NDA questions
2827 published questions with worked solutions.
- What is the sum of the intercepts of the line x a^2 + y b^2 = 2 a^2+b^2 on the coordinate axes?
- Which one of the following is the perpendicular form of the straight line 3 x+2y=7?
- If the vertices B and D of a square ABCD are (2, 3) and (4, 1) respectively, then what is the area of the square?
- What is the value of if is the acute angle between the lines whose equations are px+qy=p+q and p(x-y)+q(x+y)=2q?
- The circle x^2+y^2-2kx-2ky+k^2=0 touches the x-axis at P and y-axis at Q. What is PQ equal to?
- What is the distance between the foci of the hyperbola x^2-4y^2=1?
- Let p = a - b , q = a + b . If | a |=| b |=2 and a b =2, then what is the value of | p q |?
- How many of the following can be a vector perpendicular to both the vectors 2 i - j + k and i + j +3 k ? I. 4 i +5 j -3 k II. -8...
- What is the area of the parallelogram whose sides are represented by the vectors i +2 j +3 k and 2 i + j +2 k ?
- The position vectors of the vertices A, B, C and D of a quadrilateral ABCD are given by 3 i +4 j -2 k , 4 i -4 j -3 k , 2 i -3 j...
- A force F =2 i - j +5 k is applied at the point A(1, 2, 5). If its moment about the point B(-1, -2, 3) is 16 i -6 j +2 k , then...
- What is the degree of the differential equation ( d^2y dx^2 )^ 3 2 = ( dy dx )^ 5 2 ?
- What is _ n ^ n+1 (x-[x]) ,dx, where [ ] is the greatest integer function and n is natural number?
- Consider the following statements : I. y=xe^ 2x is the solution of dy dx =y (2+ 1 x ). II. y=x |x|+cx is the solution of dy dx =...
- If k is an arbitrary constant, then what is the general solution of the equation (x+y)^2 dy dx =k^2?
- What is dx 10^x+10^ -x equal to?
- If I_1= _ e ^ e^2 dx x and I_2= _ 1 ^ 2 e^x x ,dx, then which one of the following is correct?
- Consider the following statements regarding the function f(x)= 1 x-5 : Statement-I : f(x) is decreasing on the intervals x<5 and...
- Consider the following statements : Statement-I : The function f(x)= x^3+128 x has a minimum value 48 at x=4. Statement-II : As x...
- What is the harmonic mean of the numbers C(10, 3), C(10, 4), C(10, 5), C(10, 6) and C(10, 7)?