32581 + Interview Questions in Mathematics Page 179 InterviewSolution

8901.	Mid-point of the line-segment joining the points (– 5, 4) and (9, – 8) is:
Answer» Mid-point of the line-segment joining the points (– 5, 4) and (9, – 8) is:

Discussion

8902.	For what value of n, are the nth terms of 2 APs 63,65,67,... and 3,10,17,... are equal?
Answer» For what value of n, are the nth terms of 2 APs 63,65,67,... and 3,10,17,... are equal?

Discussion

8903.	Find the value of k for which the following system of equations has a unique solution: (5-8) 4x + ky + 8 = 0 2x + 2y + 2 =0
Answer» Find the value of k for which the following system of equations has a unique solution: (5-8) 4x + ky + 8 = 0 2x + 2y + 2 =0

8903.

Find the value of k for which the following system of equations has a unique solution: (5-8) 4x + ky + 8 = 0 2x + 2y + 2 =0

Answer»

Find the value of k for which the following system of equations has a unique solution: (5-8)

4x + ky + 8 = 0

2x + 2y + 2 =0

Discussion

8904.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:23x2-5x+3=0 [CBSE 2011]
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $2 \sqrt{3} x^{2} - 5 x + \sqrt{3} = 0$ [CBSE 2011]

Discussion

8905.	In the adjoining figure 'O' is the center of circle, ∠CAO = 25∘ and ∠CBO = 35∘. What is the value of ∠AOB?
Answer» In the adjoining figure 'O' is the center of circle, $∠$ CAO = $25^{\circ}$ and $∠$ CBO = $35^{\circ}$ . What is the value of $∠$ AOB?

8905.

In the adjoining figure 'O' is the center of circle, ∠CAO = 25∘ and ∠CBO = 35∘. What is the value of ∠AOB?

Answer»

In the adjoining figure 'O' is the center of circle, $∠$ CAO = $25^{\circ}$ and $∠$ CBO = $35^{\circ}$ . What is the value of $∠$ AOB?

Discussion

8906.	IF THE LENGHT OF TWO DIAGONAL OF A RHOMBUS ARE 12CAM AND 18CM THEN THE LENTH OF EACH ANGLE OF A RHOMBUS IS WHAT CM?
Answer» IF THE LENGHT OF TWO DIAGONAL OF A RHOMBUS ARE 12CAM AND 18CM THEN THE LENTH OF EACH ANGLE OF A RHOMBUS IS WHAT CM?

Discussion

8907.	If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Answer» If sin² θ cos² θ (1 + tan² θ) (1 + cot² θ) = λ, then find the value of λ.

Discussion

8908.	How are bank deposits useful to the public?
Answer» How are bank deposits useful to the public?

Discussion

8909.	IN HOW MANY WAYS WE CAN ARRANGE FOUR LEETERS OF THE WORD MISSISSIPPI
Answer» IN HOW MANY WAYS WE CAN ARRANGE FOUR LEETERS OF THE WORD MISSISSIPPI

Discussion

8910.	Find the coordinates of a point P on th eline segment joining A(1,2) and B(6,7) such that AP=25AB.
Answer» Find the coordinates of a point P on th eline segment joining A(1,2) and B(6,7) such that AP= $\frac{2}{5} A B .$

Discussion

8911.	12. For how many pairs of positive integers (x,y) are possible to satisfy Equation x+7y = 100
Answer» 12. For how many pairs of positive integers (x,y) are possible to satisfy Equation x+7y = 100

Discussion

8912.	If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of 'k' is.
Answer» If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of 'k' is.

Discussion

8913.	(cosec θ+cot θ)×(1−cos θ)=
Answer» $(c o s e c θ + cot θ) \times (1 - cos θ) =$

Discussion

8914.	Asha, Naveen and Shalini were partners in a firm sharing profits in the ratio of 5 : 3 : 2. Goodwill appeared in their books at a value of ₹ 80,000 and General Reserve at ₹ 40,000. Naveen decided to retire from the firm. On the date of his retirement, goodwill of the firm was valued at ₹ 1,20,000. The new profit-sharing ratio decided among Asha and Shalini is 2 : 3.Record necessary Journal entries on Naveen's retirement.
Answer» Asha, Naveen and Shalini were partners in a firm sharing profits in the ratio of 5 : 3 : 2. Goodwill appeared in their books at a value of ₹ 80,000 and General Reserve at ₹ 40,000. Naveen decided to retire from the firm. On the date of his retirement, goodwill of the firm was valued at ₹ 1,20,000. The new profit-sharing ratio decided among Asha and Shalini is 2 : 3. Record necessary Journal entries on Naveen's retirement.

Discussion

8915.	Find four different solutions of the equation 1/2x - 3/5y = 11/4
Answer» Find four different solutions of the equation 1/2x - 3/5y = 11/4

Discussion

8916.	A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string, assuming that there is no slack in the string.
Answer» A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60^{\circ}$ . Find the length of the string, assuming that there is no slack in the string.

Discussion

8917.	Solve the following inequation:x+142≥2x+28
Answer» Solve the following inequation: $\frac{x + 14}{2} \geq 2 x + 28$

Discussion

8918.	Median=? (a) l+{h×(N2−cf)f} (b) l+{h×(cf−N2)f}(c) l−{h×(N2−cf)f} (d) none of these
Answer» Median=? $(a) l + {h \times \frac{(\frac{N}{2} - c f)}{f}} (b) l + {h \times \frac{(c f - \frac{N}{2})}{f}} (c) l - {h \times \frac{(\frac{N}{2} - c f)}{f}} (d) n o n e o f t h e s e$

8918.

Median=? (a) l+{h×(N2−cf)f} (b) l+{h×(cf−N2)f}(c) l−{h×(N2−cf)f} (d) none of these

Answer»

Median=?

$(a) l + {h \times \frac{(\frac{N}{2} - c f)}{f}} (b) l + {h \times \frac{(c f - \frac{N}{2})}{f}} (c) l - {h \times \frac{(\frac{N}{2} - c f)}{f}} (d) n o n e o f t h e s e$

Discussion

8919.	P and Q are points on sides CA and CB respectively of Δ ABC right angled at C. Prove that AQ2 + BP2 = AB2 + PQ2
Answer» P and Q are points on sides CA and CB respectively of Δ ABC right angled at C. Prove that ${A Q}^{2}$ + ${B P}^{2}$ = ${A B}^{2}$ + ${P Q}^{2}$

Discussion

8920.	According to Euclid's division lemma, if a and b are two positive integers with a>b, then which of the following is true? (Here, q and r are unique integers.)
Answer» According to Euclid's division lemma, if $a$ and $b$ are two positive integers with $a > b,$ then which of the following is true? (Here, $q$ and $r$ are unique integers.)

Discussion

8921.	If D and E are points on sides AB and AC respectively of a ∆ABC such that DE \|\| BC and BD = CE. Prove that ∆ABC is isosceles.
Answer» If D and E are points on sides AB and AC respectively of a ∆ABC such that DE \|\| BC and BD = CE. Prove that ∆ABC is isosceles.

Discussion

8922.	Gas is being pumped into a spherical balloon at the rate of 30 cm3/min. The rate at which the radius increases when it reaches the value 15 cm, is ___________.
Answer» Gas is being pumped into a spherical balloon at the rate of 30 cm³/min. The rate at which the radius increases when it reaches the value 15 cm, is ___________.

Discussion

8923.	Two tangents PA and PB are drawn to the circle with centre O, such that ∠APB =120∘. What is the relation between OP and AP?
Answer» Two tangents PA and PB are drawn to the circle with centre O, such that $∠$ APB $= 120^{\circ}$ . What is the relation between OP and AP?

8923.

Two tangents PA and PB are drawn to the circle with centre O, such that ∠APB =120∘. What is the relation between OP and AP?

Answer»

Two tangents PA and PB are drawn to the circle with centre O, such that $∠$ APB $= 120^{\circ}$ . What is the relation between OP and AP?

Discussion

8924.	Every point on a number line represents(a) a rational number(b) a natural number(c) an irrational number(d) a unique number
Answer» Every point on a number line represents (a) a rational number (b) a natural number (c) an irrational number (d) a unique number

Discussion

8925.	∣∣∣∣1!2!3!2!3!4!3!4!5!∣∣∣∣=2016k, then k=_____
Answer» $∣ ∣∣ ∣ \begin{matrix} 1! & 2! & 3! 2! & 3! & 4! 3! & 4! & 5! \end{matrix} ∣ ∣∣ ∣ = 2016 k$ , then $k =$ _____

Discussion

8926.	The range of sin-1x + cos-1x + tan-1x is _______________________.
Answer» The range of sin^-1x + cos^-1x + tan^-1x is _______________________.

Discussion

8927.	In the following figure, if LM \|\| CB and LN \|\| CD, prove that
Answer» In the following figure, if LM \|\| CB and LN \|\| CD, prove that

8927.

In the following figure, if LM || CB and LN || CD, prove that

Answer»

In the following figure, if LM || CB and LN || CD, prove that

Discussion

8928.	The perimeter of the rhombus is 32 cm. Then What is the length of its side?
Answer» The perimeter of the rhombus is 32 cm. Then What is the length of its side?

Discussion

8929.	Solve the following systems of equations:10x+y+2x-y=415x+y-9x-y=-2
Answer» Solve the following systems of equations: $\frac{10}{x + y} + \frac{2}{x - y} = 4 \frac{15}{x + y} - \frac{9}{x - y} = - 2$

Discussion

8930.	Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.
Answer» Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.

Discussion

8931.	Plot the points (0,4), (0, −2), (0, 5) and (0, −4) in the cartesian plane.
Answer» Plot the points (0,4), (0, −2), (0, 5) and (0, −4) in the cartesian plane.

Discussion

8932.	The annual rainfall record of a city for 66 days is given in the following table :Rainfall (in cm ): 0-10 10-20 20-30 30-40 40-50 50-60Number of days : 22 10 8 15 5 6Calculate the median rainfall using ogives of more than type and less than type.
Answer» The annual rainfall record of a city for 66 days is given in the following table : Rainfall (in cm ): 0-10 10-20 20-30 30-40 40-50 50-60 Number of days : 22 10 8 15 5 6 Calculate the median rainfall using ogives of more than type and less than type.

Discussion

8933.	Solve the following quadratic equations by factorization:3x2 = −11x − 10
Answer» Solve the following quadratic equations by factorization: 3x² = −11x − 10

Discussion

8934.	Prove the following trigonometric identities: (1+cot2θ)tan θsec2θ=cot θ
Answer» Prove the following trigonometric identities: $\frac{(1 + c o t^{2} θ) t a n θ}{s e c^{2} θ} = c o t θ$

8934.

Prove the following trigonometric identities: (1+cot2θ)tan θsec2θ=cot θ

Answer»

Prove the following trigonometric identities:

$\frac{(1 + c o t^{2} θ) t a n θ}{s e c^{2} θ} = c o t θ$

Discussion

8935.	Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm and 7 cm. Find the radii of the circles.
Answer» Three circles touch each other externally. The distance between their centres is $5 c m, 6 c m$ and $7 c m .$ Find the radii of the circles.

Discussion

8936.	How many irrational numbers exist between two rational numbers?
Answer» How many irrational numbers exist between two rational numbers?

Discussion

8937.	Areas of some circles are given below find their diameters.(a) 176 sq cm (b) 394.24 sq cm
Answer» Areas of some circles are given below find their diameters. (a) 176 sq cm (b) 394.24 sq cm

Discussion

8938.	State whether the following are true or false. Justify your answer.(i) sin (A + B) = sin A + sin B(ii) The value of sinθ increases as θ increases(iii) The value of cos θ increases as θ increases(iv) sinθ = cos θ for all values of θ(v) cot A is not defined for A = 0°
Answer» State whether the following are true or false. Justify your answer. (i) sin (A + B) = sin A + sin B (ii) The value of sinθ increases as θ increases (iii) The value of cos θ increases as θ increases (iv) sinθ = cos θ for all values of θ (v) cot A is not defined for A = 0°

8938.

State whether the following are true or false. Justify your answer.(i) sin (A + B) = sin A + sin B(ii) The value of sinθ increases as θ increases(iii) The value of cos θ increases as θ increases(iv) sinθ = cos θ for all values of θ(v) cot A is not defined for A = 0°

Answer»

State whether the following are true or false. Justify your answer.

(i) sin (A + B) = sin A + sin B

(ii) The value of sinθ increases as θ increases

(iii) The value of cos θ increases as θ increases

(iv) sinθ = cos θ for all values of θ

(v) cot A is not defined for A = 0°

Discussion

8939.	Solve the following equation for real }x:(x^2+x-2)^3+(2x^2-x-1)^3=27(x^2-1)^3
Answer» Solve the following equation for real }x:(x^2+x-2)^3+(2x^2-x-1)^3=27(x^2-1)^3

Discussion

8940.	1+sin(90∘−θ)−cos2(90∘−θ)cos(90∘−θ) [1+sin(90∘−θ)]=
Answer» $\frac{1 + s i n (90^{\circ} - θ) - {c o s}^{2} (90^{\circ} - θ)}{c o s (90^{\circ} - θ) [1 + s i n (90^{\circ} - θ)]} =$

Discussion

8941.	A shopkeeper buys an item at a discount of 20% which has a marked price (M.P) of Rs. 3000 and pays a sales tax at the rate of 8%. The shopkeeper sells the article to a buyer at marked price, and charges a sales tax at the rate of 10%. Find the VAT paid by the shopkeeper.
Answer» A shopkeeper buys an item at a discount of 20% which has a marked price (M.P) of Rs. 3000 and pays a sales tax at the rate of 8%. The shopkeeper sells the article to a buyer at marked price, and charges a sales tax at the rate of 10%. Find the VAT paid by the shopkeeper.

Discussion

8942.	If f(x) =[x]^2+2[x+1]-10,then complete solution of f(x)=0
Answer» If f(x) =[x]^2+2[x+1]-10,then complete solution of f(x)=0

Discussion

8943.	The number of solutions of the system of the system of equations x + 2y + z = 3, 2x + 3y + z = 3, 3x + 5y + 2z = 1 is _____________.
Answer» The number of solutions of the system of the system of equations x + 2y + z = 3, 2x + 3y + z = 3, 3x + 5y + 2z = 1 is _____________.

Discussion

8944.	What is the distance between two parallel tangents of a circle of radius 4 cm?
Answer» What is the distance between two parallel tangents of a circle of radius 4 cm?

Discussion

8945.	Sides AB and AC and median AD of triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR . Show that triangle ABC is similar to triangle PQR.
Answer» Sides AB and AC and median AD of triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR . Show that triangle ABC is similar to triangle PQR.

Discussion

8946.	A child playing with building blocks, which are of the shape of cubes, has built a structure. If the edge of each cube is 3 cm, find the volume of the structure built by the child.
Answer» A child playing with building blocks, which are of the shape of cubes, has built a structure. If the edge of each cube is 3 cm, find the volume of the structure built by the child.

Discussion

8947.	A field is in the shape of a trapezium whose parallel sides are 50m and 15m. The non-parallel sides are 20m and 25 m. Find the area of the trapezium.
Answer» A field is in the shape of a trapezium whose parallel sides are 50m and 15m. The non-parallel sides are 20m and 25 m. Find the area of the trapezium.

Discussion

8948.	Tap on the bubbles with irrational numbers.
Answer» Tap on the bubbles with irrational numbers.

Discussion

8949.	ABCD is quadilateral in which AD = BC and ∠ ADC = ∠BCD Show that A B C and D are concyclic.
Answer» ABCD is quadilateral in which AD = BC and $∠$ ADC = $∠$ BCD Show that A B C and D are concyclic.

Discussion

8950.	Question 7 (ii)P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP. show that:(ii)ar(RQC)=38ar(ABC)
Answer» Question 7 (ii) P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP. show that: $(i i) a r (R Q C) = \frac{3}{8} a r (A B C)$

Discussion

Explore topic-wise InterviewSolutions in .

Mid-point of the line-segment joining the points (– 5, 4) and (9, – 8) is:

For what value of n, are the nth terms of 2 APs 63,65,67,... and 3,10,17,... are equal?

Find the value of k for which the following system of equations has a unique solution: (5-8) 4x + ky + 8 = 0 2x + 2y + 2 =0

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:23x2-5x+3=0 [CBSE 2011]

In the adjoining figure 'O' is the center of circle, ∠CAO = 25∘ and ∠CBO = 35∘. What is the value of ∠AOB?

IF THE LENGHT OF TWO DIAGONAL OF A RHOMBUS ARE 12CAM AND 18CM THEN THE LENTH OF EACH ANGLE OF A RHOMBUS IS WHAT CM?

If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.

How are bank deposits useful to the public?

IN HOW MANY WAYS WE CAN ARRANGE FOUR LEETERS OF THE WORD MISSISSIPPI

Find the coordinates of a point P on th eline segment joining A(1,2) and B(6,7) such that AP=25AB.

12. For how many pairs of positive integers (x,y) are possible to satisfy Equation x+7y = 100

If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of 'k' is.

(cosec θ+cot θ)×(1−cos θ)=

Find four different solutions of the equation 1/2x - 3/5y = 11/4

A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string, assuming that there is no slack in the string.

Solve the following inequation:x+142≥2x+28

Median=? (a) l+{h×(N2−cf)f} (b) l+{h×(cf−N2)f}(c) l−{h×(N2−cf)f} (d) none of these

P and Q are points on sides CA and CB respectively of Δ ABC right angled at C. Prove that AQ2 + BP2 = AB2 + PQ2

According to Euclid's division lemma, if a and b are two positive integers with a&gt;b, then which of the following is true? (Here, q and r are unique integers.)

If D and E are points on sides AB and AC respectively of a ∆ABC such that DE || BC and BD = CE. Prove that ∆ABC is isosceles.

Gas is being pumped into a spherical balloon at the rate of 30 cm3/min. The rate at which the radius increases when it reaches the value 15 cm, is ___________.

Two tangents PA and PB are drawn to the circle with centre O, such that ∠APB =120∘. What is the relation between OP and AP?

Every point on a number line represents(a) a rational number(b) a natural number(c) an irrational number(d) a unique number

∣∣∣∣1!2!3!2!3!4!3!4!5!∣∣∣∣=2016k, then k=_____

The range of sin-1x + cos-1x + tan-1x is _______________________.

In the following figure, if LM || CB and LN || CD, prove that

The perimeter of the rhombus is 32 cm. Then What is the length of its side?

Solve the following systems of equations:10x+y+2x-y=415x+y-9x-y=-2

Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.

Plot the points (0,4), (0, −2), (0, 5) and (0, −4) in the cartesian plane.

The annual rainfall record of a city for 66 days is given in the following table :Rainfall (in cm ): 0-10 10-20 20-30 30-40 40-50 50-60Number of days : 22 10 8 15 5 6Calculate the median rainfall using ogives of more than type and less than type.

Solve the following quadratic equations by factorization:3x2 = −11x − 10

Prove the following trigonometric identities: (1+cot2θ)tan θsec2θ=cot θ

Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm and 7 cm. Find the radii of the circles.

How many irrational numbers exist between two rational numbers?

Areas of some circles are given below find their diameters.(a) 176 sq cm (b) 394.24 sq cm

State whether the following are true or false. Justify your answer.(i) sin (A + B) = sin A + sin B(ii) The value of sinθ increases as θ increases(iii) The value of cos θ increases as θ increases(iv) sinθ = cos θ for all values of θ(v) cot A is not defined for A = 0°

Solve the following equation for real }x:(x^2+x-2)^3+(2x^2-x-1)^3=27(x^2-1)^3

1+sin(90∘−θ)−cos2(90∘−θ)cos(90∘−θ) [1+sin(90∘−θ)]=

A shopkeeper buys an item at a discount of 20% which has a marked price (M.P) of Rs. 3000 and pays a sales tax at the rate of 8%. The shopkeeper sells the article to a buyer at marked price, and charges a sales tax at the rate of 10%. Find the VAT paid by the shopkeeper.

If f(x) =[x]^2+2[x+1]-10,then complete solution of f(x)=0

The number of solutions of the system of the system of equations x + 2y + z = 3, 2x + 3y + z = 3, 3x + 5y + 2z = 1 is _____________.

What is the distance between two parallel tangents of a circle of radius 4 cm?

Sides AB and AC and median AD of triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR . Show that triangle ABC is similar to triangle PQR.

A child playing with building blocks, which are of the shape of cubes, has built a structure. If the edge of each cube is 3 cm, find the volume of the structure built by the child.

A field is in the shape of a trapezium whose parallel sides are 50m and 15m. The non-parallel sides are 20m and 25 m. Find the area of the trapezium.

Tap on the bubbles with irrational numbers.

ABCD is quadilateral in which AD = BC and ∠ ADC = ∠BCD Show that A B C and D are concyclic.

Question 7 (ii)P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP. show that:(ii)ar(RQC)=38ar(ABC)

According to Euclid's division lemma, if a and b are two positive integers with a>b, then which of the following is true? (Here, q and r are unique integers.)