____ is the angle between the normals to two planes.
1.Normal between the planes
2.The angle between the planes
3.Tangent between the planes
4.Distance between the planes
_____ planes have an angle 90 degrees between them.
1.Orthogonal
2.Tangential
3.Normal
4.Parallel
A bullet fired into a target loses half of its velocity after penetrating 2.5 cm. How much further will it penetrate?
1.0.85 cm
2.0.84 cm
3.0.83 cm
4.0.82 cm
A curve passes through (1, 1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve is in the first quadrant and has its area equal to 2. What will be the equation of the curve?
1.xy = 2
2.xy = -1
3.x – y = 2
4.x + y = 2
A motor car travelling at the rate of 40 km/hr is stopped by its brakes in 4 seconds. How long will it go from the point at which the brakes are first applied?
1.22m
2.22(2/9)m
3.22(1/9)m
4.22(4/9)m
A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds, respectively.What is the velocity of the particle in 3 seconds?
1.11m/sec
2.31 cm/sec
3.21m/sec
4.41m/sec
A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds,respectively.What is the distance described by the particle in 3 seconds?
1.30 cm
2.31 cm
3.32 cm
4.33 cm
A particle moving in a straight line with uniform acceleration has a velocity 10 cm/sec and 8 seconds later has a velocity 54 cm/sec. What will be the described by the particle during the 10th second of its motion?
1.38.5cm
2.37.5cm
3.38cm
4.39.5cm
A particle moving in a straight line with uniform acceleration has a velocity 10 cm/sec and 8 seconds later has a velocity 54 cm/sec. What will be the value of space described?
1.172 cm
2.176 cm
3.178 cm
4.174 cm
A particle moving in a straight line with uniform retardation described 7cm in 5th second and after some time comes to rest. If the particle describes 1/64 part of the total path during the last second of its motion, for how long was the particle in motion?
1.6 seconds
2.8 seconds
3. 4 seconds
4.2 seconds
∆ABC is a right angled triangle, where AB = 5cm, BC = 10cm, AC = 15cm.
1.False
2.True
Another form of Rolle’s theorem for the continuous condition is _____
1.f is continuous on [a,a-h]
2.f is continuous on [a,h]
3.f is continuous on [a,a+h]
4.f is continuous on [a,ah]
Another form of Rolle’s theorem for the differential condition is _____
1.f is differentiable on (a,ah)
2.f is differentiable on (a,a-h)
3.f is differentiable on (a,a/h)
4.f is differentiable on (a,a+h)
At which point does the normal to the hyperbola xy = 4 at (2, 2) intersects the hyperbola again?
1.(-2, -2)
2.(-2, 2)
3.(2, -2)
4.(0, 2)
Does Rolle’s theorem applicable if f(a) is not equal to f(b)?
1.Yes
2.No
3.Under particular conditions
4.May be
Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.
1.21
2.17
3. 12
4.11
Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z – 2 = 0, if they are perpendicular to each other.
1.21
2.– 7
3.12
4.– 8
Find the angle between 2x + 3y – 2z + 4 = 0 and 4x + 3y + 2z + 2 = 0.
1.38.2
2.19.64
3.89.21
4.54.54
Find the angle between the planes 5x + y + 3z + 1 = 0 and x + y – 2z + 6 = 0.
1.30.82
2.34.91
3.11.23
4.7.54
Find the angle between x + 2y + 7z + 2 = 0 and 4x + 4y + z + 2 = 0.
1.69.69
2.84.32
3.63.25
4.83.25
Find the area of the triangle with the vertices (2,3), (4,1), (5,0).
1.3 sq.units
2.2 sq.units
3.0
4.1 sq.unit
Find the equation of the line joining A(2,1) and B(6,3) using determinants.
1.2y-x=0
2.2y-x=0
3.y-x=0
4.y-2x=0
Find the equation of the line joining A(5,1), B(4,0) using determinants.
1.4x-y=4
2.x-4y=4
3.x-y=4
4.x-y=0
Find the value of k for which (1,2), (3,0), (2,k) are collinear.
1.0
2.-1
3. 2
4.1
Find the value of k for which the points (3,2), (1,2), (5,k) are collinear.
1.2
2.5
3.4
4.9
Function f is differentiable on [a,b] to satisfy Lagrange’s mean value theorem.
1.True
2.False
Function f is differential on (a,b) according to Rolle’s theorem.
1.True
2.False
Function f is not continuous on [a,b] to satisfy Lagrange’s mean value theorem.
1.False
2.True
Function f should be _____ on [a,b] according to Rolle’s theorem.
1.continuous
2.non-continuous
3.integral
4.non-existent
If a, b, c be the space described in the pth, qth and rth seconds by a particle with a given velocity and moving with uniform acceleration in a straight line then what is the value of a(q – r) + b(r – p) + c(p – q)?
1.0
2.1
3.-1
4.Can’t be determined
If, A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant length k. What kind of curve is passing through (0, k)?
1.Parabola
2.Hyperbola
3.Ellipse
4.Circle
In what ratio is the line segment joining the points A(-5, 2) and B(3, 9) divided by the x-axis?
1.2:5 (internally)
2.2:5 (externally)
3.2:9 (externally)
4.2:9 (internally)
In what ratio is the line segment joining the points A(2, 4) and B(6, 5) divided by the y-axis?
1.2:1 (internally)
2.2:1 (externally)
3.3:1 (internally)
4.3:1 (externally)
Lagrange’s mean value theorem is also called as _____
1.Euclid’s theorem
2.Rolle’s theorem
3.a special case of Rolle’s theorem
4.the mean value theorem
Rolle’s theorem is a special case of _____
1.Euclid’s theorem
2.another form of Rolle’s theorem
3.Lagrange’s mean value theorem
4.Joule’s theorem
The area of the triangle formed by three collinear points is zero.
1.True
2.False
The planes 5x + y + 3z + 1 = 0 and x + y – kz + 6 = 0 are orthogonal, find k.
1.4
2.2
3.6
4.8
Two straight railway lines meet at right angles. A train starts from the junction along one line and at the same time instant, another train starts towards the junction from a station on the other line and they move at the same uniform velocity.When will they be nearest to each other?
1.When they are equal distance from the junction
2.When they are in unequal distance from the junction
3.When they form a right angle at the junction
4.Data not sufficient
What are/is the conditions to satify Lagrange’s mean value theorem?
1.f is continuous on [a,b]
2.f is differentiable on (a,b)
3.f is differentiable and continuous on (a,b)
4.f is differentiable and non-continuous on (a,b)
What is the area of the triangle if the vertices are (0,2), (0, 0), (3, 0)?
1.1 sq.unit
2.5 sq.units
3.2 sq.units
4.3 sq.units
What is the relation between f(a) and f(b) according to Rolle’s theorem?
1.Equals to
2.Greater than
3.Less than
4.Unequal
What is the relation between f(a) and f(h) according to another form of Rolle’s theorem?
1.f(a) < f(a+h)
2.f(a) = f(a+h)
3.f(a) = f(a-h)
4.f(a) > f(a+h)
What will be ratio in which the line 3x + y – 11 = 0 divides the line segment joining the points (0, -1) and (-3, -4)?
1.1:2 (internally)
2.1:2 (externally)
3.2:1 (externally)
4.2:1 (internally)
What will be the coordinates of the fourth vertex S, if P(-1, -1), Q(2, 0), R(2, 3) are the three vertices of a parallelogram?
1.(-5, -12)
2.(5, -12)
3.(5, 12)
4.(-5, 12)
What will be the distance of the foot of ladder from the building, if the ladder of 12 m high reaches the top of a building 35 m high from the ground?
1.32.65 m
2.32.87 m
3.31.87 m
4.32.85 m
What will be the equation of the normal to the hyperbola xy = 4 at the point (2, 2)?
1.x + y = 0
2. x – y = 0
3. 2x – y = 0
4.x + 2y = 0
What will be the value of a and b, if (-5, a), (-3, -3), (-b, 0) and (-3, 3) are the vertices of the parallelogram?
1.a = 0, b = -1
2.a = -1, b = 1
3.a = 1, b = 1
4.a = 0, b = 1
Which of the following is not a property of determinant?
1.The value of determinant changes if all of its rows and columns are interchanged
2.The value of determinant changes if any two rows or columns are interchanged
3.The value of determinant is zero if any two rows and columns are identical
4.The value of determinant gets multiplied by k, if each element of row or column is multiplied by k
Which of the following sets of planes are parallel to each other?
1.2x+3y+4z=8 and 3x+9y+12z=7
2.2x+3y+4z=2 and 4x+6y+8z=9
3.3x+2y+4z=0 and 3x+4y+2z=0
4. 2x+4y+8z=9 and 4x+2y+7z=0
Which trigonometric function is used to find the angle between two planes?
1.Tangent
2.Cosecant
3.Secant
4.Sine