0$ which makes an angle of $90 °$ at the centre is

Discussion

47.	If (a,a) lies between the lines \|x + y\| = 2, then a lies in the inteval ?
Answer» If (a,a) lies between the lines \|x + y\| = 2, then a lies in the inteval ?

Discussion

48.	If (x^3+ax^2+bx+6) has (x-2) as a factor and leaves a remainder 3 when divided by (x-3),find the values of a&b
Answer» If (x^3+ax^2+bx+6) has (x-2) as a factor and leaves a remainder 3 when divided by (x-3),find the values of a&b

Discussion

49.	64. Ratio of ranges of bullet fired from a gun at angle theta, 2 theta and 4 theta is found in the ratio x : 2 : 2 then the value of x will be (assume same speed of bullets)
Answer» 64. Ratio of ranges of bullet fired from a gun at angle theta, 2 theta and 4 theta is found in the ratio x : 2 : 2 then the value of x will be (assume same speed of bullets)

Discussion

50.	Find the sum of all multiples of 7 lying between 500 and 900.
Answer» Find the sum of all multiples of 7 lying between 500 and 900.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

what is a curvillinear trapezoid?

Find a point on x + y = 10 where the Y coordinate is 1.5 times the X coordinate. [2 MARKS]

→V=2^i+^j−^k and →W=^i+3^k. If →U is a unit vector, then the maximum value of the scalar triple product [→U →V →W] is

Question 2 (iv)Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.1, 1

If sin θ=32then cosec θ+cot θ=?(a) 2+3(b) 23(c) 2(d) 3

A number is chosen at random from the number –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less then or equal to 1?

Solve the following quadratic equations by factorization:3x2-26x+2=0

Find the distance between P(x1,y1) and Q(x2,y2) when :(i) PQ is parallel to the y− axis.(ii) PQ is parallel to the x− axis.

The radius and height of a cone are in the ratio 4: 3. The area of the base is 154 cm2. The area of the curved surface of cone is ___

Proof of sine law

In the given figure, PQ and PR are two tangents to a circle with centre O. If ∠QPR = 46º, then ∠QOR is(a) 67º (b) 134º (c) 44º (d) 46º [CBSE 2014]

Two circles of same radii r and centres O and O' touch each other at P as shown in Fig. 10.91. If O O' is produced to meet the cirele C (O', r) at A and AT is a tangent to the circle C (O,r) such that O'Q ⊥ AT. Then AO : AO' = (a) 3/2(b) 2(c) 3(d) 1/4

Find the equation of a line with x intercept = 5 and passing through the point (4, –7).

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kilometres away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is

|2x+1|-2|x-2|=5

two men on either side of a temple 75 M high have angles of elevation as 45 degree each.The distance between them is

In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides Ab, BC, CD and AD at P, Q, R and S respectively.If the radius of the circle is 10 cm, BC = 38 cm, PB = 27 cm and AD ⊥ CD then the length of CD is [CBSE 2013](a) 11 cm(b) 15 cm(c) 20 cm(d) 21 cm

Find the roots of each of the following equations, if they exist, by applying the quadratic formula: 2x2+5√3x+6=0

If a hollow copper pipe of inner diameter 6cm and outer diameter 10cm is melted and changed into a solid right circular cylinder of the same height as that of the pipe,then the diameter of the solid cylinder is

The nth term of an AP is (3n + 5). Find its common difference.

if m and n are zeros of the quadratic polynomial f(x)= x^2-p(x+1)-c, show that (m+1)(n+1)=1-c

Question 2 (ii)Show that : cos38∘cos52∘−sin38∘sin52∘=0

How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius 8 cm.

Solve the following quadratic equations by factorization:x2-2+1x+2=0

If angle A and angle B are acute angels such that sin A = sin B than prove that A = B

Form the pair of linear equations in the following problems, and find their solution graphically: 5 pencil and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and a pen.

Find the polynomial from the given information. Quotient =x3+2x Divisor =x2+12x Remainder =5

Krish works in a mall and gets paid ₹70 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks

24. A sum of 700 is to be used to give 7 cash prizes to students of a school for their overall academic performance . If each prize is 20 less than is preceeding prize

'Surya Electronics' purchased an AC having taxable value of ₹35000 and sold it to a consumer for ₹40000 (taxable value). Rate of GST is 18%. Find the GST payable by Surya Electronics.

Find the area of the dotted portion if the dimensions are as specified in the figure. r = l4.

In the given figure, AOB is a diameter of the circle and C, D , E are any three points to semi circle then ∠ACD + ∠BED = _______

A person recorded the speed (in km/hr) of 10 motorists as 48, 52, 57, 55, 45, 39, 61, 49, 51 and 43. The average speed of the motorists is

Find the single discount equivalent to two successive discount 50% and 60%

Calculate the area of shaded portion

The expression a3+b3+c3−3abc can be expressed as a product of two expressions. What is the product?

ABCD is a quadrilateral in which the bisectors of angle-A and angle-C meet DC produced at Y and BA produced at X, respectively. Prove that angle-X+angle-Y=1/2(angle-A+angle-C)

Four points A (6, 3), B (-3, 5), C (4, -2) and D (x, 3x) are given in such a way that △DBC△ABC=12,find x.

Evaluate: sec29∘cosec61∘ + 2cot8∘cot17∘cot45∘cot73∘cot82∘

Reduce x2−25x2+10x+25 into its simpest form.

If alpha , beta and gamma are zeroes of the polynomial x^3 + ax + b , then the value of alpha ^3 + beta^3 + gamma^3 is ___

Question 5 Cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m×16 m. Find the area of the field in which the cow can graze.

Two numbers are selected at random from the numbers 1, 2, . .. . . n. The probability that the difference between the first and second is not less than m (where 0 &lt; m &lt; n), is

The locus of the mid points of the chords of the circle x2+y2+2x−2y−2=0 which makes an angle of 90° at the centre is

If (a,a) lies between the lines |x + y| = 2, then a lies in the inteval ?

If (x^3+ax^2+bx+6) has (x-2) as a factor and leaves a remainder 3 when divided by (x-3),find the values of a&b

64. Ratio of ranges of bullet fired from a gun at angle theta, 2 theta and 4 theta is found in the ratio x : 2 : 2 then the value of x will be (assume same speed of bullets)

Find the sum of all multiples of 7 lying between 500 and 900.

Two numbers are selected at random from the numbers 1, 2, . .. . . n. The probability that the difference between the first and second is not less than m (where 0 < m < n), is