43030 + Interview Questions in Mathematics Page 215 InterviewSolution

10701.	If the curve y=ax2+bx+c,x∈R, passes through the point (1,2) and the tangent line to this curve at origin is y=x, then the possible values of a,b,c are
Answer» If the curve $y = a x^{2} + b x + c, x \in R,$ passes through the point $(1, 2)$ and the tangent line to this curve at origin is $y = x,$ then the possible values of $a, b, c$ are

Discussion

10702.	A circle touching the x-axis at (3,0) and making an intercept of length 8 on the y-axis passes through the point :
Answer» A circle touching the $x$ -axis at $(3, 0)$ and making an intercept of length $8$ on the $y$ -axis passes through the point :

Discussion

10703.	Vectors of magnitude 21 units in the direction of the vector 3i^-6j^+2k^ are _____________.
Answer» Vectors of magnitude 21 units in the direction of the vector $3 \hat{i} - 6 \hat{j} + 2 \hat{k}$ are _____________.

Discussion

10704.	Coefficient of x1007 in (1+x)2006+x(1+x)2005+x2(1+x)2004+⋯+x2006 is
Answer» Coefficient of $x^{1007}$ in $(1 + x)^{2006} + x (1 + x)^{2005} + x^{2} (1 + x)^{2004} + \dots + x^{2006}$ is

Discussion

10705.	Solution set of the inequality log7x−2x−3<0 is
Answer» Solution set of the inequality $l o g_{7} \frac{x - 2}{x - 3} < 0$ is

Discussion

10706.	35. The sum of all 4 digit numbers that can be formed by taking the digits from 0 1 3 5 7 9 is a)1623300 b)1632300. c)1632030. b)1633200
Answer» 35. The sum of all 4 digit numbers that can be formed by taking the digits from 0 1 3 5 7 9 is a)1623300 b)1632300. c)1632030. b)1633200

Discussion

10707.	Consider the plane π:x+y=z, point A(1, 2, -3) and a line L:x−13=y−2−1=z−34 The equation of the plane containing the line L and the point A is
Answer» Consider the plane $π : x + y = z$ , point A(1, 2, -3) and a line $L : \frac{x - 1}{3} = \frac{y - 2}{- 1} = \frac{z - 3}{4}$ The equation of the plane containing the line L and the point A is

10707.

Consider the plane π:x+y=z, point A(1, 2, -3) and a line L:x−13=y−2−1=z−34 The equation of the plane containing the line L and the point A is

Answer»

Consider the plane $π : x + y = z$ , point A(1, 2, -3) and a line $L : \frac{x - 1}{3} = \frac{y - 2}{- 1} = \frac{z - 3}{4}$

The equation of the plane containing the line L and the point A is

Discussion

10708.	the range of fx equal to signum 2 power x plus signum of mod of x minus 5
Answer» the range of fx equal to signum 2 power x plus signum of mod of x minus 5

Discussion

10709.	Consider two points A(1,a) and B(5,b). If the equation of the line bisecting the line segment AB perpendicularly is x−3y=0 then \|ab\| is
Answer» Consider two points $A (1, a)$ and $B (5, b)$ . If the equation of the line bisecting the line segment $A B$ perpendicularly is $x - 3 y = 0$ then $\| a b \|$ is

Discussion

10710.	A balloon , which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.
Answer» A balloon , which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

Discussion

10711.	1.If tan x=n tan y and sin x=m sin y then prove that (m^2 - 1 )/ (n^2 - 1)=cos^2 x ?2.If x sin^3 A + y cos^3 A=sinAcosA and x sinA=y cosA.Prove that x^2+y^2=1 ?
Answer» 1.If tan x=n tan y and sin x=m sin y then prove that (m^2 - 1 )/ (n^2 - 1)=cos^2 x ? 2.If x sin^3 A + y cos^3 A=sinAcosA and x sinA=y cosA.Prove that x^2+y^2=1 ?

Discussion

10712.	If A is a 3×3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = ______________.
Answer» If A is a 3×3 non-singular matrix such that AA^T = A^TA and B = A^-1A^T, then BB^T = ______________.

Discussion

10713.	Two lines L1:x=5,y3−α=z−2 and L2:x=α,y−1=z2−α are coplanar. Then α can take value(s)
Answer» Two lines $L_{1} : x = 5, \frac{y}{3 - α} = \frac{z}{- 2}$ and $L_{2} : x = α, \frac{y}{- 1} = \frac{z}{2 - α}$ are coplanar. Then $α$ can take value(s)

Discussion

10714.	An automobile dealer provides motorcycles and scooter in 3 bod patterns and 4 different colors each the no. Of choices open to the customer is?
Answer» An automobile dealer provides motorcycles and scooter in 3 bod patterns and 4 different colors each the no. Of choices open to the customer is?

Discussion

10715.	If f:R→R+ defined by f(x)=e5x−1, then f−1(x)=
Answer» If $f : R \to R^{+}$ defined by $f (x) = e^{5 x - 1},$ then $f^{- 1} (x) =$

Discussion

10716.	Find the values of pso the line andareat right angles.
Answer» Find the values of p so the line and are at right angles.

10716.

Find the values of pso the line andareat right angles.

Answer»

Find the values of p
so the line
and

are
at right angles.

Discussion

10717.	The range of the function f(x)=8x2+40x+284x2+20x+13, where x∈R is
Answer» The range of the function $f (x) = \frac{8 x^{2} + 40 x + 28}{4 x^{2} + 20 x + 13},$ where $x \in R$ is

Discussion

10718.	For the principal values, evaluate each of the following:i tan-1(-1)+cos-1-12(ii) tan-12sin4cos-132
Answer» For the principal values, evaluate each of the following: $(i) \tan^{- 1} (- 1) + \cos^{- 1} (- \frac{1}{\sqrt{2}})$ (ii) $\tan^{- 1} \{2 \sin (4 \cos^{- 1} \frac{\sqrt{3}}{2})\}$

Discussion

10719.	Find limx→1+1x−1.
Answer» Find ${lim}_{x \to 1^{+}} \frac{1}{x - 1} .$

Discussion

10720.	If x=6 , then find the value of {x+1/x
Answer» If x=6 , then find the value of {x+1/x

Discussion

10721.	The equation of a plane containing the line of intersection of the planes 2x−y−4=0 and y+2z−4=0 and passing through the point (1,1,0) is:
Answer» The equation of a plane containing the line of intersection of the planes $2 x - y - 4 = 0$ and $y + 2 z - 4 = 0$ and passing through the point $(1, 1, 0)$ is:

Discussion

10722.	Find the equation of the circle whose diameter is the line segment joining (-4, 3) and (12, -1). Find also the intercept made by it on y-axis.
Answer» Find the equation of the circle whose diameter is the line segment joining (-4, 3) and (12, -1). Find also the intercept made by it on y-axis.

Discussion

10723.	If a \operatorname{sinθ+b\operatorname{cosθ=c, then prove that a \operatorname{cosθ-b\operatorname{sinθ=\sqrt{a^2+b^2-c^2
Answer» If a \operatorname{sinθ+b\operatorname{cosθ=c, then prove that a \operatorname{cosθ-b\operatorname{sinθ=\sqrt{a^2+b^2-c^2

Discussion

10724.	Which of the following is the solution of the DE dydx=(3x+2y+4)2?
Answer» Which of the following is the solution of the DE $\frac{dy}{dx} = (3 x + 2 y + 4)^{2}$ ?

Discussion

10725.	Consider the collection of all curves of the form y=a−bx2 that pass through the point (2,1) where a and b are positive real numbers. If the minimum area of the region bounded by y=a−bx2 and the x−axis is √A sq. units then the value of A∈N is
Answer» Consider the collection of all curves of the form $y = a - b x^{2}$ that pass through the point $(2, 1)$ where $a$ and $b$ are positive real numbers. If the minimum area of the region bounded by $y = a - b x^{2}$ and the $x -$ axis is $\sqrt{A}$ sq. units then the value of $A \in N$ is

Discussion

10726.	If 4 tan θ = 3, then 4sinθ-cosθ4sinθ+cosθ is equal to _________.
Answer» If 4 tan θ = 3, then $\frac{4 \sin θ - \cos θ}{4 \sin θ + \cos θ}$ is equal to _________.

Discussion

10727.	The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
Answer» The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is

Discussion

10728.	If f(x) = log x, then equals
Answer» If f(x) = log x, then equals

Discussion

10729.	Solve the given inequality graphically in two-dimensional plane: –3x + 2y ≥ –6
Answer» Solve the given inequality graphically in two-dimensional plane: –3x + 2y ≥ –6

Discussion

10730.	Solve each of the following initial value problems:(i) y'+y=ex, y0=12(ii) xdydx-y=log x, y1=0(iii) dydx+2y=e-2x sin x, y0=0(iv) xdydx-y=x+1e-x, y1=0(v) 1+y2 dx+x-e-tan-1y dx=0, y0=0(vi) dydx+y tan x=2x+x2 tan x, y0=1(vii) xdydx+y=x cos x+sin x, yπ2=1(viii) dydx+y cot x=4x cosec x, yπ2=0(ix) dydx+2y tan x=sin x; y=0 when x=π3(x) dydx-3y cot x=sin 2x; y=2 when x=π2(xi)(xii)
Answer» Solve each of the following initial value problems: (i) $y' + y = e^{x}, y (0) = \frac{1}{2}$ (ii) $x \frac{d y}{d x} - y = \log x, y (1) = 0$ (iii) $\frac{d y}{d x} + 2 y = e^{- 2 x} \sin x, y (0) = 0$ (iv) $x \frac{d y}{d x} - y = (x + 1) e^{- x}, y (1) = 0$ (v) $(1 + y^{2}) d x + (x - e^{- \tan^{- 1} y}) d x = 0, y (0) = 0$ (vi) $\frac{d y}{d x} + y \tan x = 2 x + x^{2} \tan x, y (0) = 1$ (vii) $x \frac{d y}{d x} + y = x \cos x + \sin x, y (\frac{π}{2}) = 1$ (viii) $\frac{d y}{d x} + y \cot x = 4 x cosec x, y (\frac{π}{2}) = 0$ (ix) $\frac{d y}{d x} + 2 y \tan x = \sin x; y = 0 when x = \frac{π}{3}$ (x) $\frac{d y}{d x} - 3 y \cot x = \sin 2 x; y = 2 when x = \frac{π}{2}$ (xi) (xii)

Discussion

10731.	The length of the latus rectum of the parabola 9x2−6x+36y+19=0
Answer» The length of the latus rectum of the parabola $9 x^{2} - 6 x + 36 y + 19 = 0$

Discussion

10732.	3.Prove the following by using the principle of mathematical induction n(n+1)+1 is an odd natural number,n belongs to N
Answer» 3.Prove the following by using the principle of mathematical induction n(n+1)+1 is an odd natural number,n belongs to N

Discussion

10733.	Fill in the gaps and complete. (3)If α, β are roots of quadratic equation,
Answer» Fill in the gaps and complete. (3)If α, β are roots of quadratic equation,

Discussion

10734.	Evaluate the following integrals:∫04x+x-2+x-4 dx
Answer» Evaluate the following integrals: $\int_{0}^{4} (\|x\| + \|x - 2\| + \|x - 4\|) d x$

Discussion

10735.	If f(x)=2x−3sinx3x+4tanx,x≠0 is continuous at x=0, then the value of \|14f(0)\| is
Answer» If $f (x) = \frac{2 x - 3 sin x}{3 x + 4 tan x}, x \neq 0$ is continuous at $x = 0$ , then the value of $\| 14 f (0) \|$ is

Discussion

10736.	Show that
Answer» Show that

Discussion

10737.	If the polynomial R(x) is the remainder upon dividing x2020 by x2−7x+12. If R(1) can be expressed as (pm−qn), where m,n∈N, and p & q are prime numbers, then the value of n+m−pq is
Answer» If the polynomial $R (x)$ is the remainder upon dividing $x^{2020}$ by $x^{2} - 7 x + 12$ . If $R (1)$ can be expressed as $(p^{m} - q^{n})$ , where $m, n \in N, and p & q$ are prime numbers, then the value of $n + m - p q$ is

Discussion

10738.	The value of cot−19+cosec−1√414 is given by
Answer» The value of $c o t^{- 1} 9 + c o s e c^{- 1} \frac{\sqrt{41}}{4}$ is given by

Discussion

10739.	if a,b,c are vectors. r.a=r.b=r.c=1/2 for some nonzero 'r' vector,then the area of triangle formed by vectors a,b,c is ?
Answer» if a,b,c are vectors. r.a=r.b=r.c=1/2 for some nonzero 'r' vector,then the area of triangle formed by vectors a,b,c is ?

Discussion

10740.	In a geometric progression of all positive terms, any term is equal to the sum of its next two terms. Then the common ratio of this progression is
Answer» In a geometric progression of all positive terms, any term is equal to the sum of its next two terms. Then the common ratio of this progression is

Discussion

10741.	If fx=∫0xtsintdt, the write the value of f'x. [CBSE 2014]
Answer» If $f (x) = \int_{0}^{x} t \sin t d t$ , the write the value of $f' (x)$ . [CBSE 2014]

Discussion

10742.	All the values of x for which x2−5x+6 is non-negative are
Answer» All the values of $x$ for which $x^{2} - 5 x + 6$ is non-negative are

Discussion

10743.	From the first 20 natural numbers, Ram selects a number at random. What is the number of favourable outcomes, if this number has to be divisible by 4?
Answer» From the first 20 natural numbers, Ram selects a number at random. What is the number of favourable outcomes, if this number has to be divisible by 4?

Discussion

10744.	The sum of 1 + 25 + 352 + 453 + .............upto n terms is
Answer» The sum of 1 + $\frac{2}{5}$ + $\frac{3}{5^{2}}$ + $\frac{4}{5^{3}}$ + .............upto n terms is

Discussion

10745.	The distance of the point (−1,2,−2) from the line of intersection of the planes 2x+3y+2z=0 and x−2y+z=0 is
Answer» The distance of the point $(- 1, 2, - 2)$ from the line of intersection of the planes $2 x + 3 y + 2 z = 0$ and $x - 2 y + z = 0$ is

Discussion

10746.	If p: Ridhi did not eat lunch q: Azad did not have lunch. Then which of the following denotes the compound statement: "Both Ridhi and Azad did not have lunch.”
Answer» If p: Ridhi did not eat lunch q: Azad did not have lunch. Then which of the following denotes the compound statement: "Both Ridhi and Azad did not have lunch.”

Discussion

10747.	If f(x)=(1+xn), then the value of f(0)+f′(0)+f"(0)2!+....+fn(0)n! is
Answer» If $f (x) = (1 + x^{n})$ , then the value of $f (0) + f^{'} (0) + \frac{f " (0)}{2!} + . . . . + \frac{f^{n} (0)}{n!}$ is

Discussion

10748.	7x−58x+3>4
Answer» $\frac{7 x - 5}{8 x + 3} > 4$

Discussion

10749.	If tan x=-15 and θ lies in the IV quadrant, then the value of cos x is(a) 56(b) 26(c) 12(d) 16
Answer» If tan $x = - \frac{1}{\sqrt{5}}$ and θ lies in the IV quadrant, then the value of cos x is (a) $\frac{\sqrt{5}}{\sqrt{6}}$ (b) $\frac{2}{\sqrt{6}}$ (c) $\frac{1}{2}$ (d) $\frac{1}{\sqrt{6}}$

Discussion

10750.	The maximum value of 4sec2x+cosec2 x is
Answer» The maximum value of $\frac{4}{{sec}^{2} x + {cosec}^{2} x}$ is

Discussion

Explore topic-wise InterviewSolutions in .

If the curve y=ax2+bx+c,x∈R, passes through the point (1,2) and the tangent line to this curve at origin is y=x, then the possible values of a,b,c are

A circle touching the x-axis at (3,0) and making an intercept of length 8 on the y-axis passes through the point :

Vectors of magnitude 21 units in the direction of the vector 3i^-6j^+2k^ are _____________.

Coefficient of x1007 in (1+x)2006+x(1+x)2005+x2(1+x)2004+⋯+x2006 is

Solution set of the inequality log7x−2x−3&lt;0 is

35. The sum of all 4 digit numbers that can be formed by taking the digits from 0 1 3 5 7 9 is a)1623300 b)1632300. c)1632030. b)1633200

Consider the plane π:x+y=z, point A(1, 2, -3) and a line L:x−13=y−2−1=z−34 The equation of the plane containing the line L and the point A is

the range of fx equal to signum 2 power x plus signum of mod of x minus 5

Consider two points A(1,a) and B(5,b). If the equation of the line bisecting the line segment AB perpendicularly is x−3y=0 then |ab| is

A balloon , which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

1.If tan x=n tan y and sin x=m sin y then prove that (m^2 - 1 )/ (n^2 - 1)=cos^2 x ?2.If x sin^3 A + y cos^3 A=sinAcosA and x sinA=y cosA.Prove that x^2+y^2=1 ?

If A is a 3×3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = ______________.

Two lines L1:x=5,y3−α=z−2 and L2:x=α,y−1=z2−α are coplanar. Then α can take value(s)

An automobile dealer provides motorcycles and scooter in 3 bod patterns and 4 different colors each the no. Of choices open to the customer is?

If f:R→R+ defined by f(x)=e5x−1, then f−1(x)=

Find the values of pso the line andareat right angles.

The range of the function f(x)=8x2+40x+284x2+20x+13, where x∈R is

For the principal values, evaluate each of the following:i tan-1(-1)+cos-1-12(ii) tan-12sin4cos-132

Find limx→1+1x−1.

If x=6 , then find the value of {x+1/x

The equation of a plane containing the line of intersection of the planes 2x−y−4=0 and y+2z−4=0 and passing through the point (1,1,0) is:

Find the equation of the circle whose diameter is the line segment joining (-4, 3) and (12, -1). Find also the intercept made by it on y-axis.

If a \operatorname{sinθ+b\operatorname{cosθ=c, then prove that a \operatorname{cosθ-b\operatorname{sinθ=\sqrt{a^2+b^2-c^2

Which of the following is the solution of the DE dydx=(3x+2y+4)2?

Consider the collection of all curves of the form y=a−bx2 that pass through the point (2,1) where a and b are positive real numbers. If the minimum area of the region bounded by y=a−bx2 and the x−axis is √A sq. units then the value of A∈N is

If 4 tan θ = 3, then 4sinθ-cosθ4sinθ+cosθ is equal to _________.

The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is

If f(x) = log x, then equals

Solve the given inequality graphically in two-dimensional plane: –3x + 2y ≥ –6

The length of the latus rectum of the parabola 9x2−6x+36y+19=0

3.Prove the following by using the principle of mathematical induction n(n+1)+1 is an odd natural number,n belongs to N

Fill in the gaps and complete. (3)If α, β are roots of quadratic equation,

Evaluate the following integrals:∫04x+x-2+x-4 dx

If f(x)=2x−3sinx3x+4tanx,x≠0 is continuous at x=0, then the value of |14f(0)| is

Show that

If the polynomial R(x) is the remainder upon dividing x2020 by x2−7x+12. If R(1) can be expressed as (pm−qn), where m,n∈N, and p &amp; q are prime numbers, then the value of n+m−pq is

The value of cot−19+cosec−1√414 is given by

if a,b,c are vectors. r.a=r.b=r.c=1/2 for some nonzero 'r' vector,then the area of triangle formed by vectors a,b,c is ?

In a geometric progression of all positive terms, any term is equal to the sum of its next two terms. Then the common ratio of this progression is

If fx=∫0xtsintdt, the write the value of f'x. [CBSE 2014]

All the values of x for which x2−5x+6 is non-negative are

From the first 20 natural numbers, Ram selects a number at random. What is the number of favourable outcomes, if this number has to be divisible by 4?

The sum of 1 + 25 + 352 + 453 + .............upto n terms is

The distance of the point (−1,2,−2) from the line of intersection of the planes 2x+3y+2z=0 and x−2y+z=0 is

If p: Ridhi did not eat lunch q: Azad did not have lunch. Then which of the following denotes the compound statement: "Both Ridhi and Azad did not have lunch.”

If f(x)=(1+xn), then the value of f(0)+f′(0)+f"(0)2!+....+fn(0)n! is

7x−58x+3&gt;4

If tan x=-15 and θ lies in the IV quadrant, then the value of cos x is(a) 56(b) 26(c) 12(d) 16

The maximum value of 4sec2x+cosec2 x is

Solution set of the inequality log7x−2x−3<0 is

If the polynomial R(x) is the remainder upon dividing x2020 by x2−7x+12. If R(1) can be expressed as (pm−qn), where m,n∈N, and p & q are prime numbers, then the value of n+m−pq is

7x−58x+3>4