43030 + Interview Questions in Mathematics Page 115 InterviewSolution

5701.	The value of x∈R for which vectors →a=(1,−2,1),→b=(−2,3,−4),→c=(1,−1,x) form a linearly dependent system, is equal to
Answer» The value of $x \in R$ for which vectors $\to a = (1, - 2, 1), \to b = (- 2, 3, - 4), \to c = (1, - 1, x)$ form a linearly dependent system, is equal to

Discussion

5702.	Algebraic sum of the intercepts made by the plane x + 3y - 4z + 6 = 0 on the axes is
Answer» Algebraic sum of the intercepts made by the plane x + 3y - 4z + 6 = 0 on the axes is

Discussion

5703.	(3) Stee The length of an elastic string is X m when the tension is 8 N, and Y m when the tension is 10 N in metres when the tension is 18 N is (1) 4X- 5Y (3) 9x-4Y . The length (2) 5Y-4X 4) 4Y-9x
Answer» (3) Stee The length of an elastic string is X m when the tension is 8 N, and Y m when the tension is 10 N in metres when the tension is 18 N is (1) 4X- 5Y (3) 9x-4Y . The length (2) 5Y-4X 4) 4Y-9x

Discussion

5704.

Match the following functions satisfying particular functional relationship Column-I (A) f(x+y)=f(x)+f(y) (B) f(xy)=f(x)+f(y) (C) f(x+y)=f(x)⋅f(y) (D) f(X)+f(y)=f(x+y1−xy) Column-II (p) log3x (q) tan−1x (r) 3x (s) 3x (t) A transcendental function

Answer» Match the following functions satisfying particular functional relationship

	Column-I
(A)	$f (x + y) = f (x) + f (y)$
(B)	$f (x y) = f (x) + f (y)$
(C)	$f (x + y) = f (x) \cdot f (y)$
(D)	$f (X) + f (y) = f (\frac{x + y}{1 - x y})$

	Column-II
(p)	${log}_{3} x$
(q)	$t a n^{- 1} x$
(r)	$3 x$
(s)	$3^{x}$
(t)	A transcendental function

Discussion

5705.	The acute angle of intersection of the curves y=[\|sinx\|+\|cosx\|] and x2+y2=5 (where [.] denotes the greatest integer function) is tan−1(k) then k is
Answer» The acute angle of intersection of the curves $y = [\| sin x \| + \| cos x \|]$ and $x^{2} + y^{2} = 5$ (where $[.]$ denotes the greatest integer function) is ${tan}^{- 1} (k)$ then $k$ is

Discussion

5706.	11.4+14.7+17.10+...
Answer» $\frac{1}{1.4} + \frac{1}{4.7} + \frac{1}{7.10} + . . .$

Discussion

5707.	If x∈R, then the range of log5/4(5x2−8x+4) is
Answer» If $x \in R$ , then the range of ${log}_{5 / 4} (5 x^{2} - 8 x + 4)$ is

Discussion

5708.	An urn contains 5 red and 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls. Drawn. What are the possible values of X? Is X a random variable ? If yes, find the mean and variance of X.
Answer» An urn contains 5 red and 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls. Drawn. What are the possible values of X? Is X a random variable ? If yes, find the mean and variance of X.

Discussion

5709.	If A={x∶x is a multiple of 3} and B={x∶x is a multiple of 5}, then A−B=
Answer» If $A = {x ∶ x is a multiple of 3}$ and $B = {x ∶ x is a multiple of 5}$ , then $A - B =$

Discussion

5710.	The figure formed by the lines ax±by±c=0 is
Answer» The figure formed by the lines $a x \pm b y \pm c = 0$ is

Discussion

5711.	Find the general solution of the equation sinx+sin3x+sin5x=0
Answer» Find the general solution of the equation $sin x + sin 3 x + sin 5 x = 0$

Discussion

5712.	In ΔABC, the median AD divides ∠BAC such that ∠BAD:∠CAD=2:1. Then cos(A3) is equal to
Answer» In $Δ A B C$ , the median $A D$ divides $∠ B A C$ such that $∠ B A D : ∠ C A D = 2 : 1.$ Then $cos (\frac{A}{3})$ is equal to

Discussion

5713.	If sin x= cos x and x is acute, state the value of x
Answer» If sin x= cos x and x is acute, state the value of x

Discussion

5714.	If tanα=2tt2−1, what is t?
Answer» If $t a n α = \frac{2 t}{t^{2} - 1}$ , what is t?

Discussion

5715.	Write the solution set of the inequation x+1x≥2
Answer» Write the solution set of the inequation $x + \frac{1}{x} \geq 2$

Discussion

5716.	Find x if cos3x+sin(2x-7/6)=-2
Answer» Find x if cos3x+sin(2x-7/6)=-2

Discussion

5717.	Evaluate the following:a+xyzxa+yzxya+z
Answer» Evaluate the following: $\|\begin{matrix} a + x & y & z \\ x & a + y & z \\ x & y & a + z \end{matrix}\|$

Discussion

5718.	81.Three symmetrical dices are thrown .The probability that the same number will appear on each of them is? options: (a)1/216 (b)1/36 (c)35/36 (d)1/35
Answer» 81.Three symmetrical dices are thrown .The probability that the same number will appear on each of them is? options: (a)1/216 (b)1/36 (c)35/36 (d)1/35

Discussion

5719.	If parabola touches the x axis at one point then there will be one zero or two overlapping zeros?
Answer» If parabola touches the x axis at one point then there will be one zero or two overlapping zeros?

Discussion

5720.	What is the condition for a function y = f(x) to be a monotonically increasing function
Answer» What is the condition for a function y = f(x) to be a monotonically increasing function

Discussion

5721.	Let (1−x+x4)10=a0+a1x+a2x2+⋯+a40x40. Then which of the following options is CORRECT?
Answer» Let ${(1 - x + x^{4})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{40} x^{40} .$ Then which of the following options is CORRECT?

Discussion

5722.	If 2 sin θ + 3 cos θ = 2, then 3 sin θ – 2 cos θ = _________.
Answer» If 2 sin θ + 3 cos θ = 2, then 3 sin θ – 2 cos θ = _________.

Discussion

5723.	{ If }l_1=∫_0^{mπ}f(\vert\operatorname{cos}x\vert)dx and }l_2=∫_0^{5π}f(\vert\operatorname{cos}x\vert)dx} then
Answer» { If }l_1=∫_0^{mπ}f(\vert\operatorname{cos}x\vert)dx and }l_2=∫_0^{5π}f(\vert\operatorname{cos}x\vert)dx} then

Discussion

5724.	An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known: P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15 Evaluate the following probabilities (i) P(A fails\| B has failed) (ii) P(A fails alone)
Answer» An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known: P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15 Evaluate the following probabilities (i) P(A fails\| B has failed) (ii) P(A fails alone)

Discussion

5725.	23.At far off distant places, electricity is supplied with high voltage and low current. Explain why
Answer» 23.At far off distant places, electricity is supplied with high voltage and low current. Explain why

Discussion

5726.	The value of 1∫−1x√1−x2⋅sin−1(2x√1−x2)dx is equal to
Answer» The value of $1 \int - 1 \frac{x}{\sqrt{1 - x^{2}}} \cdot {sin}^{- 1} (2 x \sqrt{1 - x^{2}}) d x$ is equal to

Discussion

5727.	If f(x) = exg(x), g(0) = 2, g'(0) = 1, then f'(0) = __________________.
Answer» If f(x) = e^xg(x), g(0) = 2, g'(0) = 1, then f'(0) = __________________.

Discussion

5728.	Hybridisation of Xe in XeF4 molecule isXeF4 अणु में Xe का संकरण क्या है?
Answer» Hybridisation of Xe in XeF₄ molecule is XeF₄ अणु में Xe का संकरण क्या है?

Discussion

5729.	The sum of all values of x for which the matrix [3x2xx+1x−1] is NOT invertible, is[2 marks]
Answer» The sum of all values of $x$ for which the matrix $[\begin{matrix} 3 x & 2 x x + 1 & x - 1 \end{matrix}]$ is NOT invertible, is [2 marks]

Discussion

5730.	The differential equation that represents the family of curves y=12x2−c, where c is an arbitrary constant is
Answer» The differential equation that represents the family of curves $y = \frac{1}{2 x^{2} - c},$ where $c$ is an arbitrary constant is

Discussion

5731.	Solve the given inequality for real x:
Answer» Solve the given inequality for real x:

Discussion

5732.	The value of the determinant ∆=sec2θtan2θ1tan2θsec2θ-122202 is _____________.
Answer» The value of the determinant $∆ = \|\begin{matrix} \sec^{2} θ & \tan^{2} θ & 1 \\ \tan^{2} θ & \sec^{2} θ & - 1 \\ 22 & 20 & 2 \end{matrix}\|$ is _____________.

Discussion

5733.	Find the intervals in which the following functions are increasing or decreasing.(i) f(x) = 10 − 6x − 2x2(ii) f(x) = x2 + 2x − 5(iii) f(x) = 6 − 9x − x2(iv) f(x) = 2x3 − 12x2 + 18x + 15(v) f(x) = 5 + 36x + 3x2 − 2x3(vi) f(x) = 8 + 36x + 3x2 − 2x3(vii) f(x) = 5x3 − 15x2 − 120x + 3(viii) f(x) = x3 − 6x2 − 36x + 2(ix) f(x) = 2x3 − 15x2 + 36x + 1(x) f(x) = 2x3 + 9x2 + 12x + 20(xi) f(x) = 2x3 − 9x2 + 12x − 5(xii) f(x) = 6 + 12x + 3x2 − 2x3(xiii) f(x) = 2x3 − 24x + 107(xiv) f(x) = −2x3 − 9x2 − 12x + 1(xv) f(x) = (x − 1) (x − 2)2(xvi) f(x) = x3 − 12x2 + 36x + 17(xvii) f(x) = 2x3 − 24x + 7(xviii) fx=310x4-45x3-3x2+365x+11(xix) f(x) = x4 − 4x(xx) fx=x44+23x3-52x2-6x+7(xxi) f(x) = x4 − 4x3 + 4x2 + 15(xxii) f(x) = 5x32-3x52, x > 0(xxiii) f(x) = x8 + 6x2(xxiv) f(x) = x3 − 6x2 + 9x + 15(xxv) fx=x(x-2)2(xxvi) fx=3x4-4x3-12x2+5(xxvii) fx=32x4-4x3-45x2+51(xxviii) fx=log2+x-2x2+x, x∈R(xxix) fx=x44-x3-5x2+24x+12
Answer» Find the intervals in which the following functions are increasing or decreasing. (i) f(x) = 10 − 6x − 2x² (ii) f(x) = x² + 2x − 5 (iii) f(x) = 6 − 9x − x² (iv) f(x) = 2x³ − 12x² + 18x + 15 (v) f(x) = 5 + 36x + 3x² − 2x³ (vi) f(x) = 8 + 36x + 3x² − 2x³ (vii) f(x) = 5x³ − 15x² − 120x + 3 (viii) f(x) = x³ − 6x² − 36x + 2 (ix) f(x) = 2x³ − 15x² + 36x + 1 (x) f(x) = 2x³ + 9x² + 12x + 20 (xi) f(x) = 2x³ − 9x² + 12x − 5 (xii) f(x) = 6 + 12x + 3x² − 2x³ (xiii) f(x) = 2x³ − 24x + 107 (xiv) f(x) = −2x³ − 9x² − 12x + 1 (xv) f(x) = (x − 1) (x − 2)² (xvi) f(x) = x³ − 12x² + 36x + 17 (xvii) f(x) = 2x³ − 24x + 7 (xviii) $f (x) = \frac{3}{10} x^{4} - \frac{4}{5} x^{3} - 3 x^{2} + \frac{36}{5} x + 11$ (xix) f(x) = x⁴ − 4x (xx) $f (x) = \frac{x^{4}}{4} + \frac{2}{3} x^{3} - \frac{5}{2} x^{2} - 6 x + 7$ (xxi) f(x) = x⁴ − 4x³ + 4x² + 15 (xxii) f(x) = $5 x^{\frac{3}{2}} - 3 x^{\frac{5}{2}}$ , x > 0 (xxiii) f(x) = x⁸ + 6x² (xxiv) f(x) = x³ − 6x² + 9x + 15 (xxv) $f (x) = {\{x (x - 2)\}}^{2}$ (xxvi) $f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5$ (xxvii) $f (x) = \frac{3}{2} x^{4} - 4 x^{3} - 45 x^{2} + 51$ (xxviii) $f (x) = \log (2 + x) - \frac{2 x}{2 + x}, x \in R$ (xxix) $f (x) = \frac{x^{4}}{4} - x^{3} - 5 x^{2} + 24 x + 12$

Discussion

5734.	Find the area bounded by curves (x– 1)2 + y2 = 1 and x2+ y 2 = 1
Answer» Find the area bounded by curves (x – 1)² + y² = 1 and x² + y² = 1

Discussion

5735.	Find the vector and the Cartesian equations of the line that passes through the points (3, −2, −5), (3, −2, 6).
Answer» Find the vector and the Cartesian equations of the line that passes through the points (3, −2, −5), (3, −2, 6).

Discussion

5736.	Give me value of R in all units
Answer» Give me value of R in all units

Discussion

5737.	If circle x2+y2−6x−10y+c=0 does not touch (or) intersect the coordinates axes and the point (1,4) is inside the circle, then the range of c is
Answer» If circle $x^{2} + y^{2} - 6 x - 10 y + c = 0$ does not touch (or) intersect the coordinates axes and the point $(1, 4)$ is inside the circle, then the range of $c$ is

Discussion

5738.	Question 1(vi)Check whether the following are quadratic equations:(vi) x2+3x+1=(x−2)2
Answer» Question 1(vi) Check whether the following are quadratic equations: (vi) $x^{2} + 3 x + 1 = (x - 2)^{2}$

Discussion

5739.	The side of a triangle are in the ratio 1:√3:2, then the angles of the triangle are in the ratio
Answer» The side of a triangle are in the ratio $1 : \sqrt{3} : 2$ , then the angles of the triangle are in the ratio

Discussion

5740.	The equation of the bisectors of the angle between lines represented by equation 4x2−16xy−7y2=0 is
Answer» The equation of the bisectors of the angle between lines represented by equation $4 x^{2} - 16 x y - 7 y^{2} = 0$ is

Discussion

5741.	Inverse function is defined for which of the following type of function -
Answer» Inverse function is defined for which of the following type of function -

Discussion

5742.	If the distance between the foci and the distance between two directrices of the hyperbola x2a2−y2b2=1 are in the ratio 3:2, then b:a is
Answer» If the distance between the foci and the distance between two directrices of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ are in the ratio $3 : 2$ , then $b : a$ is

Discussion

5743.	If one of the diameters of the circle x2+y2−2x−6y+6=0 is a chord to the circle with centre (2,1), then the equation of the circle is
Answer» If one of the diameters of the circle $x^{2} + y^{2} - 2 x - 6 y + 6 = 0$ is a chord to the circle with centre $(2, 1)$ , then the equation of the circle is

Discussion

5744.	If the roots of the equation px^2 + qx + r = 0, where 2p, q, 2r are in G.P, are of the form a^2 , 4a — 4. Then the value of 2p + 4q + 7r is :
Answer» If the roots of the equation px^2 + qx + r = 0, where 2p, q, 2r are in G.P, are of the form a^2 , 4a — 4. Then the value of 2p + 4q + 7r is :

Discussion

5745.	What's the angle between a diagonal of a cube and the diagonal of face of the cube
Answer» What's the angle between a diagonal of a cube and the diagonal of face of the cube

Discussion

5746.	If A and B are two independent events such that P(A)>0.5,P(B)>0.5, P(A∩¯¯¯¯B)=325, P(¯¯¯¯A∩B)=825, then P(A∩B)=k, then 25k2 is
Answer» If $A$ and $B$ are two independent events such that $P (A) > 0.5, P (B) > 0.5,$ $P (A \cap ¯ ¯¯ ¯ B) = \frac{3}{25}$ , $P (¯ ¯¯ ¯ A \cap B) = \frac{8}{25}$ , then $P (A \cap B) = k$ , then $\frac{25 k}{2}$ is

Discussion

5747.	Integrate the following integrals:∫sinx cos2x sin3x dx
Answer» Integrate the following integrals: $\int \sin x \cos 2 x \sin 3 x d x$

Discussion

5748.	The eccentricity of the conic 4x2+16y2−32x−32y=1 is
Answer» The eccentricity of the conic $4 x^{2} + 16 y^{2} - 32 x - 32 y = 1$ is

Discussion

5749.	x2−y2+5x+8y−4=0 represents
Answer» $x^{2} - y^{2} + 5 x + 8 y - 4 = 0$ represents

Discussion

5750.	The number of non-negtive integer(s) which lie in between the maximum and minimum value of x if −5≤2x−4≤−1 is
Answer» The number of non-negtive integer(s) which lie in between the maximum and minimum value of $x$ if $- 5 \leq 2 x - 4 \leq - 1$ is

Discussion

Explore topic-wise InterviewSolutions in .

The value of x∈R for which vectors →a=(1,−2,1),→b=(−2,3,−4),→c=(1,−1,x) form a linearly dependent system, is equal to

Algebraic sum of the intercepts made by the plane x + 3y - 4z + 6 = 0 on the axes is

(3) Stee The length of an elastic string is X m when the tension is 8 N, and Y m when the tension is 10 N in metres when the tension is 18 N is (1) 4X- 5Y (3) 9x-4Y . The length (2) 5Y-4X 4) 4Y-9x

Match the following functions satisfying particular functional relationship Column-I (A) f(x+y)=f(x)+f(y) (B) f(xy)=f(x)+f(y) (C) f(x+y)=f(x)⋅f(y) (D) f(X)+f(y)=f(x+y1−xy) Column-II (p) log3x (q) tan−1x (r) 3x (s) 3x (t) A transcendental function

The acute angle of intersection of the curves y=[|sinx|+|cosx|] and x2+y2=5 (where [.] denotes the greatest integer function) is tan−1(k) then k is

11.4+14.7+17.10+...

If x∈R, then the range of log5/4(5x2−8x+4) is

An urn contains 5 red and 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls. Drawn. What are the possible values of X? Is X a random variable ? If yes, find the mean and variance of X.

If A={x∶x is a multiple of 3} and B={x∶x is a multiple of 5}, then A−B=

The figure formed by the lines ax±by±c=0 is

Find the general solution of the equation sinx+sin3x+sin5x=0

In ΔABC, the median AD divides ∠BAC such that ∠BAD:∠CAD=2:1. Then cos(A3) is equal to

If sin x= cos x and x is acute, state the value of x

If tanα=2tt2−1, what is t?

Write the solution set of the inequation x+1x≥2

Find x if cos3x+sin(2x-7/6)=-2

Evaluate the following:a+xyzxa+yzxya+z

81.Three symmetrical dices are thrown .The probability that the same number will appear on each of them is? options: (a)1/216 (b)1/36 (c)35/36 (d)1/35

If parabola touches the x axis at one point then there will be one zero or two overlapping zeros?

What is the condition for a function y = f(x) to be a monotonically increasing function

Let (1−x+x4)10=a0+a1x+a2x2+⋯+a40x40. Then which of the following options is CORRECT?

If 2 sin θ + 3 cos θ = 2, then 3 sin θ – 2 cos θ = _________.

{ If }l_1=∫_0^{mπ}f(\vert\operatorname{cos}x\vert)dx and }l_2=∫_0^{5π}f(\vert\operatorname{cos}x\vert)dx} then

23.At far off distant places, electricity is supplied with high voltage and low current. Explain why

The value of 1∫−1x√1−x2⋅sin−1(2x√1−x2)dx is equal to

If f(x) = exg(x), g(0) = 2, g'(0) = 1, then f'(0) = __________________.

Hybridisation of Xe in XeF4 molecule isXeF4 अणु में Xe का संकरण क्या है?

The sum of all values of x for which the matrix [3x2xx+1x−1] is NOT invertible, is[2 marks]

The differential equation that represents the family of curves y=12x2−c, where c is an arbitrary constant is

Solve the given inequality for real x:

The value of the determinant ∆=sec2θtan2θ1tan2θsec2θ-122202 is _____________.

Find the area bounded by curves (x– 1)2 + y2 = 1 and x2+ y 2 = 1

Find the vector and the Cartesian equations of the line that passes through the points (3, −2, −5), (3, −2, 6).

Give me value of R in all units

If circle x2+y2−6x−10y+c=0 does not touch (or) intersect the coordinates axes and the point (1,4) is inside the circle, then the range of c is

Question 1(vi)Check whether the following are quadratic equations:(vi) x2+3x+1=(x−2)2

The side of a triangle are in the ratio 1:√3:2, then the angles of the triangle are in the ratio

The equation of the bisectors of the angle between lines represented by equation 4x2−16xy−7y2=0 is

Inverse function is defined for which of the following type of function -

If the distance between the foci and the distance between two directrices of the hyperbola x2a2−y2b2=1 are in the ratio 3:2, then b:a is

If one of the diameters of the circle x2+y2−2x−6y+6=0 is a chord to the circle with centre (2,1), then the equation of the circle is

If the roots of the equation px^2 + qx + r = 0, where 2p, q, 2r are in G.P, are of the form a^2 , 4a — 4. Then the value of 2p + 4q + 7r is :

What's the angle between a diagonal of a cube and the diagonal of face of the cube

If A and B are two independent events such that P(A)&gt;0.5,P(B)&gt;0.5, P(A∩¯¯¯¯B)=325, P(¯¯¯¯A∩B)=825, then P(A∩B)=k, then 25k2 is

Integrate the following integrals:∫sinx cos2x sin3x dx

The eccentricity of the conic 4x2+16y2−32x−32y=1 is

x2−y2+5x+8y−4=0 represents

The number of non-negtive integer(s) which lie in between the maximum and minimum value of x if −5≤2x−4≤−1 is

If A and B are two independent events such that P(A)>0.5,P(B)>0.5, P(A∩¯¯¯¯B)=325, P(¯¯¯¯A∩B)=825, then P(A∩B)=k, then 25k2 is