24740 + Interview Questions in Mathematics Page 93 InterviewSolution

4601.	Prepare accounting equation from the following:(i) Started a business with cash ₹ 1,00,000 and goods worth ₹ 20,000.(ii) Sold 50% of above goods at a profit of ₹ 2,000 on credit to Ram.(iii) Rent paid ₹ 5,000.(iv) Ram paid 50% of his balance in cash.
Answer» Prepare accounting equation from the following: (i) Started a business with cash ₹ 1,00,000 and goods worth ₹ 20,000. (ii) Sold 50% of above goods at a profit of ₹ 2,000 on credit to Ram. (iii) Rent paid ₹ 5,000. (iv) Ram paid 50% of his balance in cash.

Discussion

4602.	Manish and Nitish are brothers. Manish is three years younger than Nitish. If Nitish age is x then Manish’s age could be represented by the algebraic expression.
Answer» Manish and Nitish are brothers. Manish is three years younger than Nitish. If Nitish age is $x$ then Manish’s age could be represented by the algebraic expression.

Discussion

4603.	If A={3,5,7,9,11},B={7,9,11,13}C={11,13,15} and D={15,17};(i) A∩B(ii) B∩C(iii) A∩C∩D(iv) A∩C(v) B∩D(vi) A∩(B∪C)(vii) A∩D(viii) A∩(B∪D)(ix) (A∩B)∩(B∪C)(x) (A∪D)∩(B∪C)
Answer» If $A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}$ $C = {11, 13, 15}$ and $D = {15, 17}$ ; $(i) A \cap B$ $(i i) B \cap C$ $(i i i) A \cap C \cap D$ $(i v) A \cap C$ $(v) B \cap D$ $(v i) A \cap (B \cup C)$ $(v i i) A \cap D$ $(v i i i) A \cap (B \cup D)$ $(i x) (A \cap B) \cap (B \cup C)$ $(x) (A \cup D) \cap (B \cup C)$

Discussion

4604.	Factorise: (x−y)3+(y−x)2
Answer» Factorise: $(x - y)^{3} + (y - x)^{2}$

Discussion

4605.	In Fig.alongside, O is the centre of the circle.(a) Name all chords of the circle(b) Name all radii of the circle.(c) Name a chord, which is not the diameter of the circle.(d) Shade sectors OAC and OPB.[4 MARKS]
Answer» In Fig.alongside, O is the centre of the circle. (a) Name all chords of the circle (b) Name all radii of the circle. (c) Name a chord, which is not the diameter of the circle. (d) Shade sectors OAC and OPB. [4 MARKS]

4605.

In Fig.alongside, O is the centre of the circle.(a) Name all chords of the circle(b) Name all radii of the circle.(c) Name a chord, which is not the diameter of the circle.(d) Shade sectors OAC and OPB.[4 MARKS]

Answer» In Fig.alongside, O is the centre of the circle.

(a) Name all chords of the circle

(b) Name all radii of the circle.

(c) Name a chord, which is not the diameter of the circle.

(d) Shade sectors OAC and OPB.

[4 MARKS]

Discussion

4606.	How did Holmes' digressions sometimes prove in the end to have a bearing on the matter on hand?
Answer» How did Holmes' digressions sometimes prove in the end to have a bearing on the matter on hand?

Discussion

4607.	Show that set B={y:2y+1<3 and y∈W} is a singleton set.
Answer» Show that set $B = {y : 2 y + 1 < 3 a n d y \in W}$ is a singleton set.

Discussion

4608.	Write the coordinates of each of the points P, Q, R, S, T and O from the figure.
Answer» Write the coordinates of each of the points P, Q, R, S, T and O from the figure.

Discussion

4609.	Sum of two numbers is 4 more than the twice of difference of the two numbers. If one of the two numbers is three more than the other number, then find the numbers.
Answer» Sum of two numbers is 4 more than the twice of difference of the two numbers. If one of the two numbers is three more than the other number, then find the numbers.

Discussion

4610.	In a cube if the length of diagonal is √12cm cm, then the volume of the cube is
Answer» In a cube if the length of diagonal is $\sqrt{12} c m$ cm, then the volume of the cube is

Discussion

4611.	The value of sin47∘+sin61∘−sin11∘−sin25∘ is
Answer» The value of $sin 47^{\circ} + sin 61^{\circ} - sin 11^{\circ} - sin 25^{\circ}$ is

Discussion

4612.	In Δ ABC, if AB is the greatest side, then prove that ∠C>60∘.
Answer» In Δ ABC, if AB is the greatest side, then prove that $∠ C > 60^{\circ}$ .

Discussion

4613.	If (2,2) lies on 4x+5y = k, the value of k is ___
Answer» If (2,2) lies on 4x+5y = k, the value of k is ___

Discussion

4614.	Two angles of a triangle are equal and the third angle is greater than each of those angles by 30°. Determine all the angles of the triangle.
Answer» Two angles of a triangle are equal and the third angle is greater than each of those angles by 30°. Determine all the angles of the triangle.

Discussion

4615.	If A(3, y) is equidistant from points P(8, −3) and Q(7, 6), find the value of y and find the distance AQ. [CBSE 2014]
Answer» If A(3, y) is equidistant from points P(8, −3) and Q(7, 6), find the value of y and find the distance AQ. [CBSE 2014]

Discussion

4616.	Add: 3+2y−5y2+6y3,−8+3y+7y3 and 5−6y−8y3+y2
Answer» Add: $3 + 2 y - 5 y^{2} + 6 y^{3}, - 8 + 3 y + 7 y^{3}$ and $5 - 6 y - 8 y^{3} + y^{2}$

Discussion

4617.	What is the area of △ABC (in square cm) if AD is the median and area △ADB= 18 square cm? __
Answer» What is the area of $△ A B C$ (in square cm) if AD is the median and area $△ A D B$ = 18 square cm? __

4617.

What is the area of △ABC (in square cm) if AD is the median and area △ADB= 18 square cm? __

Answer»

What is the area of $△ A B C$ (in square cm) if AD is the median and area $△ A D B$ = 18 square cm?

__

Discussion

4618.	If point 0 represents the origin (0,0), then coordinates of point J shown below is _____ .
Answer» If point 0 represents the origin (0,0), then coordinates of point J shown below is _____ .

4618.

If point 0 represents the origin (0,0), then coordinates of point J shown below is _____ .

Answer»

If point 0 represents the origin (0,0), then coordinates of point J shown below is _____ .

Discussion

4619.	Fill in the blanks to make the given statements true.(i) A point in which the x-coordinate is 0 and y-coordinate is 5 will lie on ..... .(ii) All point with y-coordinate as 0 lie on ...... .(iii) The x-coordinate of any point lying on the y-axis is always ..... .(iv) The point where the two axes intersect is called the ..... .(v) For the point (5, 2), the distance from the x-axis is ...... units.(vi) The distance of any point from the y-axis is the ...... coordinate.(vii) The coordinates of the origin are ...... .
Answer» Fill in the blanks to make the given statements true. (i) A point in which the x-coordinate is 0 and y-coordinate is 5 will lie on ..... . (ii) All point with y-coordinate as 0 lie on ...... . (iii) The x-coordinate of any point lying on the y-axis is always ..... . (iv) The point where the two axes intersect is called the ..... . (v) For the point (5, 2), the distance from the x-axis is ...... units. (vi) The distance of any point from the y-axis is the ...... coordinate. (vii) The coordinates of the origin are ...... .

Discussion

4620.	Given:define distance between two points P(x1, y1) and (x2, y2) as d(P, Q)= max. {\|x2-x1\|, \|y2-y1\|}Suppose that points A and B have coordinates (1,0) and (-1,0) respectively, then for a variable point P on this plane the equation d(P, A) + d(P,B)= 2 represents:A) a line segment joining A and BB) an ellipse with foci at A and BC) region lying inside a square of area 2D) region inside a semicircle with AB as diameter
Answer» Given: define distance between two points P(x1, y1) and (x2, y2) as d(P, Q)= max. {\|x2-x1\|, \|y2-y1\|} Suppose that points A and B have coordinates (1,0) and (-1,0) respectively, then for a variable point P on this plane the equation d(P, A) + d(P,B)= 2 represents: A) a line segment joining A and B B) an ellipse with foci at A and B C) region lying inside a square of area 2 D) region inside a semicircle with AB as diameter

Discussion

4621.	Find 1)the lateral surface area of a closed cylindrical petrol storage tank that is 4.2m in diameter and 4.5m high. 2)howuch steel was actually used,if 1/12 of the steel actually used was wasted in making the tank.
Answer» Find 1)the lateral surface area of a closed cylindrical petrol storage tank that is 4.2m in diameter and 4.5m high. 2)howuch steel was actually used,if 1/12 of the steel actually used was wasted in making the tank.

4621.

Find 1)the lateral surface area of a closed cylindrical petrol storage tank that is 4.2m in diameter and 4.5m high. 2)howuch steel was actually used,if 1/12 of the steel actually used was wasted in making the tank.

Answer»

Find

1)the lateral surface area of a closed cylindrical petrol storage tank that is 4.2m in diameter and 4.5m high.

2)howuch steel was actually used,if 1/12 of the steel actually used was wasted in making the tank.

Discussion

4622.	18. A big cube of 4cm is cut into 1cm cubes. Calculate the TSA of all the small cubes. Also find the ratio of summer of of TSA of small cubes to the TSA of the big cube
Answer» 18. A big cube of 4cm is cut into 1cm cubes. Calculate the TSA of all the small cubes. Also find the ratio of summer of of TSA of small cubes to the TSA of the big cube

Discussion

4623.	State in which quadrant or on which axis do the following points lie. • A(-3, 2), • B(-5, -2), • K(3.5, 1.5), • D(2, 10), • E(37, 35), • F(15, -18), • G(3, -7), • H(0, -5), • M(12, 0), • N(0, 9), • P(0, 2.5), • Q(-7, -3)
Answer» State in which quadrant or on which axis do the following points lie. • A( $-$ 3, 2), • B( $-$ 5, $-$ 2), • K(3.5, 1.5), • D(2, 10), • E(37, 35), • F(15, -18), • G(3, $-$ 7), • H(0, $-$ 5), • M(12, 0), • N(0, 9), • P(0, 2.5), • Q( $-$ 7, $-$ 3)

Discussion

4624.	53.Let a.bb,c be three unit vectors such that a(bc)=3/2(b+cc).If vector b is not parallel to vector c,then the angle between a and b is:
Answer» 53.Let a.bb,c be three unit vectors such that a(bc)=3/2(b+cc).If vector b is not parallel to vector c,then the angle between a and b is:

Discussion

4625.	Find the volume, curved surface area and the total surface area of a cone whose height is 6 cm and slant height 10 cm.(Take π=3.14)
Answer» Find the volume, curved surface area and the total surface area of a cone whose height is 6 cm and slant height 10 cm. $(T a k e π = 3.14)$

Discussion

4626.	How can we know that whether a particular fraction is a terminating decimal or not?
Answer» How can we know that whether a particular fraction is a terminating decimal or not?

Discussion

4627.	Question 46The sixth class interval for a grouped data whose first two class intervals are 10-15 and 15-20 is ___
Answer» Question 46 The sixth class interval for a grouped data whose first two class intervals are 10-15 and 15-20 is ___

4627.

Question 46The sixth class interval for a grouped data whose first two class intervals are 10-15 and 15-20 is ___

Answer»

Question 46

The sixth class interval for a grouped data whose first two class intervals are 10-15 and 15-20 is ___

Discussion

4628.	Question 12 (ii)In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the:(ii) shaded region.
Answer» Question 12 (ii) In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the: (ii) shaded region.

4628.

Question 12 (ii)In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the:(ii) shaded region.

Answer»

Question 12 (ii)

In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the:

(ii) shaded region.

Discussion

4629.	P is any point on the side BC of a ΔABC. P is joined to A. If D and E are the midpoints of the sides AB and AC respectively and M and N are the midpoints of BP and CP respectively then quadrilateral DENM is (a) a trapezium (b) a parallelogram (c) a rectangle (d) a rhombus
Answer» P is any point on the side BC of a $Δ A B C$ . P is joined to A. If D and E are the midpoints of the sides AB and AC respectively and M and N are the midpoints of BP and CP respectively then quadrilateral DENM is (a) a trapezium (b) a parallelogram (c) a rectangle (d) a rhombus

4629.

P is any point on the side BC of a ΔABC. P is joined to A. If D and E are the midpoints of the sides AB and AC respectively and M and N are the midpoints of BP and CP respectively then quadrilateral DENM is (a) a trapezium (b) a parallelogram (c) a rectangle (d) a rhombus

Answer»

P is any point on the side BC of a $Δ A B C$ . P is joined to A. If D and E are the midpoints of the sides AB and AC respectively and M and N are the midpoints of BP and CP respectively then quadrilateral DENM is

(a) a trapezium

(b) a parallelogram

(c) a rectangle

(d) a rhombus

Discussion

4630.	If AB + BC = 16 cm and BC = 7 cm then AB =
Answer» If AB + BC = 16 cm and BC = 7 cm then AB =

Discussion

4631.	Find the locus of a point P when three normals drawn from it are such that area of the triangle formed by their feet is constant.
Answer» Find the locus of a point P when three normals drawn from it are such that area of the triangle formed by their feet is constant.

Discussion

4632.	The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =(a) 94°(b) 54°(c) 40°(d) 44°
Answer» The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC = (a) 94° (b) 54° (c) 40° (d) 44°

Discussion

4633.	Question 9A ΔABC is right angled at A. L is a point on BC such that AL ⊥ BC. Prove that ∠BAL=∠ACB.
Answer» Question 9 A $Δ A B C$ is right angled at A. L is a point on BC such that AL $⊥$ BC. Prove that $∠ B A L = ∠ A C B$ .

Discussion

4634.	Are all the parallelogram a rectangle ? If not,then why?
Answer» Are all the parallelogram a rectangle ? If not,then why?

Discussion

4635.	For a given matrix A=⎡⎢⎣2−23−2−16120⎤⎥⎦, one of the eigen values is 3. The other two eigen values are.
Answer» For a given matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & - 2 & 3 - 2 & - 1 & 6 1 & 2 & 0 \end{matrix} ⎤ ⎥ ⎦$ , one of the eigen values is 3. The other two eigen values are.

Discussion

4636.	Three athletes A, B and C participate in a race. Both A and B have the same probability of winning the race and each is twice as likely to win as C. The probability that B or C wins the race is:
Answer» Three athletes A, B and C participate in a race. Both A and B have the same probability of winning the race and each is twice as likely to win as C. The probability that B or C wins the race is:

Discussion

4637.	The measure of angle subtended by a diameter in a semicircle is
Answer» The measure of angle subtended by a diameter in a semicircle is

Discussion

4638.	find the angle between the lines (x-2)/3 =(y+1)/-2,z=2 and (x-1)/1=(2y+3)/3=(z+5)/2
Answer» find the angle between the lines (x-2)/3 =(y+1)/-2,z=2 and (x-1)/1=(2y+3)/3=(z+5)/2

Discussion

4639.	Show that: a+1bm×a-1bnb+1am×b-1an=abm+n
Answer» Show that: $\frac{{(a + \frac{1}{b})}^{m} \times {(a - \frac{1}{b})}^{n}}{{(b + \frac{1}{a})}^{m} \times {(b - \frac{1}{a})}^{n}} = {(\frac{a}{b})}^{m + n}$

Discussion

4640.	In triangle ABC, right angled at C, if tanA is equal to one by route 3, then sinAcosB plus cosAsinB is equal to
Answer» In triangle ABC, right angled at C, if tanA is equal to one by route 3, then sinAcosB plus cosAsinB is equal to

Discussion

4641.	A dice is thrown twice. Find the probability of getting a bigger value on the first throw.
Answer» A dice is thrown twice. Find the probability of getting a bigger value on the first throw.

Discussion

4642.	A LPG cylinder making company is taking the order of manufacturing cylinders. What is the measurement they should keep in mind when they bring iron for production?
Answer» A LPG cylinder making company is taking the order of manufacturing cylinders. What is the measurement they should keep in mind when they bring iron for production?

Discussion

4643.	Which of the following expressions are polynomials? In case of a polynomial, write its degree.(i) x5-2x3+x+3(ii) y3+3y(iii) t2-25t+5(iv) x100-1(v) 12x2-2x+2(vi) x-2+2x-1+3(vii) 1(viii) -35(ix) x22-2x2(x) 23x2-8(xi) 12x2(xii) 15x12+1(xiii) 35x2-73x+9(xiv) x4-x32+x-3(xv) 2x3+3x2+x-1
Answer» Which of the following expressions are polynomials? In case of a polynomial, write its degree. (i) $x^{5} - 2 x^{3} + x + \sqrt{3}$ (ii) $y^{3} + \sqrt{3} y$ (iii) $t^{2} - \frac{2}{5} t + \sqrt{5}$ (iv) $x^{100} - 1$ (v) $\frac{1}{\sqrt{2}} x^{2} - \sqrt{2} x + 2$ (vi) $x^{- 2} + 2 x^{- 1} + 3$ (vii) 1 (viii) $\frac{- 3}{5}$ (ix) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$ (x) $\sqrt[3]{2} x^{2} - 8$ (xi) $\frac{1}{2 x^{2}}$ (xii) $\frac{1}{\sqrt{5}} x^{\frac{1}{2}} + 1$ (xiii) $\frac{3}{5} x^{2} - \frac{7}{3} x + 9$ (xiv) $x^{4} - x^{\frac{3}{2}} + x - 3$ (xv) $2 x^{3} + 3 x^{2} + \sqrt{x} - 1$

Discussion

4644.	Give two rational numbers lying between 0.232332333233332... and 0.212112111211112.
Answer» Give two rational numbers lying between 0.232332333233332... and 0.212112111211112.

Discussion

4645.	Find the volume of a sphere whose radius is 3 inches.
Answer» Find the volume of a sphere whose radius is 3 inches.

Discussion

4646.	Two like parallel vectors →a and →b are such that (x−5)→a+(x−2)→b=0, then the set of value(s) of x is ?
Answer» Two like parallel vectors $\to a$ and $\to b$ are such that $(x - 5) \to a + (x - 2) \to b = 0,$ then the set of value(s) of $x$ is ?

Discussion

4647.	If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC∼ΔPQR. Prove that ABPQ=ADPM.
Answer» If AD and PM are medians of triangles ABC and PQR, respectively where $Δ A B C \sim Δ P Q R$ . Prove that $\frac{A B}{P Q} = \frac{A D}{P M}$ .

Discussion

4648.	The length and width of a tape are 2 m and 28 cm. What is the ratio of breadth to two times of length?
Answer» The length and width of a tape are 2 m and 28 cm. What is the ratio of breadth to two times of length?

Discussion

4649.	Three angles of a quadrilateral are 75∘,90∘ and 75∘. The measure of the fourth angle is _____________ .
Answer» Three angles of a quadrilateral are $75^{\circ}, 90^{\circ}$ and $75^{\circ}$ . The measure of the fourth angle is _____________ .

Discussion

4650.	In the given figure, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ΔSAT.
Answer» In the given figure, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ΔSAT.

Discussion

Explore topic-wise InterviewSolutions in .

Prepare accounting equation from the following:(i) Started a business with cash ₹ 1,00,000 and goods worth ₹ 20,000.(ii) Sold 50% of above goods at a profit of ₹ 2,000 on credit to Ram.(iii) Rent paid ₹ 5,000.(iv) Ram paid 50% of his balance in cash.

Manish and Nitish are brothers. Manish is three years younger than Nitish. If Nitish age is x then Manish’s age could be represented by the algebraic expression.

If A={3,5,7,9,11},B={7,9,11,13}C={11,13,15} and D={15,17};(i) A∩B(ii) B∩C(iii) A∩C∩D(iv) A∩C(v) B∩D(vi) A∩(B∪C)(vii) A∩D(viii) A∩(B∪D)(ix) (A∩B)∩(B∪C)(x) (A∪D)∩(B∪C)

Factorise: (x−y)3+(y−x)2

In Fig.alongside, O is the centre of the circle.(a) Name all chords of the circle(b) Name all radii of the circle.(c) Name a chord, which is not the diameter of the circle.(d) Shade sectors OAC and OPB.[4 MARKS]

How did Holmes' digressions sometimes prove in the end to have a bearing on the matter on hand?

Show that set B={y:2y+1&lt;3 and y∈W} is a singleton set.

Write the coordinates of each of the points P, Q, R, S, T and O from the figure.

Sum of two numbers is 4 more than the twice of difference of the two numbers. If one of the two numbers is three more than the other number, then find the numbers.

In a cube if the length of diagonal is √12cm cm, then the volume of the cube is

The value of sin47∘+sin61∘−sin11∘−sin25∘ is

In Δ ABC, if AB is the greatest side, then prove that ∠C&gt;60∘.

If (2,2) lies on 4x+5y = k, the value of k is ___

Two angles of a triangle are equal and the third angle is greater than each of those angles by 30°. Determine all the angles of the triangle.

If A(3, y) is equidistant from points P(8, −3) and Q(7, 6), find the value of y and find the distance AQ. [CBSE 2014]

Add: 3+2y−5y2+6y3,−8+3y+7y3 and 5−6y−8y3+y2

What is the area of △ABC (in square cm) if AD is the median and area △ADB= 18 square cm? __

If point 0 represents the origin (0,0), then coordinates of point J shown below is _____ .​​

Find 1)the lateral surface area of a closed cylindrical petrol storage tank that is 4.2m in diameter and 4.5m high. 2)howuch steel was actually used,if 1/12 of the steel actually used was wasted in making the tank.

18. A big cube of 4cm is cut into 1cm cubes. Calculate the TSA of all the small cubes. Also find the ratio of summer of of TSA of small cubes to the TSA of the big cube

State in which quadrant or on which axis do the following points lie. • A(-3, 2), • B(-5, -2), • K(3.5, 1.5), • D(2, 10), • E(37, 35), • F(15, -18), • G(3, -7), • H(0, -5), • M(12, 0), • N(0, 9), • P(0, 2.5), • Q(-7, -3)

53.Let a.bb,c be three unit vectors such that a(bc)=3/2(b+cc).If vector b is not parallel to vector c,then the angle between a and b is:

Find the volume, curved surface area and the total surface area of a cone whose height is 6 cm and slant height 10 cm.(Take π=3.14)

How can we know that whether a particular fraction is a terminating decimal or not?

Question 46The sixth class interval for a grouped data whose first two class intervals are 10-15 and 15-20 is ___

Question 12 (ii)In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the:(ii) shaded region.

P is any point on the side BC of a ΔABC. P is joined to A. If D and E are the midpoints of the sides AB and AC respectively and M and N are the midpoints of BP and CP respectively then quadrilateral DENM is (a) a trapezium (b) a parallelogram (c) a rectangle (d) a rhombus

If AB + BC = 16 cm and BC = 7 cm then AB =

Find the locus of a point P when three normals drawn from it are such that area of the triangle formed by their feet is constant.

The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =(a) 94°(b) 54°(c) 40°(d) 44°

Question 9A ΔABC is right angled at A. L is a point on BC such that AL ⊥ BC. Prove that ∠BAL=∠ACB.

Are all the parallelogram a rectangle ? If not,then why?

For a given matrix A=⎡⎢⎣2−23−2−16120⎤⎥⎦, one of the eigen values is 3. The other two eigen values are.

Three athletes A, B and C participate in a race. Both A and B have the same probability of winning the race and each is twice as likely to win as C. The probability that B or C wins the race is:

The measure of angle subtended by a diameter in a semicircle is

find the angle between the lines (x-2)/3 =(y+1)/-2,z=2 and (x-1)/1=(2y+3)/3=(z+5)/2

Show that: a+1bm×a-1bnb+1am×b-1an=abm+n

In triangle ABC, right angled at C, if tanA is equal to one by route 3, then sinAcosB plus cosAsinB is equal to

A dice is thrown twice. Find the probability of getting a bigger value on the first throw.

A LPG cylinder making company is taking the order of manufacturing cylinders. What is the measurement they should keep in mind when they bring iron for production?

Which of the following expressions are polynomials? In case of a polynomial, write its degree.(i) x5-2x3+x+3(ii) y3+3y(iii) t2-25t+5(iv) x100-1(v) 12x2-2x+2(vi) x-2+2x-1+3(vii) 1(viii) -35(ix) x22-2x2(x) 23x2-8(xi) 12x2(xii) 15x12+1(xiii) 35x2-73x+9(xiv) x4-x32+x-3(xv) 2x3+3x2+x-1

Give two rational numbers lying between 0.232332333233332... and 0.212112111211112.

Find the volume of a sphere whose radius is 3 inches.

Two like parallel vectors →a and →b are such that (x−5)→a+(x−2)→b=0, then the set of value(s) of x is ?

If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC∼ΔPQR. Prove that ABPQ=ADPM.

The length and width of a tape are 2 m and 28 cm. What is the ratio of breadth to two times of length?

Three angles of a quadrilateral are 75∘,90∘ and 75∘. The measure of the fourth angle is _____________ .

In the given figure, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ΔSAT.

Show that set B={y:2y+1<3 and y∈W} is a singleton set.

In Δ ABC, if AB is the greatest side, then prove that ∠C>60∘.

If point 0 represents the origin (0,0), then coordinates of point J shown below is _____ .