Author Archives: Priyanka

In This Post we are  providing Chapter-12 Linear Programming NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON LINEAR PROGRAMMING

Question 1.
Feasible region in the set of points which satisfy
(a) The objective functions
(b) Some the given constraints
(c) All of the given constraints
(d) None of these

Answer: (c) All of the given constraints

Question 2.
Of all the points of the feasible region for maximum or minimum of objective function the points
(a) Inside the feasible region
(b) At the boundary line of the feasible region
(c) Vertex point of the boundary of the feasible region
(d) None of these

Answer: (c) Vertex point of the boundary of the feasible region

Question 3.
Objective function of a linear programming problem is
(a) a constraint
(b) function to be optimized
(c) A relation between the variables
(d) None of these

Answer: (b) function to be optimized

Question 4.
A set of values of decision variables which satisfies the linear constraints and n-negativity conditions of a L.P.P. is called its
(a) Unbounded solution
(b) Optimum solution
(c) Feasible solution
(d) None of these

Answer: (c) Feasible solution

Question 5.
The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x ≥ 0, y ≥ 0 is
(a) 300
(b) 600
(c) 400
(d) 800

Answer: (b) 600

Question 6.
The maximum value of Z = 4x + 2y subject to the constraints 2x + 3y ≤ 18, x + y ≥ 10, x, y ≤ 0 is
(a) 36
(b) 40
(c) 30
(d) None of these

Answer: (d) None of these

Question 7.
In equation 3x – y ≥ 3 and 4x – 4y > 4
(a) Have solution for positive x and y
(b) Have no solution for positive x and y
(c) Have solution for all x
(d) Have solution for all y

Answer: (a) Have solution for positive x and y

Question 8.
The maximum value of Z = 3x + 4y subjected to constraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is
(a) 120
(b) 140
(c) 100
(d) 160

Answer: (b) 140

Question 9.
Maximize Z = 11 x + 8y subject to x ≤ 4, y ≤ 6, x + y ≤ 6, x ≥ 0, y ≥ 0.
(a) 44 at (4, 2)
(b) 60 at (4, 2)
(c) 62 at (4, 0)
(d) 48 at (4, 2)

Answer: (b) 60 at (4, 2)

Question 10.
Maximize Z = 3x + 5y, subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0
(a) 20 at (1, 0)
(b) 30 at (0, 6)
(c) 37 at (4, 5)
(d) 33 at (6, 3)

Answer: (c) 37 at (4, 5)

Question 11.
Maximize Z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0
(a) 16 at (4, 0)
(b) 24 at (0, 4)
(c) 24 at (6, 0)
(d) 36 at (0, 6)

Answer: (d) 36 at (0, 6)

Question 12.
Maximize Z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0
(a) 59 at (92, 52)
(b) 42 at (6, 0)
(c) 49 at (7, 0)
(d) 57.2 at (0, 5.2)

Answer: (a) 59 at (92, 52)

Question 13.
Maximize Z = 6x + 4y, subject to x ≤ 2, x + y ≤ 3, -2x + y ≤ 1, x ≥ 0, y ≥ 0
(a) 12 at (2, 0)
(b) 1403 at (23, 13)
(c) 16 at (2, 1)
(d) 4 at (0, 1)

Answer: (c) 16 at (2, 1)

Question 14.
Maximize Z = 10 x₁ + 25 x₂, subject to 0 ≤ x₁ ≤ 3, 0 ≤ x₂ ≤ 3, x₁ + x₂ ≤ 5
(a) 80 at (3, 2)
(b) 75 at (0, 3)
(c) 30 at (3, 0)
(d) 95 at (2, 3)

Answer: (d) 95 at (2, 3)

Question 15.
Z = 20x₁ + 20₂, subject to x₁ ≥ 0, x₂ ≥ 0, x₁ + 2x₂ ≥ 8, 3x₁ + 2x₂ ≥ 15, 5x₁ + 2x₂ ≥ 20. The minimum value of Z occurs at
(a) (8, 0)
(b) (52, 154)
(c) (72, 94)
(d) (0, 10)

Answer: (c) (72, 94)

In This Post we are  providing Chapter-11 Three Dimensional Geometry NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON THREE DIMENSIONAL GEOMETRY

Question 1.
Distance between two planes:
2x + 3y + 4z = 5 and 4x + 6y + 8z = 12 is
(a) 2 units
(b) 4 units
(c) 8 units
(d) 129√ units.

Answer: (d) 129√ units.

Question 2.
The planes 2x – y + 4z = 3 and 5x – 2.5y +10 z = 6 are
(a) perpendicular
(b) parallel
(c) intersect along y-axis
(d) passes through (0, 0, 54)

Answer: (b) parallel

Question 3.
The co-ordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:
(a) (2, 0, 0)
(b) (0, 5, 0)
(c) (0, 0, 7)
(d) (0, 5, 7).

Answer: (a) (2, 0, 0)

Question 4.
If α, ß, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction-cosines of the line are:
(a) < sin α, sin ß, sin γ >
(b) < cos α, cos ß, cos γ >
(c) < tan α, tan ß, tan γ >
(d) < cos² α, cos² ß, cos² γ >

Answer: (b) < cos α, cos ß, cos γ >

Question 5.
The distance of a point P(a, b, c) from x-axis is
(a)  √ a2+c2
(b)  √ a2+b2
(c)  √ b2+c2
(d) b² + c².

Answer: (c) √  b2+c2

Question 6.
If the direction-cosines of a line are < k, k, k >, then
(a) k > 0
(b) 0 < k < 1
(c) k = 1
(d) k = 1√3 or –1√3

Answer: (c) k = 1

Question 7.
The reflection of the point (α, ß, γ) in the xy-plane is:
(a) (α, ß, 0)
(b) (0, 0, γ)
(c) (-α, -ß, γ)
(d) (α, ß, -γ).

Answer: (d) (α, ß, -γ).

Question 8.
What is the distance (in units) between two planes:
3x + 5y + 7z = 3 and 9x + 15y + 21z = 9?
(a) 0
(b) 3
(c) 68√3
(d) 6

Answer: (a) 0

Question 9.
The equation of the line in vector form passing through the point (-1, 3, 5) and parallel to line x−32 = y−43, z = 2 is
(a) r⃗  = (-i^ + 3j^ + 5k^) + λ(2i^ +3j^ + k^)
(b) r⃗  = (-i^+ 3j^ + 5k^) + λ(2i^ + 3j^)
(c) r⃗  = (2i^+ 3j^ – 2k^) + λ(-i^ + 3j^ + 5k^)
(d) r⃗  = (2i^ + 3j^]) + λ(-i^ + 3j^ + 5k^).

Answer: (b) r⃗  = (-i^+ 3j^ + 5k^) + λ(2i^ + 3j^)

Question 10.
Let the line x−23 = y−1−5 = z−22 lie in the plane x + 3y – αz + ß = 0. Then (α, ß) equals:
(a) (-6, -17)
(b) (5, -15)
(c) (-5, 5)
(d) (6, -17).

Answer: (a) (-6, -17)

Question 11.
The projections of a vector on the three co-ordinate axes are 6, -3, 2 respectively. The direction-cosines of the vector are:
(a) 65, –35, 25
(b) 67, –37, 27
(c) −67, −37, 17
(d) 6, -3, 2.

Answer: (b) 67, –37, 27

Question 12.
A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals:
(a) 30°
(b) 45°
(c) 60°
(d) 15°.

Answer: (c) 60°

Question 13.
If the angle between the line x = y−12 = z−3λ and the plane x + 2y + 3z = 4is cos^-1 (√514) then λ, equals:
(a) 23
(b) 32
(c) 25
(d) 53

Answer: (a) 23

Question 14.
The length of the perpendicular drawn from the point (3, -1, 11) to the line x2 = y−23 = z−34 is
(a) √29
(b) √33
(c) √53
(d) √65

Answer: (c) √53

Question 15.
The distance of the point (1, -5, 9) from the plane x – y + z = 5, measured along a straight line x = y = z is:
(a) 10√3
(b) 5√3
(c) 10 √3
(d) 3√5

Answer: (a) 10√3

In This Post we are  providing Chapter-10 Vector Algebra NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON VECTOR ALGEBRA

Question 1.
In ΔABC, which of the following is not true?

(a) AB→ + BC→ + CA→ = 0⃗ 
(b) AB→ + BC→ – AC→ = 0⃗ 
(c) AB→ + BC→ – CA→ = 0⃗ 
(d) AB→ – CB→ + CA→ = 0⃗ 

Answer: (c) AB→ + BC→ – CA→ = 0⃗ 

Question 2.
If a⃗  and b⃗  are two collinear vectors, then which of the following are incorrect:
(a) b⃗  = λa⃗  tor some scalar λ.
(b) a⃗  = ±b⃗ 
(c) the respective components of a⃗  and b⃗  are proportional
(d) both the vectors a⃗  and b⃗  have the same direction, but different magnitudes.

Answer: (d) both the vectors a⃗  and b⃗  have the same direction, but different magnitudes.

Question 3.
If a is a non-zero vector of magnitude ‘a’ and λa non-zero scalar, then λa⃗  is unit vector if:
(a) λ = 1
(b) λ = -1
(c) a = |λ|
(d) a = 1|λ|

Answer: (d) a = 1|λ|

Question 4.
Let λ be any non-zero scalar. Then for what possible values of x, y and z given below, the vectors 2i^ – 3j^ + 4k^ and xi^ – yj^ + zk^ are perpendicular:
(a) x = 2λ. y = λ, z = λ
(b) x = λ, y = 2λ, z = -λ
(c) x = -λ, y = 2λ, z = λ
(d) x = -λ, y = -2λ, z = λ.

Answer: (c) x = -λ, y = 2λ, z = λ

Question 5.
Let the vectors a⃗  and b⃗  be such that |a⃗ | = 3 and |b⃗ | = √23, then a⃗  × b⃗  is a unit vector if the angle between a⃗  and b⃗  is:
(a) π6
(b) π4
(c) π3
(d) π2

Answer: (b) π4

Question 6.
Area of a rectangle having vertices
A(-i^ + 12 j^ + 4k^),
B(i^ + 12 j^ + 4k^),
C(i^ – 12 j^ + 4k^),
D(-i^ – 12 j^ + 4k^) is
(a) 12 square unit
(b) 1 square unit
(c) 2 square units
(d) 4 square units.

Answer: (c) 2 square units

Question 7.
If θ is the angle between two vectors a⃗ , b⃗ , then a⃗ .b⃗  ≥ 0 only when
(a) 0 < θ < π2
(b) 0 ≤ θ ≤ π2
(c) 0 < θ < π
(d) 0 ≤ θ ≤ π

Answer: (b) 0 ≤ θ ≤ π2

Question 8.
Let a⃗  and b⃗  be two unit vectors and 6 is the angle between them. Then a⃗  + b⃗  is a unit vector if:
(a) θ = π4
(b) θ = π3
(c) θ = π2
(d) θ = 2π3

Answer: (d) θ = 2π3

Question 9.
If {i^, j^, k^} are the usual three perpendicular unit vectors, then the value of:
i^.(j^ × k^) + j^.(i^ × k^) + k^.(i^ × j^) is
(a) 0
(b) -1
(c) 1
(d) 3

Answer: (d) 3

Question 10.
If θ is the angle between two vectors a⃗  and b⃗ , then |a⃗ .b⃗ | = |a⃗  × b⃗ | when θ is equal to:
(a) 0
(b) π4
(c) π2
(d) π

Answer: (b) π4

Question 11.
The area of the triangle whose adjacent sides are
a⃗  = 3i^ + j^ + 4k^ and b⃗  = i^ – j^ + k^ is
(a) 1/2 42√
(b) 42
(c) 42√
(d) 21√

Answer: (a) 1/2 42√

Question 12.
The magnitude of the vector 6i^ + 2j^ + 3k^ is
(a) 5
(b) 7
(c) 12
(d) 1.

Answer: (b) 7

Question 13.
The vector with initial point P (2, -3, 5) and terminal point Q (3, -4, 7) is
(a) i^ – j^ + 2k^
(b) 5i^ – 7j^ + 12k^
(c) –i^ + j^ – 2k^
(d) None of these.

Answer: (a) i^ – j^ + 2k^

Question 14.
The angle between the vectors i^ – j^ and j^ – k^ is
(a) π3
(b) 2π3
(c) –π3
(d) 5π6

Answer: (b) 2π3

Question 15.
The value of ‘λ’ for which the two vectors:
2i^ – j^ + 2k^ and 3i^ + λj^ + k^ are perpendicular is
(a) 2
(b) 4
(c) 6
(d) 8.

Answer: (d) 8.

In This Post we are  providing Chapter-9 Differential Equations NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON DIFFERENTIAL EQUATIONS

Question 1.
Integration factor of differential equation dydx + py = Q, where P and IQ are functions of x is
(a) ∫e^pdx
(b) e∫pdx
(c) e-∫pdx
(d) None of these

Answer: (d) None of these

Question 2.
The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is
(a) 0.4 π cm/s
(b) 0.8 π cm/s
(c) 0.8 cm/s
(d) None of these

Answer: (b) 0.8 π cm/s

Question 3.
The solution of dydx = 1 + x + y + xy is
(a) x – y = k(1 + xy)
(b) log (1 + y) = x + x22 + k
(c) log (1 + x) + y + y22 = k
(d) None of these

Answer: (b) log (1 + y) = x + x22 + k

Question 4.
The degree of the differential equation
(d2ydx)² + (dydx)² = x sin dydx is
(a) 1
(b) 2
(c) 3
(d) not defined

Answer: (d) not defined

Question 5.
The degree of differential equation
[1 + (dydx)²]³² = d2ydx2 is
(a) 4
(b) 32
(c) 2
(d) not defined

Answer: (c) 2

Question 6.
The order and degree of the differential equation
d2ydx2 + (dydx)¹⁴ + x¹³ = 0 respectively, are
(a) 2 and not defined
(b) 2 and 2
(c) 2 and 3
(d) 3 and 3Answer

Answer: (a) 2 and not defined

Question 7.
If y = e^-x (A cos x + B sin x), then y is a solution of
(a) d2ydx2 + 2dydx = 0
(b) d2ydx2 – 2dydx + 2y = 0
(c) d2ydx2 + 2dydx + 2y = 0
(d) d2ydx2 + 2y = 0

Answer: (c) d2ydx2 + 2dydx + 2y = 0

Question 8.
The differential equation for y = A cos αx + B sin αx where A and B are arbitrary constants is
(a) d2ydx2 – α²y = 0
(b) d2ydx2 + α²y = 0
(c) d2ydx2 + αy = 0
(d) d2ydx2 – αy = 0

Answer: (b) d2ydx2 + α²y = 0

Question 9.
Solution of differential equation xdy – ydx = Q represents
(a) a rectangular hyperbola
(b) parabola whose vertex is at origin
(c) straight line passing through origin
(d) a circle whose center is at origin

Answer: (c) straight line passing through origin

Question 10.
Integrating factor of the differential equation cos x dydx + y sin x = 1 is
(a) cos x
(b) tan x
(c) sec x
(d) sin x

Answer: (c) sec x

Question 11.
Solution of the differential equation tan y sec² x dx + tan x sec² y dy + 0 is .
(a) tan x + tan y = k
(b) tan x – tan y = k
(c) tan x*tan y = k
(d) tan x.tan y = k

Answer: (d) tan x.tan y = k

Question 12.
Family r = Ax + A³ of curves is represented by the differential equation of degree
(a) 1
(b) 2
(c) 3
(d) 4

Answer: (b) 2

Question 13.
Integrating factor of xdydx – y = x⁴ – 3x is
(a) x
(b) log x
(c) 12
(d) -x

Answer: (c) 12

Question 14.
Solution of dydx – y = 1 y(0) = 1 is given by
(a) xy = -e^x
(b) xy = -e^-x
(c) xy = -1
(d) y = 2e^x – 1

Answer: (d) y = 2e^x – 1

Question 15.
The number of solutions of dydx = y+1x−1 when y(1) = 2 is
(a) none
(b) one
(c) two
(d) infinite

Answer: (b) one

In This Post we are  providing Chapter-8 Application of Integrals NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON APPLICATION OF INTEGRALS

Question 1.
The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ π2 is
(a) √2 sq. units
(b) (√2 + 1) sq. units
(c) (√2 – 1) sq. units
(d) (2√2 – 1) sq. units

Answer: (c) (√2 – 1) sq. units

Question 2.
The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is
(a) 38 sq. units
(b) 58 sq. units
(c) 78 sq. units
(d) 98 sq. units

Answer: (d) 98 sq. units

Question 3.
The area of the region bounded by the curve y = 16−x2√ and x-axis is
(a) 8π sq. units
(b) 20π sq. units
(c) 16π sq. units
(d) 256π sq. units

Answer: (a) 8π sq. units

Question 4.
Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x² + y² = 32 is
(a) 16π sq. units
(b) 4π sq. units
(c) 32π sq. units
(d) 24π sq. units

Answer: (b) 4π sq. units

Question 5.
Area of the region bounded by the curve y = cos x between x = 0 and x = π is
(a) 2 sq. units
(b) 4 sq. units
(c) 3 sq. units
(d) 1 sq. units

Answer: (a) 2 sq. units

Question 6.
The area of the region bounded by parabola y² = x and the straight line 2y = x is
(a) 43 sq. unit
(b) 1 sq. unit
(c) 23 sq. units
(d) 13 sq. units

Answer: (a) 43 sq. unit

Question 7.
The area of the region bounded by the curve y = sin x between the ordinates x = 0, x = π2 and the x-axis is
(a) 2 sq. units
(b) 4 sq. units
(c) 3 sq. units
(d) 1 sq. unit

Answer: (d) 1 sq. unit

Question 8.
The area of the region bounded by the ellipse x²25 + y²16 = 1 is
(a) 20π sq. units
(b) 20π² sq. units
(c) 16π² sq. units
(d) 25π sq. units

Answer: (a) 20π sq. units

Question 9.
The area of the region bounded by the circle x² + y² = 1 is
(a) 2π sq. units
(b) 7π sq. units
(c) 3π sq. units
(d) 4π sq. units

Answer: (b) 7π sq. units

Question 10.
The area of the region bounded by the and the lines x = 2 and x = 3
(a) 72 sq. unit
(b) 92 sq. unit
(c) 112 sq. units
(d) 132 sq. units

Answer: (a) 72 sq. unit

Question 11.
The area of the region bounded by the curve x = 2y + 3 and the lines y = 1 and y = -1 is
(a) 4 sq. units
(b) 32 sq. units
(c) 6 sq. units
(d) 8 sq., units

Answer: (c) 6 sq. units

Question 12.
If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and x-axis is
(a) 92 sq. units
(b) 8 sq. units
(c) 12 sq. units
(d) 4 sq. units

Answer: (c) 12 sq. units

Question 13.
The area bounded by the curve y = x² – 1 and the straight line x + y = 3 is
(a) 92 sq. units
(b) 4 sq. units
(c) 717√6 sq. units
(d) 1717√6 sq. units

Answer: (d) 1717√6 sq. units

Question 14.
Area bounded by the lines y = |x| – 2 and y = 1 – |x – 1| is equal to
(a) 4 sq. units
(b) 6 sq. units
(c) 2 sq. units
(d) 8 sq. units

Answer: (a) 4 sq. units

Question 15.
The area bounded by the lines y = |x| – 1 and y = -|x| + 1 is
(a) 1 sq. unit
(b) 2 sq. unit
(c) 2√2 sq. units
(d) 4 sq. units

Answer: (b) 2 sq. unit

In This Post we are  providing Chapter-6 Application of Derivatives NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON APPLICATION OF DERIVATIVES

Question 1.
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is:
(a) 10π
(b) 12π
(c) 8π
(d) 11π

Answer: (b) 12π

Question 2.
The total revenue received from the sale of x units of a product is given by R (x) = 3x² + 36x + 5. The marginal revenue, when x = 15 is:
(a) 116
(b) 96
(c) 90
(d) 126.

Answer: (d) 126.

Question 3.
The interval in which y = x² e^-x is increasing with respect to x is:
(a) (-∞, ∞)
(b) (-2,0)
(c) (2, ∞)
(d) (0, 2).

Answer: (d) (0, 2).

Question 4.
The slope of the normal to the curve y = 2x² + 3 sin x at x = 0 is
(a) 3
(b) 13
(c) -3
(d) –13

Answer: (d) –13

Question 5.
The line y = x + 1 is a tangent to the curve y² = 4x at the point:
(a) (1, 2)
(b) (2, 1)
(c) (1, -2)
(d) (-1, 2).

Answer: (a) (1, 2)

Question 6.
If f(x) = 3x² + 15x + 5, then the approximate value of f(3.02) is:
(a) 47.66
(b) 57.66
(c) 67.66
(d) 77.66.

Answer: (d) 77.66.

Question 7.
The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is:
(a) 0.06 x³ m³
(b) 0.6 x³ m³
(c) 0.09 x³m³
(d) 0.9 x³ m³

Answer: (c) 0.09 x³m³

Question 8.
The point on the curve x² = 2y, which is nearest to the point (0, 5), is:
(a) (2 √2, 4)
(b) (2 √2, 0)
(c) (0, 0)
(d) (2, 2).

Answer: (a) (2 √2, 4)

Question 9.
For all real values of x, the minimum value of 1−x+x21+x+x2 is
(a) 0
(b) 1
(c) 3
(d) 13

Answer: (d) 13

Question 10.
The maximum value of [x (x – 1) + 1]^1/3, 0 ≤ x ≤ 1 is
(a) (13)¹³
(b) 12
(c) 1
(d) 0

Answer: (c) 1

Question 11.
A cylindrical tank of radius 10 m being filled with wheat at the rate of 314 cubic m per minute. Then the depth of the wheat is increasing at the rate of:
(a) 1 m/minute
(b) 0 × 1 m/minute
(c) 1 × 1 m/minute
(d) 0 × 5 m/minute.

Answer: (a) 1 m/minute

Question 12.
The slope of the tangent to the curve x = t² + 3t – 8, y = 2 t² – 2t – 5 at the point (2, -1) is:
(a) 227
(b) 67
(c) 76
(d) −67

Answer: (b) 67

Question 13.
The line y = mx + 1 is a tangent to the curve y² = 4x if the value of m is:
(a) 1
(b) 2
(c) 3
(d) 12

Answer: (a) 1

Question 14.
The normal at the point (1, 1) on the curve 2y + x² = 3 is
(a) x + y = 0
(b) x – y = 0
(c) x + y + 1 = 0
(d) x – y + 1 = 0.

Answer: (b) x – y = 0

Question 15.
The normal to the curve x² = 4y passing through (2, 1) is:
(a) x + y = 3
(b) x – y = 3
(c) x + y = 1
(d) x – y = 1.

Answer: (a) x + y = 3

In This Post we are  providing Chapter-5 Continuity And Differentiability NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON CONTINUITY AND DIFFERENTIABILITY

Question 1.
If f (x) = 2x and g (x) = x22 + 1, then which of the following can be a discontinuous function
(a) f(x) + g(x)
(b) f(x) – g(x)
(c) f(x).g(x)
(d) g(x)f(x)

Answer: (d) g(x)f(x)

Question 2.
The function f(x) = 4−x24x−x3 is
(a) discontinuous at only one point at x = 0
(b) discontinuous at exactly two points
(c) discontinuous at exactly three points
(d) None of these

Answer: (a) discontinuous at only one point at x = 0

Question 3.
The set of points where the function f given by f (x) =| 2x – 1| sin x is differentiable is
(a) R
(b) R = {12}
(c) (0, ∞)
(d) None of these

Answer: (b) R = {12}

Question 4.
The function f(x) = cot x is discontinuous on the set
(a) {x = nπ, n ∈ Z}
(b) {x = 2nπ, n ∈ Z}
(c) {x = (2n + 1) π2 n ∈ Z}
(d) {x – nπ2 n ∈ Z}

Answer: (a) {x = nπ, n ∈ Z}

Question 5.
The function f(x) = e^|x| is
(a) continuous everywhere but not differentiable at x = 0
(b) continuous and differentiable everywhere
(c) not continuous at x = 0
(d) None of theseAnswer

Answer: (a) continuous everywhere but not differentiable at x = 0

Question 6.
If f(x) = x² sin1x, where x ≠ 0, then the value of the function f(x) at x = 0, so that the function is continuous at x = 0 is
(a) 0
(b) -1
(c) 1
(d) None of these

Answer: (a) 0

Question 7.
If f(x) =is continuous at x = π2, then
(a) m = 1, n = 0
(b) m = nπ2 + 1
(c) n = mπ2
(d) m = n = π2

Answer: (c) n = mπ2

Question 8.
If y = log(1−x21+x2), then dydx is equal to
(a) 4×31−x4
(b) −4×1−x4
(c) 14−x4
(d) −4×31−x4

Answer: (b) −4×1−x4

Question 9.
Let f(x) = |sin x| Then
(a) f is everywhere differentiable
(b) f is everywhere continuous but not differentiable at x = nπ, n ∈ Z
(c) f is everywhere continuous but no differentiable at x = (2n + 1) π2 n ∈ Z
(d) None of these

Answer: (b) f is everywhere continuous but not differentiable at x = nπ, n ∈ Z

Question 10.
If y = sinx+y√ then dydx is equal to
(a) cosx2y−1
(b) cosx1−2y
(c) sinx1−xy
(d) sinx2y−1

Answer: (a) cosx2y−1

Question 11.
The derivative of cos^-1 (2x² – 1) w.r.t cos^-1 x is
(a) 2
(b) −121−x2√
(c) 2x
(d) 1 – x²

Answer: (a) 2

Question 12.
If x = t², y = t³, then d2ydx2
(a) 32
(b) 34t
(c) 32t
(d) 34t

Answer: (b) 34t

Question 13.
The value of c in Rolle’s theorem for the function f(x) = x³ – 3x in the interval [o, √3] is
(a) 1
(b) -1
(c) 32
(d) 13

Answer: (a) 1

Question 14.
For the function f(x) = x + 1x, x ∈ [1, 3] the value of c for mean value theorem is
(a) 1
(b) √3
(c) 2
(d) None of these

Answer: (b) √3

Question 15.
Let f be defined on [-5, 5] as
f(x) = {x ,if x is rational−x, if x is irrational Then f(x) is
(a) continuous at every x except x = 0
(b) discontinuous at every x except x = 0
(c) continuous everywhere
(d) discontinuous everywhere

Answer: (b) discontinuous at every x except x = 0

In This Post we are  providing Chapter-7 Integrals NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON INTEGRALS

Question 1.
The anti-derivative of (√x + 1√x) equals

Answer: (c) 23 x²³ + 2x¹² + c

Question 2.
If 1dx (f(x)) = 4x³ – 3×4 such that f(2) = 0 then f(x) is ……………

Answer: (a) x⁴ + 1×3 – 1298

Question 3.
∫10×9+10xloge10x10+10x dx equals
(a) 10^x -x¹⁰ + c
(b) 10^x + x¹⁰ + c
(c) (10^x – x¹⁰)^-1 + c
(d) log (10^x + x¹⁰) + c.

Answer: (d) log (10^x + x¹⁰) + c.

Question 4.
∫dxsin2xcos2x equals
(a) tan x + cot x + c
(b) tan x – cot x + c
(c) tan x cot x + c
(d) tan x – cot 2x + c.

Answer: (b) tan x – cot x + c

Question 5.
∫sin2x–cos2xsin2xcos2x dx is equals to
(a) tan x + cot x + c
(b) tan x + cosec x + c
(c) -tan x + cot x + c
(d) tan x + sec x + c.

Answer: (a) tan x + cot x + c

Question 6.
∫ex(1+x)cos2(xe2) dx is equals to
(a) -cot (xe^x) + c
(b) tan (xe^x) + c
(c) tan (e^x) + c
(d) cot (e^x) + c

Answer: (b) tan (xe^x) + c

Question 7.
∫dxx2+2x+2 equals
(a) x tan^-1 (x + 1) + c
(b) tan^-1 (x + 1) + c
(c) (x + 1) tan^-1 x + c
(d) tan^-1 x + c

Answer: (b) tan^-1 (x + 1) + c

Question 8.
∫dx9−25×2√ equals

Answer: (b) 15 sin^-1 (5×3) + c

Question 9.
∫xdx(x−1)(x−2) equals

(d) log |(x – 1) (x – 2)| + c.

Answer: (b) log |(x−2)2x−1| + c

Question 10.
∫dxx(x2+1) equals
(a) log |x| – 12 log (x² + 1) + c
(b) 12 log |x| + 12 log (x² + 1) + c
(c) -log |x| + 12 log (x² + 1) + c
(d) log |x| + log (x² + 1) + c

Answer: (a) log |x| – 12 log (x² + 1) + c

Question 11.
∫x² e^x³ dx equals
(a) 13 e^x³ + c
(b) 13 e^x² + c
(c) 12 e^x³ + c
(d) 12 e^x² + c

Answer: (a) 13 e^x³ + c

Question 12.
∫e^x sec x (1 + tan x) dx equals
(a) e^x cos x + c
(b) e^x sec x + c
(c) e^x sin x + c
(d) e^x tan x + c

Answer: (b) e^x sec x + c

Question 13.
∫1+x2−−−−−√ dx is equal to

Answer:

Question 14.
∫x2–8x+7−−−−−−−−√ dx is equal to

Answer:

Question 15.
∫3√1 dx1+x2 equals
(a) π3
(b) 2π3
(c) π6
(d) π112

Answer: (d) π112

In This Post we are  providing Chapter-4 Determinants NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON DETERMINANTS

Question 1.
[[[111xyzx2y2z2]]]
(a) (x – y) (y + z)(z + x)
(b) (x + y) (y – z)(z – x)
(c) (x – y) (y – z)(z + x)
(d) (x – y) (y – z) (z – x)

Answer: (d) (x – y) (y – z) (z – x)

Question 2.
The value of the determinant
[[[ 352105723]]]
(a) 124
(b) 125
(c) 134
(d) 144

Answer: (c) 134

Question 3.
If a, b, c are in A.P. then the determinant[[[x+2x+3x+4x+3x+4x+5x+2ax+2bx+2c]]]
(a) 1
(b) x
(c) 0
(d) 2x

Answer: (c) 0

Question 4.
If w is a non-real root of the equation x² – 1 = 0. then
[[[1ωω2ωω21ω21ω]]] =
(a) 0
(b) 1
(c) ω
(d) ω²

Answer: (a) 0

Question 5.
If Δ = [103026] then A =
(a) 0
(b) 10
(c) 12
(d) 60

Answer: (a) 0

Question 6.
If 7 and 2 are two roots of the equation [[[x273x672x]]] then the third root is
(a) -9
(b) 14
(c) 12
(d) None of these

Answer: (a) -9

Question 7.
If [x182x] = [61826] x is equal to
(a) 6
(b) ±6
(c) -1
(d) -6

Answer: (b) ±6

Question 8.
[[[111abca2−bcb2−cac2−ab]]] is equal to
(a) abc
(b) ab + bc + ca
(c) 0
(d) (a – b)(b – c)(c – a)

Answer: (c) 0

Question 9.
A = [αqqα] |A³| = 125 then α =
(a) ±3
(b) ±2
(c) ±5
(d) 0

Answer: (a) ±3

Question 10.
If a ≠ 0 and [[[1+a1111+a1111+a]]] = 0 then a =
(a) a = -3
(b) a = 0
(c) a = 1
(d) a = 3

Answer: (a) a = -3

Question 11.
If x > 0 and x ≠ 1. y > 0. and y ≠ 1, z > 0 and z ≠ 1 then
[[[1logyxlogzxlogxy1logzylogxzlogyz1]]] is equal to
(a) 1
(b) -1
(c) 0
(d) None of these

Answer: (c) 0

Question 12.
[[[y+zyzzz+xzxyx+y]]] is equal to
(a) 6xyz
(b) xyz
(c) 4xyz
(d) xy + yz + zx

Answer: (c) 4xyz

Question 13.
If [2541] = [2x64x] then the value of x is
(a) ±2
(b) ±13
(c) ±√3
(d) ± (0.5)

Answer: (c) ±√3

Question 14.
If [2x85x] = [67−23] then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6

Answer: (c) ±6

Question 15.
The value of determinant [[[a−bb−cc−ab+cc+aa+babc]]]
(a) a³ + b³ + c ³
(b) 3bc
(c) a³ + b³ + c³ – 3abc
(d) None of these

Answer: (c) a³ + b³ + c³ – 3abc

In This Post we are  providing Chapter-3 R NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON MATRICES

Question 1.
If A = [a_ij]_{m × n} is a square matrix, if:
(a) m < n
(b) m > n
(c) m = n
(d) None of these.

Answer: (c) m = n

Question 2.
Which of the given values of x and y make the following pair of matrices equal:
[3x+7y+152−3x] [08y−24]
(a) x = –13, y = 7
(b) Not possible to find
(c) y = 7, x = –23
(d) x = –13, y = –23

Answer: (b) Not possible to find

Question 3.
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
(a) 27
(b) 18
(c) 81
(d) 512.Answer

Answer: (d) 512.

Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × 1, 2 × p, n × 3 and p × k respectively. Now answer the following (4-5):
Question 4.
The restrictions on n, k and p so that PY + WY will be defined are
(a) k = 3, p = n
(b) k is arbitrary, p = 2
(c) p is arbitrary
(d) k = 2,p = 3.

Answer: (a) k = 3, p = n

Question 5.
If n =p, then the order of the matrix 7X – 5Z is:
(a) p × 2
(b) 2 × n
(c) n × 3
(d) p × n.

Answer: (b) 2 × n

Question 6.
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: (a) Skew-symmetric matrix

Question 7.
If A = [cosα−sinαsinαcosα] then A + A’ = I, the value of α is
(a) π6
(b) π3
(c) π
(d) 3π2

Answer: (a) π6

Question 8.
Matrices A and B will be inverse of each other only if:
(a) AB = BA
(b) AB – BA = O
(c) AB = O, BA = I
(d) AB = BA = I.

Answer: (d) AB = BA = I.

Question 9.
If A = [αγβ−α] is such that A² = I, then
(a) 1 + α² + ßγ = 0
(b) 1 – α² + ßγ = 0
(c) 1 – α² – ßγ = 0
(d) 1 + α² – ßγ = 0

Answer: (c) 1 – α² – ßγ = 0

Question 10.
If a matrix is both symmetric and skew- symmetric matrix, then:
(a) A is a diagonal matrix
(b) A is a zero matrix
(c) A is a square matrix
(d) None of these.

Answer: (b) A is a zero matrix

Question 11.
If A is a square matrix such that A² = A, then (I + A)³ – 7A is equal to :
(a) A
(b) I – A
(c) I
(d) 3A.

Answer: (c) I

Question 12.
The matrix A = ⎡⎣⎢005050500⎤⎦⎥ is a
(a) scalar matrix
(b) diagonal matrix
(c) unit matrix
(d) square matrix.

Answer: (d) square matrix.

Question 13.
If matrix A = [a_ij]_2×2
where a_ij = 1 if i ≠ j = 0 if i = j,
(a) I
(b) A
(c) O
(d) None of these

Answer: (a) I

Question 14.

then A – B is equal to
(a) 1
(b) O
(c) 21

Answer: (c) 21

Question 15.
If A is a matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, then order of matrix B is
(a) m × m
(b) n × n
(c) n × m
(d) m × n.

Answer: (d) m × n.