32581 + Interview Questions in Mathematics Page 128 InterviewSolution

6351.	A man walks a certain distance with certain speed. If he walks 1/2 km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.
Answer» A man walks a certain distance with certain speed. If he walks 1/2 km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.

Discussion

6352.	For a pair of linear equations, a1=12, b1= 2, c1= 6 and a2=24, b2=4, c2=7. Then the linear equation has
Answer» For a pair of linear equations, $a_{1}$ =12, $b_{1}$ = 2, $c_{1}$ = 6 and $a_{2}$ =24, $b_{2}$ =4, $c_{2}$ =7. Then the linear equation has

Discussion

6353.	Question 1 (iv)Find the sum of the following APs(iv) 115,112,110,……,to 11 terms
Answer» Question 1 (iv) Find the sum of the following APs (iv) $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \dots \dots, t o 11 t e r m s$

Discussion

6354.	In a △ABC, ∠A=60∘, ∠B=30∘ and ∠C=90∘.Then find the ratio of the sides AC: BC: AB.
Answer» In a $△ A B C, ∠ A = 60^{\circ}, ∠ B = 30^{\circ} a n d ∠ C = 90^{\circ} .$ Then find the ratio of the sides AC: BC: AB.

Discussion

6355.	A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is black or king.
Answer» A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is black or king.

Discussion

6356.	The shapes formed by rotating a right triangle about its height is:
Answer» The shapes formed by rotating a right triangle about its height is:

Discussion

6357.	7. Find the discriminant for the quadratic equation.Also determine the nature of the root (x-2p)(x-2q)=4pq;p not equal to q
Answer» 7. Find the discriminant for the quadratic equation.Also determine the nature of the root (x-2p)(x-2q)=4pq;p not equal to q

Discussion

6358.	Let a matrix A=[103−1], then A15 can be
Answer» Let a matrix $A = [\begin{matrix} 1 & 0 3 & - 1 \end{matrix}],$ then $A^{15}$ can be

Discussion

6359.	FOR ANY POSITIVE INTEGER n , prove that n3 - n is divisible by 6.
Answer» FOR ANY POSITIVE INTEGER n , prove that n³- n is divisible by 6.

Discussion

6360.	If the square of the difference of the zeroes of the quadratic polynomial, f(x)=x2+px+15 is equal to 196, then find out the value of p.
Answer» If the square of the difference of the zeroes of the quadratic polynomial, $f (x) = x^{2} + p x + 15$ is equal to 196, then find out the value of p.

Discussion

6361.	The value of the polynomial 5z-4x×4x+3 when x=-1
Answer» The value of the polynomial 5z-4x×4x+3 when x=-1

Discussion

6362.	Find the solution of the following pair of equations.3x−5y=−1 and x−y=−1
Answer» Find the solution of the following pair of equations. $3 x - 5 y = - 1$ and $x - y = - 1$

Discussion

6363.	In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then angle BAC is ________
Answer» In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then angle BAC is ________

Discussion

6364.	Ritu can row down stream 20 k. In 2 hrs and up stream 4km in 2 hrs find her speed of rowing in still water and the speed of the current
Answer» Ritu can row down stream 20 k. In 2 hrs and up stream 4km in 2 hrs find her speed of rowing in still water and the speed of the current

Discussion

6365.	The length of the tangent drawn from a point 8 cm away form the centre of a circle of radius 6 cm is(a) 7 cm(b) 27(c) 10 cm(d) 5 cm
Answer» The length of the tangent drawn from a point 8 cm away form the centre of a circle of radius 6 cm is (a) $\sqrt{7} c m$ (b) $2 \sqrt{7}$ (c) 10 cm (d) 5 cm

Discussion

6366.	The sum of the squares of two consecutive even numbers is 340. Find the numbers.
Answer» The sum of the squares of two consecutive even numbers is 340. Find the numbers.

Discussion

6367.	A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed . If it takes 3 hours to complete total journey , what is its original average speed ?133007
Answer» A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed . If it takes 3 hours to complete total journey , what is its original average speed ?133007

Discussion

6368.	Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.
Answer» Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.

Discussion

6369.	If x=23 is a solution of the quadratic equation 7x2+mx−3=0, find the value of m.
Answer» If $x = \frac{2}{3}$ is a solution of the quadratic equation $7 x^{2} + m x - 3 = 0$ , find the value of m.

Discussion

6370.	If A(-2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides. OR If A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.
Answer» If A(-2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides. OR If A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

Discussion

6371.	A rectangular paper of length l and breadth h is wrapped around a cylindrical can of radius r and height h.S1 : The length of rectangular sheet required equals circumference of circleS2 : The area of rectangular sheet required = 2πrh
Answer» A rectangular paper of length l and breadth h is wrapped around a cylindrical can of radius r and height h. S1 : The length of rectangular sheet required equals circumference of circle S2 : The area of rectangular sheet required = 2πrh

6371.

A rectangular paper of length l and breadth h is wrapped around a cylindrical can of radius r and height h.S1 : The length of rectangular sheet required equals circumference of circleS2 : The area of rectangular sheet required = 2πrh

Answer»

A rectangular paper of length l and breadth h is wrapped around a cylindrical can of radius r and height h.

S1 : The length of rectangular sheet required equals circumference of circle

S2 : The area of rectangular sheet required = 2πrh

Discussion

6372.	The polynomials ax3+4x2+3x−4 and x3−4x+a leave the same remainder when divided by (x−3). Find the value of a.
Answer» The polynomials $a x^{3} + 4 x^{2} + 3 x - 4$ and $x^{3} - 4 x + a$ leave the same remainder when divided by $(x - 3)$ . Find the value of $a$ .

Discussion

6373.	If 2(2n + 5) = 3(3n - 10), then n =(a) 5 (b) 3 (c) 7 (d) 8
Answer» If 2(2n + 5) = 3(3n $-$ 10), then n = (a) 5 (b) 3 (c) 7 (d) 8

Discussion

6374.	Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, ∠A = 700 PR = 9 cm, ∠P = 700 and PQ = 4.5 cm. Show that△ABC ∼ △PQR and state similarity theorem.
Answer» Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, ∠A = 70⁰ PR = 9 cm, ∠P = 70⁰ and PQ = 4.5 cm. Show that △ABC ∼ △PQR and state similarity theorem.

Discussion

6375.	Find the values of k for the following quadratic equation, so that they have two equal roots. kx (x - 2) + 6 = 0
Answer» Find the values of k for the following quadratic equation, so that they have two equal roots. kx (x - 2) + 6 = 0

Discussion

6376.	Which of the following logic gate corresponds to the truth table given below?ABY110101011001
Answer» Which of the following logic gate corresponds to the truth table given below? $\begin{matrix} A & B & Y 1 & 1 & 0 1 & 0 & 1 0 & 1 & 1 0 & 0 & 1 \end{matrix}$

Discussion

6377.	Question 5 (i) Find the number of terms in each of the following A.P. (i) 7, 13, 19, .., 205
Answer» Question 5 (i) Find the number of terms in each of the following A.P. (i) 7, 13, 19, .., 205

Discussion

6378.	If two vertices of a parallelogram are (3, 2) (−1, 0) and the diagonals cut at (2, −5), find the other vertices of the parallelogram.
Answer» If two vertices of a parallelogram are (3, 2) (−1, 0) and the diagonals cut at (2, −5), find the other vertices of the parallelogram.

Discussion

6379.	Match the following columns: Column IColumn II(a)The most frequent value in a data is known as ........(p)standard deviation(b)which of the following cannot be determined graphically out of mean,mode and median?(q)median(c)An ogive is used to determine.......(r)mean(d)Out ofmean,mode,median andstandard deviation, which is not a measure of central tendency?(s)mode
Answer» Match the following columns: $\begin{matrix} C o l u m n I & C o l u m n I I (a) T h e m o s t f r e q u e n t v a l u e i n a d a t a i s k n o w n a s . . . . . . . . & (p) s t a n d a r d d e v i a t i o n (b) w h i c h o f t h e f o l l o w i n g c a n n o t b e d e t e r m i n e d g r a p h i c a l l y o u t o f m e a n, m o d e a n d m e d i a n ? & (q) m e d i a n (c) A n o g i v e i s u s e d t o d e t e r m i n e . . . . . . . & (r) m e a n (d) O u t o f m e a n, m o d e, m e d i a n a n d s t a n d a r d d e v i a t i o n, w h i c h i s n o t a m e a s u r e o f c e n t r a l t e n d e n c y ? & (s) m o d e \end{matrix}$

6379.

Match the following columns: Column IColumn II(a)The most frequent value in a data is known as ........(p)standard deviation(b)which of the following cannot be determined graphically out of mean,mode and median?(q)median(c)An ogive is used to determine.......(r)mean(d)Out ofmean,mode,median andstandard deviation, which is not a measure of central tendency?(s)mode

Answer»

Match the following columns:

$\begin{matrix} C o l u m n I & C o l u m n I I (a) T h e m o s t f r e q u e n t v a l u e i n a d a t a i s k n o w n a s . . . . . . . . & (p) s t a n d a r d d e v i a t i o n (b) w h i c h o f t h e f o l l o w i n g c a n n o t b e d e t e r m i n e d g r a p h i c a l l y o u t o f m e a n, m o d e a n d m e d i a n ? & (q) m e d i a n (c) A n o g i v e i s u s e d t o d e t e r m i n e . . . . . . . & (r) m e a n (d) O u t o f m e a n, m o d e, m e d i a n a n d s t a n d a r d d e v i a t i o n, w h i c h i s n o t a m e a s u r e o f c e n t r a l t e n d e n c y ? & (s) m o d e \end{matrix}$

Discussion

6380.	In the given figure, CD is the tangent at Q and ∠RQD=x∘, then the measure of ∠RPQ is equal to
Answer» In the given figure, CD is the tangent at Q and $∠ R Q D = x^{\circ},$ then the measure of $∠ R P Q$ is equal to

Discussion

6381.	If a number x is chosen from the numbers 1, 2, 3, and a number y is selected from the numbers 1, 4, 9. Then, P(xy < 9)(a) 79(b) 59(c) 23(d) 19
Answer» If a number x is chosen from the numbers 1, 2, 3, and a number y is selected from the numbers 1, 4, 9. Then, P(xy < 9) (a) $\frac{7}{9}$ (b) $\frac{5}{9}$ (c) $\frac{2}{3}$ (d) $\frac{1}{9}$

Discussion

6382.	26. Let f(x) be a polynomial with real coefficient such that f(x)=0 is satisfied by x = 1, 2, 3 only. then the value of f(1)f(2)f(3) =? 1. Positive 2.negative 3.zero 4.information insufficient
Answer» 26. Let f(x) be a polynomial with real coefficient such that f(x)=0 is satisfied by x = 1, 2, 3 only. then the value of f(1)f(2)f(3) =? 1. Positive 2.negative 3.zero 4.information insufficient

Discussion

6383.	A tower subtends an angle of 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60°. The height of the tower is(a) h2 m(b) 3h m(c) h3 m(d) h3m
Answer» A tower subtends an angle of 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60°. The height of the tower is (a) $\frac{h}{2} m$ (b) $\sqrt{3 h} m$ (c) $\frac{h}{3} m$ (d) $\frac{h}{\sqrt{3}} m$

Discussion

6384.	If A=[0α00] and (A+I)50−50A=[abcd], then the value of a+b+c+d is
Answer» If $A = [\begin{matrix} 0 & α 0 & 0 \end{matrix}]$ and $(A + I)^{50} - 50 A = [\begin{matrix} a & b c & d \end{matrix}],$ then the value of $a + b + c + d$ is

Discussion

6385.	u=10m/sAngle with horizontal=60 degreeProjected from height =11.25To find:horizontal range
Answer» u=10m/s Angle with horizontal=60 degree Projected from height =11.25 To find:horizontal range

Discussion

6386.	Which of the following is a rational number?(a) 1+3(b) π(c) 23(d) 0
Answer» Which of the following is a rational number? (a) $1 + \sqrt{3}$ (b) π (c) $2 \sqrt{3}$ (d) 0

Discussion

6387.	The areas of two similar triangles are 49 cm2 and 64 cm2 respectively. The ratio of their corresponding sides is
Answer» The areas of two similar triangles are 49 $c m^{2}$ and 64 $c m^{2}$ respectively. The ratio of their corresponding sides is

Discussion

6388.	If ΔPQR≅ΔEFD then(a) Which side of ΔPQR equals ED?(b) Which angle of ΔPQR equals angle E?
Answer» If $Δ P Q R ≅ Δ E F D$ then (a) Which side of ΔPQR equals ED? (b) Which angle of ΔPQR equals angle E?

Discussion

6389.	Let p(x) be a polynomial satisfying p(x3)=x2p(x2) and p(0)=−3, p′(13)=0, p(1)=2. Then the value of p(3) is
Answer» Let $p (x)$ be a polynomial satisfying $p (x^{3}) = x^{2} p (x^{2})$ and $p (0) = - 3,$ $p^{'} (\frac{1}{3}) = 0,$ $p (1) = 2 .$ Then the value of $p (3)$ is

Discussion

6390.	The 16th term of an AP is 1 more than twice its 8th term. If the 12th term of the AP is 47, then find its nth term.
Answer» The $16^{t h}$ term of an AP is 1 more than twice its $8^{t h}$ term. If the $12^{t h}$ term of the AP is 47, then find its $n^{t h}$ term.

Discussion

6391.	13. In a quadratic polynomial if f(1) = 1, f(2) = 2, f(3) = 3, f(4) = 16 then find f(5)
Answer» 13. In a quadratic polynomial if f(1) = 1, f(2) = 2, f(3) = 3, f(4) = 16 then find f(5)

Discussion

6392.	The angles of depression of two ships from the top of a light house are 45° and 30° towards east. If the ships are 100 m apart. the height of the light house is(a) 503+1 m(b) 503-1 m(c) 50 3-1 m(d) 50 3+1 m
Answer» The angles of depression of two ships from the top of a light house are 45° and 30° towards east. If the ships are 100 m apart. the height of the light house is (a) $\frac{50}{\sqrt{3 + 1}} m$ (b) $\frac{50}{\sqrt{3 - 1}} m$ (c) $50 (\sqrt{3} - 1) m$ (d) $50 (\sqrt{3} + 1) m$

Discussion

6393.	The radii of two right circular cylinders are in the ratio 3 : 4 and their heights are in the ratio 1 : 2. Calculate the ratio of their curved surface areas
Answer» The radii of two right circular cylinders are in the ratio 3 : 4 and their heights are in the ratio 1 : 2. Calculate the ratio of their curved surface areas

Discussion

6394.	If ABC and DEF are similar triangles such that ∠A = 57° and ∠E = 73°, what is the measure of ∠C?
Answer» If ABC and DEF are similar triangles such that ∠A = 57° and ∠E = 73°, what is the measure of ∠C?

Discussion

6395.	The logically equivalent proposition of p⇔q is
Answer» The logically equivalent proposition of $p \Leftrightarrow q$ is

Discussion

6396.	Solve the following systems of equations: 10x+y+2x−y=4 15x+y−9x−y=−2
Answer» Solve the following systems of equations: $\frac{10}{x + y} + \frac{2}{x - y} = 4$ $\frac{15}{x + y} - \frac{9}{x - y} = - 2$

6396.

Solve the following systems of equations: 10x+y+2x−y=4 15x+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

6397.	In the following question, two equations numbered I and II are given. You have to solve both the equations and choose the apropriate answer. I. 3x2 + 8x + 4 = 0 II. 4y2 - 19y + 12 = 0
Answer» In the following question, two equations numbered I and II are given. You have to solve both the equations and choose the apropriate answer. I. 3x $^{2}$ + 8x + 4 = 0 II. 4y $^{2}$ - 19y + 12 = 0

6397.

In the following question, two equations numbered I and II are given. You have to solve both the equations and choose the apropriate answer. I. 3x2 + 8x + 4 = 0 II. 4y2 - 19y + 12 = 0

Answer»

In the following question, two equations numbered I and II are given. You have to solve both the equations and choose the apropriate answer.

I. 3x $^{2}$ + 8x + 4 = 0

II. 4y $^{2}$ - 19y + 12 = 0

Discussion

6398.	Solve the following quadratic equation by factorization. (x−4)(x+2)=0
Answer» Solve the following quadratic equation by factorization. $(x - 4) (x + 2) = 0$

Discussion

6399.	An AP 8, 10, 12, ... has 60 terms. Find its last term. Hence, find the sum of its last 10 terms. [CBSE 2015]
Answer» An AP 8, 10, 12, ... has 60 terms. Find its last term. Hence, find the sum of its last 10 terms. [CBSE 2015]

Discussion

6400.	21. Find sum of all two digit natural numbers which are divisible by 4
Answer» 21. Find sum of all two digit natural numbers which are divisible by 4

Discussion

Explore topic-wise InterviewSolutions in .

A man walks a certain distance with certain speed. If he walks 1/2 km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.

For a pair of linear equations, a1=12, b1= 2, c1= 6 and a2=24, b2=4, c2=7. Then the linear equation has

Question 1 (iv)Find the sum of the following APs(iv) 115,112,110,……,to 11 terms

In a △ABC, ∠A=60∘, ∠B=30∘ and ∠C=90∘.Then find the ratio of the sides AC: BC: AB.

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is black or king.

The shapes formed by rotating a right triangle about its height is:

7. Find the discriminant for the quadratic equation.Also determine the nature of the root (x-2p)(x-2q)=4pq;p not equal to q

Let a matrix A=[103−1], then A15 can be

FOR ANY POSITIVE INTEGER n , prove that n​​​​​​3 - n is divisible by 6.

If the square of the difference of the zeroes of the quadratic polynomial, f(x)=x2+px+15 is equal to 196, then find out the value of p.

The value of the polynomial 5z-4x×4x+3 when x=-1

Find the solution of the following pair of equations.3x−5y=−1 and x−y=−1

In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then angle BAC is ________

Ritu can row down stream 20 k. In 2 hrs and up stream 4km in 2 hrs find her speed of rowing in still water and the speed of the current

The length of the tangent drawn from a point 8 cm away form the centre of a circle of radius 6 cm is(a) 7 cm(b) 27(c) 10 cm(d) 5 cm

The sum of the squares of two consecutive even numbers is 340. Find the numbers.

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed . If it takes 3 hours to complete total journey , what is its original average speed ?133007

Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.

If x=23 is a solution of the quadratic equation 7x2+mx−3=0, find the value of m.

If A(-2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides. OR If A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

A rectangular paper of length l and breadth h is wrapped around a cylindrical can of radius r and height h.S1 : The length of rectangular sheet required equals circumference of circleS2 : The area of rectangular sheet required = 2πrh

The polynomials ax3+4x2+3x−4 and x3−4x+a leave the same remainder when divided by (x−3). Find the value of a.

If 2(2n + 5) = 3(3n - 10), then n =(a) 5 (b) 3 (c) 7 (d) 8

Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, ∠A = 700 PR = 9 cm, ∠P = 700 and PQ = 4.5 cm. Show that△ABC ∼ △PQR and state similarity theorem.

Find the values of k for the following quadratic equation, so that they have two equal roots. kx (x - 2) + 6 = 0

Which of the following logic gate corresponds to the truth table given below?ABY110101011001

Question 5 (i) Find the number of terms in each of the following A.P. (i) 7, 13, 19, .., 205

If two vertices of a parallelogram are (3, 2) (−1, 0) and the diagonals cut at (2, −5), find the other vertices of the parallelogram.

In the given figure, CD is the tangent at Q and ∠RQD=x∘, then the measure of ∠RPQ is equal to

If a number x is chosen from the numbers 1, 2, 3, and a number y is selected from the numbers 1, 4, 9. Then, P(xy < 9)(a) 79(b) 59(c) 23(d) 19

26. Let f(x) be a polynomial with real coefficient such that f(x)=0 is satisfied by x = 1, 2, 3 only. then the value of f(1)f(2)f(3) =? 1. Positive 2.negative 3.zero 4.information insufficient

A tower subtends an angle of 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60°. The height of the tower is(a) h2 m(b) 3h m(c) h3 m(d) h3m

If A=[0α00] and (A+I)50−50A=[abcd], then the value of a+b+c+d is

u=10m/sAngle with horizontal=60 degreeProjected from height =11.25To find:horizontal range

Which of the following is a rational number?(a) 1+3(b) π(c) 23(d) 0

The areas of two similar triangles are 49 cm2 and 64 cm2 respectively. The ratio of their corresponding sides is

If ΔPQR≅ΔEFD then(a) Which side of ΔPQR equals ED?(b) Which angle of ΔPQR equals angle E?

Let p(x) be a polynomial satisfying p(x3)=x2p(x2) and p(0)=−3, p′(13)=0, p(1)=2. Then the value of p(3) is

The 16th term of an AP is 1 more than twice its 8th term. If the 12th term of the AP is 47, then find its nth term.

13. In a quadratic polynomial if f(1) = 1, f(2) = 2, f(3) = 3, f(4) = 16 then find f(5)

The angles of depression of two ships from the top of a light house are 45° and 30° towards east. If the ships are 100 m apart. the height of the light house is(a) 503+1 m(b) 503-1 m(c) 50 3-1 m(d) 50 3+1 m

The radii of two right circular cylinders are in the ratio 3 : 4 and their heights are in the ratio 1 : 2. Calculate the ratio of their curved surface areas

If ABC and DEF are similar triangles such that ∠A = 57° and ∠E = 73°, what is the measure of ∠C?

The logically equivalent proposition of p⇔q is

Solve the following systems of equations: 10x+y+2x−y=4 15x+y−9x−y=−2

In the following question, two equations numbered I and II are given. You have to solve both the equations and choose the apropriate answer. I. 3x2 + 8x + 4 = 0 II. 4y2 - 19y + 12 = 0

Solve the following quadratic equation by factorization. (x−4)(x+2)=0

An AP 8, 10, 12, ... has 60 terms. Find its last term. Hence, find the sum of its last 10 terms. [CBSE 2015]

21. Find sum of all two digit natural numbers which are divisible by 4

FOR ANY POSITIVE INTEGER n , prove that n3 - n is divisible by 6.