Practice questions
88551 published questions with worked solutions.
- If the system of linear equations 2x + 2y + 3z = a, 3x − y + 5z = b, x − 3y + 2z = c where a, b, c are non zero real numbers, has...
- The sum of the real values of x for which the middle term in the binomial expansion of ( x^3 3 + 3x )^8 equals 5670 is:
- Let a = i + 2 j + 4 k, b = i + j + 4 k and c = 2 i + 4 j + ( ^2 - 1) k be coplanar vectors. Then the non-zero vector a c is:
- The plane containing the line x-3 2 = y+2 -1 = z-1 3 and also containing its projection on the plane 2x + 3y − z = 5, contains...
- The maximum value of the function f(x) = 3x^3 - 18x^2 + 27x - 40 on the set S = x R : x^2 + 30 11x is:
- The outcome of each of 30 items was observed; 10 items gave an outcome 12 - d each, 10 items gave outcome 12 each and the...
- The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of...
- If one real root of the quadratic equation 81x^2 + kx + 256 = 0 is cube of the other root, then a value of k is:
- A square is inscribed in the circle x^2 + y^2 - 6x + 8y - 103 = 0 with its sides parallel to the coordinate axes. Then the...
- If y(x) is the solution of the differential equation dy dx + ( 2x + 1 x )y = e^ -2x , x > 0, where y(1) = 12e^ -2 , then:
- Let [x] denote the greatest integer less than or equal to x. Then _ x 0 ( ^2x) + (|x| - (x[x]))^2 x^2
- The direction ratios of normal to the plane through the points (0, −1, 0) and (0, 0, 1) and making an angle 4 with the plane y −...
- Let A = pmatrix 0 & 2q & r p & q & -r p & -q & r pmatrix . If AA^T = I_3, then |p| is:
- If tangents are drawn to the ellipse x^2 + 2y^2 = 2 at all points on the ellipse other than its four vertices then the mid points...
- If x _e( _ex) - x^2 + y^2 = 4 (y > 0), then dy dx at x = e is equal to:
- The area (in sq. units) of the region bounded by the curve x^2 = 4y and the straight line x = 4y − 2 is:
- Let f: R → R be defined by f(x) = x 1 + x^2 , x ∈ R. Then the range of f is:
- Let (-2 - 13i )^3 = x + iy 27 (i = -1 ), where x and y are real numbers, then y − x equals:
- Two integers are selected at random from the set 1, 2, …., 11 . Given that the sum of selected numbers is even, the conditional...
- Two circles with equal radii are intersecting at the points (0, 1) and (0, −1). The tangent at the point (0, 1) to one of the...