A bullet fired into a target loses half of its velocity after penetrating 2.5 cm. How much further will it penetrate?
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?
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?
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?
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?
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?
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?
3. 4 seconds
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]
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?
3.Under particular conditions
Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.
Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z – 2 = 0, if they are perpendicular to each other.
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)?
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)?
In what ratio is the line segment joining the points A(-5, 2) and B(3, 9) divided by the x-axis?
In what ratio is the line segment joining the points A(2, 4) and B(6, 5) divided by the y-axis?
3.a special case of Rolle’s theorem
4.the mean value theorem
2.another form of Rolle’s theorem
3.Lagrange’s mean value theorem
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
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)
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)?
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?
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.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
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
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
1.Normal between the planes
2.The angle between the planes
3.Tangent between the planes
4.Distance between the planes