32581 + Interview Questions in Mathematics Page 96 InterviewSolution

4751.	Question 8An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Answer» Question 8 An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

Discussion

4752.	Mark the correct alternative in each of the following:A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q such that OQ = 12 cm. Length PQ is(a) 12 cm(b) 13 cm(c) 8.5 cm(d) 119 cm
Answer» Mark the correct alternative in each of the following: A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q such that OQ = 12 cm. Length PQ is (a) 12 cm (b) 13 cm (c) 8.5 cm (d) $\sqrt{119} c m$

Discussion

4753.	Obtain all other zeroes of 3x4+6x3−2x2−10x−5, if two of its zeroes are √53 and −√53.
Answer» Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$ , if two of its zeroes are $\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ .

Discussion

4754.	For any positive integer n, prove that n3 – n divisible by 6.
Answer» For any positive integer n, prove that n³ – n divisible by 6.

Discussion

4755.	Question 4Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.
Answer» Question 4 Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

Discussion

4756.	Question 1 (ii)Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.2x + y = 5 ; 3x +2y =8
Answer» Question 1 (ii) Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. 2x + y = 5 ; 3x +2y =8

Discussion

4757.	Prove that(i) cos (2π+x) cosec (2π+x) tan (π/2+x)sec(π/2+x)cos x cot(π+x)=1(ii) cosec(90°+x)+cot(450°+x)cosec(90°-x)+tan(180°-x)+tan(180°+x)+sec(180°-x)tan(360°+x)-sec(-x)=2(iii) sin(180°+x) cos(90°+x) tan(270°-x) cot(360°-x)sin(360°-x) cos(360°+x) cosec(-x) sin(270°+x)=1(iv) 1+cot x-secπ2+x1+cot x+secπ2+x=2cot x(v) tan (90°-x) sec(180°-x) sin(-x)sin(180°+x) cot(360°-x) cosec(90°-x)=1
Answer» Prove that (i) $\frac{\cos (2 π + x) cosec (2 π + x) \tan (π / 2 + x)}{\sec (π / 2 + x) \cos x \cot (π + x)} = 1$ (ii) $\frac{cosec (90 ° + x) + \cot (450 ° + x)}{cosec (90 ° - x) + \tan (180 ° - x)} + \frac{\tan (180 ° + x) + \sec (180 ° - x)}{\tan (360 ° + x) - \sec (- x)} = 2$ (iii) $\frac{\sin (180 ° + x) \cos (90 ° + x) \tan (270 ° - x) \cot (360 ° - x)}{\sin (360 ° - x) \cos (360 ° + x) cosec (- x) \sin (270 ° + x)} = 1$ (iv) $\{1 + \cot x - \sec (\frac{π}{2} + x)\} \{1 + \cot x + \sec (\frac{π}{2} + x)\} = 2 \cot x$ (v) $\frac{\tan (90 ° - x) \sec (180 ° - x) \sin (- x)}{\sin (180 ° + x) \cot (360 ° - x) cosec (90 ° - x)} = 1$

Discussion

4758.	The parking charges of a car in a parking lot are Rs.30 for the first two hours and Rs.10 for subsequent hours. Taking total parking time to be 'X hours and total charges as 'y, write a linear equation in two variables to express the above statement. Draw a graph for the linear equation and tell the charges for five hours.
Answer» The parking charges of a car in a parking lot are Rs.30 for the first two hours and Rs.10 for subsequent hours. Taking total parking time to be 'X hours and total charges as 'y, write a linear equation in two variables to express the above statement. Draw a graph for the linear equation and tell the charges for five hours.

Discussion

4759.	If points (1,2,3).(0,-4,3). (2,3,5) and (1,-5,-3)are vertices of tetra-hedron. Then thepoints where lines joining the mid-points of opposite edges are concurrent is
Answer» If points (1,2,3).(0,-4,3). (2,3,5) and (1,-5,-3)are vertices of tetra-hedron. Then thepoints where lines joining the mid-points of opposite edges are concurrent is

Discussion

4760.	Question 13x + 1 is a factor of the polynomialA) x3+x2−x+1B) x3+x2+x+1C) x4+x3+x2+1D) x4+3x3+3x2+x+1
Answer» Question 13 x + 1 is a factor of the polynomial A) $x^{3} + x^{2} - x + 1$ B) $x^{3} + x^{2} + x + 1$ C) $x^{4} + x^{3} + x^{2} + 1$ D) $x^{4} + 3 x^{3} + 3 x^{2} + x + 1$

Discussion

4761.	Radius of a sector of a circle is 3.5 cm and length of its arc is 2.2 cm. Find the area of the sector.
Answer» Radius of a sector of a circle is 3.5 cm and length of its arc is 2.2 cm. Find the area of the sector.

Discussion

4762.	In the following figure, ABCD is a trapezium of area 24.5 cm2 , If AD \|\| BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region. [CBSE 2014]
Answer» In the following figure, ABCD is a trapezium of area 24.5 cm² , If AD \|\| BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region. [CBSE 2014]

Discussion

4763.	In fig, the line segment XY is parallel to side AC of △ABC and it divides the triangle into two parts of equal areas. Find the ratio AXAB
Answer» In fig, the line segment XY is parallel to side AC of $△$ ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{A X}{A B}$

4763.

In fig, the line segment XY is parallel to side AC of △ABC and it divides the triangle into two parts of equal areas. Find the ratio AXAB

Answer»

In fig, the line segment XY is parallel to side AC of $△$ ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{A X}{A B}$

Discussion

4764.	If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1:S2=(2n+1):(n+1)
Answer» If $S_{1}$ be the sum of (2n + 1) terms of an A.P. and $S_{2}$ be the sum of its odd terms, then prove that: $S_{1} : S_{2} = (2 n + 1) : (n + 1)$

4764.

If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1:S2=(2n+1):(n+1)

Answer»

If $S_{1}$ be the sum of (2n + 1) terms of an A.P. and $S_{2}$ be the sum of its odd terms, then prove that:

$S_{1} : S_{2} = (2 n + 1) : (n + 1)$

Discussion

4765.	Which of the following is the factor of the polynomialx3−3x2−10x+12 ?
Answer» Which of the following is the factor of the polynomial $x^{3} - 3 x^{2} - 10 x + 12$ ?

Discussion

4766.	If PA and PB are two tangents to a circle with centre O, such that ∠AOB = 110°, find ∠APB.(a) 55° (b) 60°(c) 70°(d) 90°
Answer» If PA and PB are two tangents to a circle with centre O, such that ∠AOB = 110°, find ∠APB. (a) 55° (b) 60° (c) 70° (d) 90°

Discussion

4767.	Mark the correct alternative in the following question:If 2x-32=5x+34, then x=a 34 b -34 c 43 d -43
Answer» Mark the correct alternative in the following question: $If 2 x - \frac{3}{2} = 5 x + \frac{3}{4}, then x = (a) \frac{3}{4} (b) - \frac{3}{4} (c) \frac{4}{3} (d) - \frac{4}{3}$

Discussion

4768.	In given figure △ ABC and △ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54cm2 find the area of △ DEF __ cm2
Answer» In given figure $△$ ABC and $△$ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54 $c m^{2}$ find the area of $△$ DEF __ $c m^{2}$

4768.

In given figure △ ABC and △ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54cm2 find the area of △ DEF __ cm2

Answer»

In given figure $△$ ABC and $△$ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54 $c m^{2}$ find the area of $△$ DEF

__

c m^{2}

Discussion

4769.	5. If 45% of a number is added to another number, the first number becomes 135 times of the another number. What is the ratio of these two numbers?
Answer» 5. If 45% of a number is added to another number, the first number becomes 135 times of the another number. What is the ratio of these two numbers?

Discussion

4770.	Question 20Area of a quadrilateral ABCD is 20 cm2 and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is(a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm
Answer» Question 20 Area of a quadrilateral ABCD is $20 c m^{2}$ and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is (a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

4770.

Question 20Area of a quadrilateral ABCD is 20 cm2 and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is(a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

Answer»

Question 20

Area of a quadrilateral ABCD is $20 c m^{2}$ and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is

(a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

Discussion

4771.	If sin A = 817, find the value of secA cosA + cosecA cosA.
Answer» If sin A = $\frac{8}{17}$ , find the value of secA cosA + cosecA cosA.

Discussion

4772.	Length of the common tangent of the circles x^2+y^2+2x+3y+1=0andx^2+y^2+4x+3y+4=0is
Answer» Length of the common tangent of the circles x^2+y^2+2x+3y+1=0andx^2+y^2+4x+3y+4=0is

Discussion

4773.	What is incenter?
Answer» What is incenter?

Discussion

4774.	23. An ellipse with axis parallel to coordinate axis cuts the parabola y=4x at (1,-2) and touches it at (4,4) then the coordinate of other point of intersection is
Answer» 23. An ellipse with axis parallel to coordinate axis cuts the parabola y=4x at (1,-2) and touches it at (4,4) then the coordinate of other point of intersection is

Discussion

4775.	In Fig. 7.143, ∠A=∠CED, prove that ΔCAB∼ΔCED. Also, find the value of x.
Answer» In Fig. 7.143, $∠ A = ∠ C E D$ , prove that $Δ C A B \sim Δ C E D$ . Also, find the value of x.

4775.

In Fig. 7.143, ∠A=∠CED, prove that ΔCAB∼ΔCED. Also, find the value of x.

Answer»

In Fig. 7.143, $∠ A = ∠ C E D$ , prove that $Δ C A B \sim Δ C E D$ . Also, find the value of x.

Discussion

4776.	Question 15A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 411921m3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?
Answer» Question 15 A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41 \frac{19}{21} m^{3}$ of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?

Discussion

4777.	The area of ∆ABO with vertices A(a, 0), O(0, 0) and B(0, b) in square units is(a) ab (b) 12ab (c) 12a2b2 (d) 12b2
Answer» The area of $∆ A B O$ with vertices A(a, 0), O(0, 0) and B(0, b) in square units is (a) ab (b) $\frac{1}{2} a b$ (c) $\frac{1}{2} a^{2} b^{2}$ (d) $\frac{1}{2} b^{2}$

Discussion

4778.	A bag contains 4 white, 5 red and 6 blue balls. A ball is drawn at random from the bag. The probability that it is not a red ball is
Answer» A bag contains 4 white, 5 red and 6 blue balls. A ball is drawn at random from the bag. The probability that it is not a red ball is

Discussion

4779.	A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60∘ and from the same point the angle of elevation of the top of the pedestal is 45∘. Find the height of the pedestal.
Answer» A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point the angle of elevation of the top of the pedestal is $45^{\circ}$ . Find the height of the pedestal.

Discussion

4780.	Write down the number sequence from the following pattern taking only the smallest square as a unit square.
Answer» Write down the number sequence from the following pattern taking only the smallest square as a unit square.

Discussion

4781.	6. The long and short hand of a clock are 6cm and 4cm respectively.find the sum of distance travelled by their tips in a day.write importance of time in student life
Answer» 6. The long and short hand of a clock are 6cm and 4cm respectively.find the sum of distance travelled by their tips in a day.write importance of time in student life

Discussion

4782.	If (x4+x2y+y2) is one of the factors of an expression which is the difference of two cubes, then the other factor is ___.
Answer» If ${(x}^{4} + x^{2} y + y^{2})$ is one of the factors of an expression which is the difference of two cubes, then the other factor is ___.

Discussion

4783.	In the figure, given below, AD = BC, ∠ BAC=30∘ and ∠CBD=70∘. Find: ∠ ABC
Answer» In the figure, given below, AD = BC, $∠ B A C = 30^{\circ}$ and $∠ C B D = 70^{\circ}$ . Find: $∠ A B C$

4783.

In the figure, given below, AD = BC, ∠ BAC=30∘ and ∠CBD=70∘. Find: ∠ ABC

Answer»

In the figure, given below, AD = BC, $∠ B A C = 30^{\circ}$ and $∠ C B D = 70^{\circ}$ . Find: $∠ A B C$

Discussion

4784.	The distance between the points P(3, 2) and Q(–4, 5) is
Answer» The distance between the points P(3, 2) and Q(–4, 5) is

Discussion

4785.	In the given figure, PAQ is the tangent. BC is the diameter of the circle. If ∠BAQ=60∘, then ∠ABC = _____.
Answer» In the given figure, PAQ is the tangent. BC is the diameter of the circle. If $∠ B A Q = 60^{\circ}$ , then $∠ A B C$ = _____.

4785.

In the given figure, PAQ is the tangent. BC is the diameter of the circle. If ∠BAQ=60∘, then ∠ABC = _____.

Answer»

In the given figure, PAQ is the tangent. BC is the diameter of the circle. If $∠ B A Q = 60^{\circ}$ , then $∠ A B C$ = _____.

Discussion

4786.	In Fig. 7.222, angle B is greater than 90 degrees and segement AD⊥BC, show that (i) b2=h2+a2+x2−2ax (ii) b2=a2+c2−2ax
Answer» In Fig. 7.222, angle B is greater than 90 degrees and segement $A D ⊥ B C$ , show that (i) $b^{2} = h^{2} + a^{2} + x^{2} - 2 a x$ (ii) $b^{2} = a^{2} + c^{2} - 2 a x$

4786.

In Fig. 7.222, angle B is greater than 90 degrees and segement AD⊥BC, show that (i) b2=h2+a2+x2−2ax (ii) b2=a2+c2−2ax

Answer»

In Fig. 7.222, angle B is greater than 90 degrees and segement $A D ⊥ B C$ , show that
(i) $b^{2} = h^{2} + a^{2} + x^{2} - 2 a x$
(ii) $b^{2} = a^{2} + c^{2} - 2 a x$

Discussion

4787.	Find the next term in the following sequence: a-2d, a-d, a, a+d,...
Answer» Find the next term in the following sequence: a-2d, a-d, a, a+d,...

Discussion

4788.	If α and β are the zeroes of the quadratic polynomial 2x2−8x+4, then the value of αβ+βα+2(1α+1β)+3αβ is ___.16
Answer» If $α a n d β$ are the zeroes of the quadratic polynomial $2 x^{2} - 8 x + 4$ , then the value of $\frac{α}{β} + \frac{β}{α} + 2 (\frac{1}{α} + \frac{1}{β}) + 3 α β$ is ___. 16

Discussion

4789.	For what value of k does the system of equations kx+2y=5,3x−4y=10 have (i) a unique solution, (ii) no solution?
Answer» For what value of k does the system of equations $k x + 2 y = 5, 3 x - 4 y = 10$ have (i) a unique solution, (ii) no solution?

4789.

For what value of k does the system of equations kx+2y=5,3x−4y=10 have (i) a unique solution, (ii) no solution?

Answer»

For what value of k does the system of equations $k x + 2 y = 5, 3 x - 4 y = 10$ have

(i) a unique solution,

(ii) no solution?

Discussion

4790.	Find the remainder when the polynomial f(x)=2x4−6x3+2x2−x+2 is divided by x + 2
Answer» Find the remainder when the polynomial $f (x) = 2 x^{4} - 6 x^{3} + 2 x^{2} - x + 2$ is divided by x + 2

Discussion

4791.	Question 3The points (0,5), (0,-9) and (3,6) are collinear.
Answer» Question 3 The points (0,5), (0,-9) and (3,6) are collinear.

Discussion

4792.	With a cylindrical bucket of radius 14 cm and height 16 cm, 27 buckets of lime was poured to form a conical heap. If the area of its base is 5544 cm, then the canvas required to cover it will be
Answer» With a cylindrical bucket of radius 14 cm and height 16 cm, 27 buckets of lime was poured to form a conical heap. If the area of its base is 5544 cm, then the canvas required to cover it will be

Discussion

4793.	Solve the following quadratic equations by factorization:12a+b+2x=12a+1b+12x
Answer» Solve the following quadratic equations by factorization: $\frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}$

Discussion

4794.	From the given figure, find ∠P. [2 MARKS]
Answer» From the given figure, find $∠ P$ . [2 MARKS]

4794.

From the given figure, find ∠P. [2 MARKS]

Answer»

From the given figure, find $∠ P$ . [2 MARKS]

Discussion

4795.	Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.
Answer» Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.

Discussion

4796.	Question 4Two AP’s have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms?Why?
Answer» Question 4 Two AP’s have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their $10^{t h}$ terms is the same as the difference between their $21^{s t}$ terms, which is the same as the difference between any two corresponding terms?Why?

Discussion

4797.	Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years ago, the product of their ages in years was 48.
Answer» Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years ago, the product of their ages in years was 48.

Discussion

4798.	The area of the triangle ABC is 25.6 sq. cm XY is drawn parallel to BC and it divides AB in the ratio 5:3. Find the area of the triangle AXY.
Answer» The area of the triangle ABC is 25.6 sq. cm XY is drawn parallel to BC and it divides AB in the ratio 5:3. Find the area of the triangle AXY.

Discussion

4799.	If a card is drawn from a well shuffled pack of playing cards, then the probability that the card drawn is an honor is
Answer» If a card is drawn from a well shuffled pack of playing cards, then the probability that the card drawn is an honor is

Discussion

4800.	Draw a 'more than' ogive for the data given below which gives the marks of 100 students. Number of wickets0−1010−2020−3030−4040−5050−6060−7070−80Number of students4610102522185
Answer» Draw a 'more than' ogive for the data given below which gives the marks of 100 students. $\begin{matrix} N u m b e r o f w i c k e t s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 N u m b e r o f s t u d e n t s & 4 & 6 & 10 & 10 & 25 & 22 & 18 & 5 \end{matrix}$

4800.

Draw a 'more than' ogive for the data given below which gives the marks of 100 students. Number of wickets0−1010−2020−3030−4040−5050−6060−7070−80Number of students4610102522185

Answer»

Draw a 'more than' ogive for the data given below which gives the marks of 100 students.

$\begin{matrix} N u m b e r o f w i c k e t s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 N u m b e r o f s t u d e n t s & 4 & 6 & 10 & 10 & 25 & 22 & 18 & 5 \end{matrix}$

Discussion

Explore topic-wise InterviewSolutions in .

Question 8An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

Mark the correct alternative in each of the following:A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q such that OQ = 12 cm. Length PQ is(a) 12 cm(b) 13 cm(c) 8.5 cm(d) 119 cm

Obtain all other zeroes of 3x4+6x3−2x2−10x−5, if two of its zeroes are √53 and −√53.

For any positive integer n, prove that n3 – n divisible by 6.

Question 4Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

Question 1 (ii)Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.2x + y = 5 ; 3x +2y =8

If points (1,2,3).(0,-4,3). (2,3,5) and (1,-5,-3)are vertices of tetra-hedron. Then thepoints where lines joining the mid-points of opposite edges are concurrent is

Question 13x + 1 is a factor of the polynomialA) x3+x2−x+1B) x3+x2+x+1C) x4+x3+x2+1D) ​​​​​​​x4+3x3+3x2+x+1​​​​​​​

Radius of a sector of a circle is 3.5 cm and length of its arc is 2.2 cm. Find the area of the sector.

In the following figure, ABCD is a trapezium of area 24.5 cm2 , If AD || BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region. [CBSE 2014]

In fig, the line segment XY is parallel to side AC of △ABC and it divides the triangle into two parts of equal areas. Find the ratio AXAB

If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1:S2=(2n+1):(n+1)

Which of the following is the factor of the polynomialx3−3x2−10x+12 ?

If PA and PB are two tangents to a circle with centre O, such that ∠AOB = 110°, find ∠APB.(a) 55° (b) 60°(c) 70°(d) 90°

Mark the correct alternative in the following question:If 2x-32=5x+34, then x=a 34 b -34 c 43 d -43

In given figure △ ABC and △ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54cm2 find the area of △ DEF __ cm2

5. If 45% of a number is added to another number, the first number becomes 135 times of the another number. What is the ratio of these two numbers?

Question 20Area of a quadrilateral ABCD is 20 cm2 and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is(a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

If sin A = 817, find the value of secA cosA + cosecA cosA.

Length of the common tangent of the circles x^2+y^2+2x+3y+1=0andx^2+y^2+4x+3y+4=0is

What is incenter?

23. An ellipse with axis parallel to coordinate axis cuts the parabola y=4x at (1,-2) and touches it at (4,4) then the coordinate of other point of intersection is

In Fig. 7.143, ∠A=∠CED, prove that ΔCAB∼ΔCED. Also, find the value of x.

Question 15A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 411921m3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?

The area of ∆ABO with vertices A(a, 0), O(0, 0) and B(0, b) in square units is(a) ab (b) 12ab (c) 12a2b2 (d) 12b2

A bag contains 4 white, 5 red and 6 blue balls. A ball is drawn at random from the bag. The probability that it is not a red ball is

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60∘ and from the same point the angle of elevation of the top of the pedestal is 45∘. Find the height of the pedestal.

Write down the number sequence from the following pattern taking only the smallest square as a unit square.

6. The long and short hand of a clock are 6cm and 4cm respectively.find the sum of distance travelled by their tips in a day.write importance of time in student life

If (x4+x2y+y2) is one of the factors of an expression which is the difference of two cubes, then the other factor is ___.

In the figure, given below, AD = BC, ∠ BAC=30∘ and ∠CBD=70∘. Find: ∠ ABC

The distance between the points P(3, 2) and Q(–4, 5) is

In the given figure, PAQ is the tangent. BC is the diameter of the circle. If ∠BAQ=60∘, then ∠ABC = _____.

In Fig. 7.222, angle B is greater than 90 degrees and segement AD⊥BC, show that (i) b2=h2+a2+x2−2ax (ii) b2=a2+c2−2ax

Find the next term in the following sequence: a-2d, a-d, a, a+d,...

If α and β are the zeroes of the quadratic polynomial 2x2−8x+4, then the value of αβ+βα+2(1α+1β)+3αβ is ___.16

For what value of k does the system of equations kx+2y=5,3x−4y=10 have (i) a unique solution, (ii) no solution?

Find the remainder when the polynomial f(x)=2x4−6x3+2x2−x+2 is divided by x + 2

Question 3The points (0,5), (0,-9) and (3,6) are collinear.

With a cylindrical bucket of radius 14 cm and height 16 cm, 27 buckets of lime was poured to form a conical heap. If the area of its base is 5544 cm, then the canvas required to cover it will be

Solve the following quadratic equations by factorization:12a+b+2x=12a+1b+12x

From the given figure, find ∠P. [2 MARKS]

Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.

Question 4Two AP’s have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms?Why?

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years ago, the product of their ages in years was 48.

The area of the triangle ABC is 25.6 sq. cm XY is drawn parallel to BC and it divides AB in the ratio 5:3. Find the area of the triangle AXY.

If a card is drawn from a well shuffled pack of playing cards, then the probability that the card drawn is an honor is

Draw a 'more than' ogive for the data given below which gives the marks of 100 students. Number of wickets0−1010−2020−3030−4040−5050−6060−7070−80Number of students4610102522185

Question 13x + 1 is a factor of the polynomialA) x3+x2−x+1B) x3+x2+x+1C) x4+x3+x2+1D) x4+3x3+3x2+x+1