43030 + Interview Questions in Mathematics

1.	The value of limx→2⎛⎝(x3−4xx3−8)−1−(x+√2xx−2−√2√x−√2)−1⎞⎠ is equal to
Answer» The value of $lim x \to 2 ⎛ ⎝ {(\frac{x^{3} - 4 x}{x^{3} - 8})}^{- 1} - {(\frac{x + \sqrt{2 x}}{x - 2} - \frac{\sqrt{2}}{\sqrt{x} - \sqrt{2}})}^{- 1} ⎞ ⎠$ is equal to

Discussion

2.	The value of the determinant Δ=∣∣∣∣394457525876657295∣∣∣∣ is
Answer» The value of the determinant $Δ = ∣ ∣∣ ∣ \begin{matrix} 39 & 44 & 57 52 & 58 & 76 65 & 72 & 95 \end{matrix} ∣ ∣∣ ∣$ is

Discussion

3.	Which of the following represents the graph of f(x)=ax2+bx+c where a<b<0<c ?
Answer» Which of the following represents the graph of $f (x) = a x^{2} + b x + c$ where $a < b < 0 < c$ ?

Discussion

4.	If A(cosα,sinα), B(cosβ,sinβ), C(cosγ,sinγ) are the vertices of △ABC and H,G,S are the orthocentre, centroid and circumcentre of △ABC respectively, then which of the following is/are true?
Answer» If $A (cos α, sin α),$ $B (cos β, sin β),$ $C (cos γ, sin γ)$ are the vertices of $△ A B C$ and $H, G, S$ are the orthocentre, centroid and circumcentre of $△ A B C$ respectively, then which of the following is/are true?

Discussion

5.	If A , B are symmetric matrices of same order, then AB − BA is a A. Skew symmetric matrix B. Symmetric matrix C. Zero matrix D. Identity matrix
Answer» If A , B are symmetric matrices of same order, then AB − BA is a A. Skew symmetric matrix B. Symmetric matrix C. Zero matrix D. Identity matrix

Discussion

6.	The length of the string between a kite and a point on the ground is 90 meters. If the string makes angle theta with the ground level such that tan theta is equal to 15 by 8 how high is the kite flying assuming that there is no slack in the string.
Answer» The length of the string between a kite and a point on the ground is 90 meters. If the string makes angle theta with the ground level such that tan theta is equal to 15 by 8 how high is the kite flying assuming that there is no slack in the string.

Discussion

7.	Find the distance of the line 4 x + 7 y + 5 = 0 from the point (1, 2) along the line 2 x – y = 0.
Answer» Find the distance of the line 4 x + 7 y + 5 = 0 from the point (1, 2) along the line 2 x – y = 0.

Discussion

8.	Find the equation of a family of circles touching the lines x2−y2+2y−1=0. (where h and k are parameters)
Answer» Find the equation of a family of circles touching the lines $x^{2} - y^{2} + 2 y - 1 = 0$ . (where $h$ and $k$ are parameters)

Discussion

9.	Diffrentiate y= sin^2(3x+4)
Answer» Diffrentiate y= sin^2(3x+4)

Discussion

10.	∫0π4a2cos2x+b2sin2xdx
Answer» $\int_{0}^{\frac{π}{4}} (a^{2} \cos^{2} x + b^{2} \sin^{2} x) d x$

Discussion

11.	If x,\|x+1\|,\|x−1\| are first three terms of an A.P. then the sum of its first 20 terms is
Answer» If $x, \| x + 1 \|, \| x - 1 \|$ are first three terms of an A.P. then the sum of its first $20$ terms is

Discussion

12.	If x is an acute angle and tan x=17, then the value of cosec2 x-sec2 xcosec2 x+sec2 x is(a) 3/4(b) 1/2(c) 2(d) 5/4
Answer» If x is an acute angle and $\tan x = \frac{1}{\sqrt{7}}$ , then the value of $\frac{{cosec}^{2} x - \sec^{2} x}{{cosec}^{2} x + \sec^{2} x}$ is (a) 3/4 (b) 1/2 (c) 2 (d) 5/4

Discussion

13.	Let →a=2^i−^j+2^k and →b=^i+2^j−^k. Let a vector →v be in the plane containing →a and →b. If →v is perpendicular to the vector 3^i+2^j−^k and its projection on →a is 19 units, then \|2→v\|2 is equal to
Answer» Let $\to a = 2^i -^j + 2^k$ and $\to b =^i + 2^j -^k$ . Let a vector $\to v$ be in the plane containing $\to a$ and $\to b$ . If $\to v$ is perpendicular to the vector $3^i + 2^j -^k$ and its projection on $\to a$ is $19$ units, then $\| 2 \to v \|^{2}$ is equal to

Discussion

14.	Find the quadratic equation whose one root is 1−i√292.
Answer» Find the quadratic equation whose one root is $\frac{1 - i \sqrt{29}}{2}$ .

Discussion

15.	Determine whether each of the following relations are reflexive, symmetric and transitive: (i)Relation R in the set A = {1, 2, 3...13, 14} defined as R = {(x, y): 3x − y = 0} (ii) Relation R in the set N of natural numbers defined as R = {(x, y): y = x + 5 and x < 4} (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y): y is divisible by x} (iv) Relation R in the set Z of all integers defined as R = {(x, y): x − y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x, y): x and y work at the same place} (b) R = {(x, y): x and y live in the same locality} (c) R = {(x, y): x is exactly 7 cm taller than y} (d) R = {(x, y): x is wife of y} (e) R = {(x, y): x is father of y}
Answer» Determine whether each of the following relations are reflexive, symmetric and transitive: (i)Relation R in the set A = {1, 2, 3...13, 14} defined as R = {(x, y): 3x − y = 0} (ii) Relation R in the set N of natural numbers defined as R = {(x, y): y = x + 5 and x < 4} (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y): y is divisible by x} (iv) Relation R in the set Z of all integers defined as R = {(x, y): x − y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x, y): x and y work at the same place} (b) R = {(x, y): x and y live in the same locality} (c) R = {(x, y): x is exactly 7 cm taller than y} (d) R = {(x, y): x is wife of y} (e) R = {(x, y): x is father of y}

15.

Determine whether each of the following relations are reflexive, symmetric and transitive: (i)Relation R in the set A = {1, 2, 3...13, 14} defined as R = {(x, y): 3x − y = 0} (ii) Relation R in the set N of natural numbers defined as R = {(x, y): y = x + 5 and x < 4} (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y): y is divisible by x} (iv) Relation R in the set Z of all integers defined as R = {(x, y): x − y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x, y): x and y work at the same place} (b) R = {(x, y): x and y live in the same locality} (c) R = {(x, y): x is exactly 7 cm taller than y} (d) R = {(x, y): x is wife of y} (e) R = {(x, y): x is father of y}

Answer»

Determine whether each of the following relations are reflexive, symmetric and transitive:
(i)Relation R in the set A = {1, 2, 3...13, 14} defined as
R = {(x, y): 3x − y = 0}

(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}

(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y): y is divisible by x}

(iv) Relation R in the set Z of all integers defined as R = {(x, y): x − y is an integer}

(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y): x and y work at the same place}
(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
(d) R = {(x, y): x is wife of y}
(e) R = {(x, y): x is father of y}

Discussion

16.	the combined equation of three sides of triangle(x2-y2)(2x+3y-6)=0 . if (sectheta,1) is an interior point of the triangle then find value of theta.
Answer» the combined equation of three sides of triangle(x2-y2)(2x+3y-6)=0 . if (sectheta,1) is an interior point of the triangle then find value of theta.

Discussion

17.	The correct graph of y=\|log10x\| is
Answer» The correct graph of $y = \| {log}_{10} x \|$ is

Discussion

18.	Let a,b∈R,(a≠0). If the function f defined asf(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩2x2a ,0≤x<1a ,1≤x<√22b2−4bx3 ,√2≤x<∞is continuous in the interval [0,∞),,then an ordered pair (a,b) is:
Answer» Let $a, b \in R, (a \neq 0) .$ If the function $f$ defined as $f (x) = ⎧ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪ ⎩ \begin{matrix} \frac{2 x^{2}}{a}, 0 \leq x < 1 a, 1 \leq x < \sqrt{2} \frac{2 b^{2} - 4 b}{x^{3}}, \sqrt{2} \leq x < \infty \end{matrix}$ is continuous in the interval $[0, \infty),$ ,then an ordered pair $(a, b)$ is:

Discussion

19.	Let A = {-2, -1, 0, 1, 2} and f:A→Z be a function defined by f(x)=x2−2x−3. Find : i) Range of f i.e. f(A) ii) Pre-images of 6, -3 and 5.
Answer» Let A = {-2, -1, 0, 1, 2} and $f : A \to Z$ be a function defined by $f (x) = x^{2} - 2 x - 3$ . Find : i) Range of f i.e. f(A) ii) Pre-images of 6, -3 and 5.

Discussion

20.	The locus of the centre of a circle, which touches externally the circle x2+y2−6x−6y+14=0 and also touches the y-axis, is given by the equation
Answer» The locus of the centre of a circle, which touches externally the circle $x^{2} + y^{2} - 6 x - 6 y + 14 = 0$ and also touches the y-axis, is given by the equation

Discussion

21.	42. sin A / (cot A + cosec A) = 2 + sin A / (cot A - cosec A)
Answer» 42. sin A / (cot A + cosec A) = 2 + sin A / (cot A - cosec A)

Discussion

22.	An urn contains fair tickets with numbers 112, 121, 211, 222 and one ticket is drawn. Let Ai (i = 1,2,3) be the event that the ith digit of the number of ticket drawn is 1 then
Answer» An urn contains fair tickets with numbers 112, 121, 211, 222 and one ticket is drawn. Let $A_{i}$ (i = 1,2,3) be the event that the i $^{t h}$ digit of the number of ticket drawn is 1 then

Discussion

23.	Find the inverse of the matrix A=⎡⎢⎣123111234⎤⎥⎦
Answer» Find the inverse of the matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 1 & 1 & 1 2 & 3 & 4 \end{matrix} ⎤ ⎥ ⎦$

Discussion

24.	Find the value of x in each of the following diagrams:(i)(ii)(iii)(iv)(v)(vi)
Answer» Find the value of x in each of the following diagrams: (i) (ii) (iii) (iv) (v) (vi)

24.

Find the value of x in each of the following diagrams:(i)(ii)(iii)(iv)(v)(vi)

Answer»

Find the value of x in each of the following diagrams:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Discussion

25.	Consider the family of circles x2 + y2 − 2x − 2λy − 8 = 0 passing through two fixed points A and B. Then the distance between the points A and B, is –––––––––––––––
Answer» Consider the family of circles $x^{2} + y^{2} - 2 x - 2 λ y - 8 = 0$ passing through two fixed points A and B. Then the distance between the points A and B, is $- ------------- -$

Discussion

26.	The centre of a circle is (2, –3) and the circumference is 10π. Then the equation of the circle is
Answer» The centre of a circle is (2, –3) and the circumference is $10 π .$ Then the equation of the circle is

Discussion

27.	A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (that is, if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?
Answer» A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (that is, if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

Discussion

28.	If y=y(x) is the solution of the differential equation dydx−y=1−e−x and y has a finite value, when x→∞, and y(0)=y0, then the value of ∣∣∣2y0∣∣∣ is
Answer» If $y = y (x)$ is the solution of the differential equation $\frac{d y}{d x} - y = 1 - e^{- x}$ and $y$ has a finite value, when $x \to \infty,$ and $y (0) = y_{0},$ then the value of $∣ ∣ ∣ \frac{2}{y_{0}} ∣ ∣ ∣$ is

Discussion

29.	If total number of runs scored in n matches is (n+14)(2n+1−n−2) where n>1, and the runs scored in the kth match are given by k⋅2n+1−k where 1≤k≤n, then the value of n is
Answer» If total number of runs scored in $n$ matches is $(\frac{n + 1}{4}) (2^{n + 1} - n - 2)$ where $n > 1,$ and the runs scored in the $k^{th}$ match are given by $k \cdot 2^{n + 1 - k}$ where $1 \leq k \leq n,$ then the value of $n$ is

Discussion

30.	In a box, there are 20 cards out of which 10 are labelled as A and remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A -card appears before the third B-card is :
Answer» In a box, there are $20$ cards out of which $10$ are labelled as $A$ and remaining $10$ are labelled as $B$ . Cards are drawn at random, one after the other and with replacement, till a second $A$ -card is obtained. The probability that the second $A$ -card appears before the third $B$ -card is :

Discussion

31.	The solution of the differential equation ydx−(x+2y2)dy=0 is x=f(y). If f(−1)=1, then f(1)=
Answer» The solution of the differential equation $y d x - (x + 2 y^{2}) d y = 0$ is $x = f (y)$ . If $f (- 1) = 1$ , then $f (1) =$

Discussion

32.	There are 12 unbaised coins in a bag. Out of them 4 coins have head on both sides. One coin is selected from the bag at random and tossed. The probability of getting a head is
Answer» There are $12$ unbaised coins in a bag. Out of them $4$ coins have head on both sides. One coin is selected from the bag at random and tossed. The probability of getting a head is

Discussion

33.	In previous question, we have shown that the locus of the feet of the perpendicular draw from the focus of the hyperbola x2a2 − y2b2 = 1 upon ay tangent is its auxiliary circle x2 + y2 = a2 then the product of these perpendiculars from the focusupon ay tangent is _____
Answer» In previous question, we have shown that the locus of the feet of the perpendicular draw from the focus of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ upon ay tangent is its auxiliary circle $x^{2} + y^{2} = a^{2}$ then the product of these perpendiculars from the focusupon ay tangent is _____

Discussion

34.	A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is
Answer» A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Discussion

35.	Find the image of P (2, 5) about x - axis
Answer» Find the image of P (2, 5) about x - axis

Discussion

36.	Let a and b respectively be the points of local maximum and local minimum of the function f(x)=2x3−3x2−12x.If A is the total area of the region bounded by y=f(x), the x−axis and the lines x=a and x=b, then 4A is equal to .
Answer» Let $a$ and $b$ respectively be the points of local maximum and local minimum of the function $f (x) = 2 x^{3} - 3 x^{2} - 12 x .$ If $A$ is the total area of the region bounded by $y = f (x),$ the $x -$ axis and the lines $x = a$ and $x = b,$ then $4 A$ is equal to .

Discussion

37.	Evaluate the following integrals:∫e2x1-sin2x1-cos2xdx
Answer» Evaluate the following integrals: $\int e^{2 x} (\frac{1 - \sin 2 x}{1 - \cos 2 x}) d x$

Discussion

38.	Area lying in the first quadrant andbounded by the circle x2 + y2 = 4and the lines x = 0 and x = 2 isA. πB. C. D.
Answer» Area lying in the first quadrant and bounded by the circle x² + y² = 4 and the lines x = 0 and x = 2 is A. π B. C. D.

38.

Area lying in the first quadrant andbounded by the circle x2 + y2 = 4and the lines x = 0 and x = 2 isA. πB. C. D.

Answer»

Area lying in the first quadrant and
bounded by the circle x² + y² = 4
and the lines x = 0 and x = 2 is

A. π

B.

C.

D.

Discussion

39.	If the least distance between a point on x2+2y2=6 and x+y−7=0 is k√2 unit, then k=
Answer» If the least distance between a point on $x^{2} + 2 y^{2} = 6$ and $x + y - 7 = 0$ is $\frac{k}{\sqrt{2}}$ unit, then $k =$

Discussion

40.	Integration of √1 + cos theta d theta is equal to-
Answer» Integration of √1 + cos theta d theta is equal to-

Discussion

41.	If x&y be real, show that the equation sin2θ=(x2+y2)/2xy is possible only when x=y is not equal to zero.
Answer» If $x & y$ be real, show that the equation $s i n^{2} θ = (x^{2} + y^{2}) / 2 x y$ is possible only when x=y is not equal to zero.

Discussion

42.	Solve the followingIf Prakash sowed jowar on 75% of the 19500 sq m of his land, on how many sq m did he actually plant jowar?
Answer» Solve the following If Prakash sowed jowar on 75% of the 19500 sq m of his land, on how many sq m did he actually plant jowar?

Discussion

43.	If the area (in sq.units)of bounded region enclosed between curves y=x−bx2 and y=x2b is maximum, then the possible positive value of b is
Answer» If the area (in $sq.units$ )of bounded region enclosed between curves $y = x - b x^{2}$ and $y = \frac{x^{2}}{b}$ is maximum, then the possible positive value of $b$ is

Discussion

44.	Solve, then x is equal to (A) (B) (C) 0 (D)
Answer» Solve, then x is equal to (A) (B) (C) 0 (D)

44.

Solve, then x is equal to (A) (B) (C) 0 (D)

Answer»

Solve,
then x
is equal to

(A)

(B)

(C)
0 (D)

Discussion

45.	If ∫1x+2x2+1dx=alog1+x2+btan-1x+15logx+2+C, then(a) a=-110, b=-25(b) a=110, b=-25(c) a=-110, b=25(d) a=110, b=25
Answer» If $\int \frac{1}{(x + 2) (x^{2} + 1)} d x = a \log \|1 + x^{2}\| + b \tan^{- 1} x + \frac{1}{5} \log \|x + 2\| + C$ , then $(a) a = - \frac{1}{10}, b = - \frac{2}{5} (b) a = \frac{1}{10}, b = - \frac{2}{5} (c) a = - \frac{1}{10}, b = \frac{2}{5} (d) a = \frac{1}{10}, b = \frac{2}{5}$

Discussion

46.	findthe sum of all two digit numbers each of which leaves remainder 3 when divided by 5
Answer» findthe sum of all two digit numbers each of which leaves remainder 3 when divided by 5

Discussion

47.	If P(1,-1,2), Q(3,2,-1) and R(5,0,3) are the three vertices of a triangle ,then determine the area of that triangle
Answer» If P(1,-1,2), Q(3,2,-1) and R(5,0,3) are the three vertices of a triangle ,then determine the area of that triangle

Discussion

48.	log a base 2a=x, log 2a base 3a=y, log 3a base 4a=z; then xyz-2yz=
Answer» log a base 2a=x, log 2a base 3a=y, log 3a base 4a=z; then xyz-2yz=

Discussion

49.	how to convert degrees to seconds in sexagesimal system/ french system?
Answer» how to convert degrees to seconds in sexagesimal system/ french system?

Discussion

50.	Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is 3r2, then r2−d is equal to
Answer» Three numbers are in an increasing geometric progression with common ratio $r .$ If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference $d .$ If the fourth term of GP is $3 r^{2},$ then $r^{2} - d$ is equal to

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The value of limx→2⎛⎝(x3−4xx3−8)−1−(x+√2xx−2−√2√x−√2)−1⎞⎠ is equal to

The value of the determinant Δ=∣∣∣∣394457525876657295∣∣∣∣ is

Which of the following represents the graph of f(x)=ax2+bx+c where a&lt;b&lt;0&lt;c ?

If A(cosα,sinα), B(cosβ,sinβ), C(cosγ,sinγ) are the vertices of △ABC and H,G,S are the orthocentre, centroid and circumcentre of △ABC respectively, then which of the following is/are true?

If A , B are symmetric matrices of same order, then AB − BA is a A. Skew symmetric matrix B. Symmetric matrix C. Zero matrix D. Identity matrix

The length of the string between a kite and a point on the ground is 90 meters. If the string makes angle theta with the ground level such that tan theta is equal to 15 by 8 how high is the kite flying assuming that there is no slack in the string.

Find the distance of the line 4 x + 7 y + 5 = 0 from the point (1, 2) along the line 2 x – y = 0.

Find the equation of a family of circles touching the lines x2−y2+2y−1=0. (where h and k are parameters)

Diffrentiate y= sin^2(3x+4)

∫0π4a2cos2x+b2sin2xdx

If x,|x+1|,|x−1| are first three terms of an A.P. then the sum of its first 20 terms is

If x is an acute angle and tan x=17, then the value of cosec2 x-sec2 xcosec2 x+sec2 x is(a) 3/4(b) 1/2(c) 2(d) 5/4

Let →a=2^i−^j+2^k and →b=^i+2^j−^k. Let a vector →v be in the plane containing →a and →b. If →v is perpendicular to the vector 3^i+2^j−^k and its projection on →a is 19 units, then |2→v|2 is equal to

Find the quadratic equation whose one root is 1−i√292.

the combined equation of three sides of triangle(x2-y2)(2x+3y-6)=0 . if (sectheta,1) is an interior point of the triangle then find value of theta.

The correct graph of y=|log10x| is

Let a,b∈R,(a≠0). If the function f defined asf(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩2x2a ,0≤x&lt;1a ,1≤x&lt;√22b2−4bx3 ,√2≤x&lt;∞is continuous in the interval [0,∞),,then an ordered pair (a,b) is:

Let A = {-2, -1, 0, 1, 2} and f:A→Z be a function defined by f(x)=x2−2x−3. Find : i) Range of f i.e. f(A) ii) Pre-images of 6, -3 and 5.

The locus of the centre of a circle, which touches externally the circle x2+y2−6x−6y+14=0 and also touches the y-axis, is given by the equation

42. sin A / (cot A + cosec A) = 2 + sin A / (cot A - cosec A)

An urn contains fair tickets with numbers 112, 121, 211, 222 and one ticket is drawn. Let Ai (i = 1,2,3) be the event that the ith digit of the number of ticket drawn is 1 then

Find the inverse of the matrix A=⎡⎢⎣123111234⎤⎥⎦

Find the value of x in each of the following diagrams:(i)(ii)(iii)(iv)(v)(vi)

Consider the family of circles x2 + y2 − 2x − 2λy − 8 = 0 passing through two fixed points A and B. Then the distance between the points A and B, is –––––––––––––––

The centre of a circle is (2, –3) and the circumference is 10π. Then the equation of the circle is

If y=y(x) is the solution of the differential equation dydx−y=1−e−x and y has a finite value, when x→∞, and y(0)=y0, then the value of ∣∣∣2y0∣∣∣ is

If total number of runs scored in n matches is (n+14)(2n+1−n−2) where n&gt;1, and the runs scored in the kth match are given by k⋅2n+1−k where 1≤k≤n, then the value of n is

In a box, there are 20 cards out of which 10 are labelled as A and remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A -card appears before the third B-card is :

The solution of the differential equation ydx−(x+2y2)dy=0 is x=f(y). If f(−1)=1, then f(1)=

There are 12 unbaised coins in a bag. Out of them 4 coins have head on both sides. One coin is selected from the bag at random and tossed. The probability of getting a head is

In previous question, we have shown that the locus of the feet of the perpendicular draw from the focus of the hyperbola x2a2 − y2b2 = 1 upon ay tangent is its auxiliary circle x2 + y2 = a2 then the product of these perpendiculars from the focusupon ay tangent is _____

A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Find the image of P (2, 5) about x - axis

Let a and b respectively be the points of local maximum and local minimum of the function f(x)=2x3−3x2−12x.If A is the total area of the region bounded by y=f(x), the x−axis and the lines x=a and x=b, then 4A is equal to .

Evaluate the following integrals:∫e2x1-sin2x1-cos2xdx

Area lying in the first quadrant andbounded by the circle x2 + y2 = 4and the lines x = 0 and x = 2 isA. πB. C. D.

If the least distance between a point on x2+2y2=6 and x+y−7=0 is k√2 unit, then k=

Integration of √1 + cos theta d theta is equal to-

If x&amp;y be real, show that the equation sin2θ=(x2+y2)/2xy is possible only when x=y is not equal to zero.

Solve the followingIf Prakash sowed jowar on 75% of the 19500 sq m of his land, on how many sq m did he actually plant jowar?

If the area (in sq.units)of bounded region enclosed between curves y=x−bx2 and y=x2b is maximum, then the possible positive value of b is

Solve, then x is equal to (A) (B) (C) 0 (D)

If ∫1x+2x2+1dx=alog1+x2+btan-1x+15logx+2+C, then(a) a=-110, b=-25(b) a=110, b=-25(c) a=-110, b=25(d) a=110, b=25

findthe sum of all two digit numbers each of which leaves remainder 3 when divided by 5

If P(1,-1,2), Q(3,2,-1) and R(5,0,3) are the three vertices of a triangle ,then determine the area of that triangle

log a base 2a=x, log 2a base 3a=y, log 3a base 4a=z; then xyz-2yz=

how to convert degrees to seconds in sexagesimal system/ french system?

Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is 3r2, then r2−d is equal to

Which of the following represents the graph of f(x)=ax2+bx+c where a<b<0<c ?

Let a,b∈R,(a≠0). If the function f defined asf(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩2x2a ,0≤x<1a ,1≤x<√22b2−4bx3 ,√2≤x<∞is continuous in the interval [0,∞),,then an ordered pair (a,b) is:

If total number of runs scored in n matches is (n+14)(2n+1−n−2) where n>1, and the runs scored in the kth match are given by k⋅2n+1−k where 1≤k≤n, then the value of n is

If x&y be real, show that the equation sin2θ=(x2+y2)/2xy is possible only when x=y is not equal to zero.