Class 12 Maths Online Test

1. Evaluate \(\int_3^7\)2f(x)-g(x)dx, if \(\int_3^7\)f(x) = 4 and \(\int_3^7\)g(x)dx = 2.

2. At which point does f(x) = |x – 1| has itslocal minimum?

3. The length of a side of a cube is 10cm; if an error of 0.05cm is made in measuring the side, then what is the value of percentage error in calculating its volume?

4. Bernoulli trials are also called as _____ or _____ questions.

5. What is the condition for a function f to be decreasing if f be continuous and differentiable on (a,b)?

6. Does Rolle’s theorem applicable if f(a) is not equal to f(b)?

7. Find the particular solution of the differential equation \(\frac{dy}{dx}=\frac{9y \,log⁡x}{5x \,log⁡y}\).

8. What is the name of the property \(\int_a^b\)f(x)dx=-\(\int_b^a\)f(x)dx?

9. What is the solution of the equation(y + x(√xy)(x + y))dx – (y + y(√xy)(x + y))dy = 0?

10. What is the order of the differential equation of the family of circles with one diameter along the line y = x axis?

11. Find the inverse of matrix A=\(\begin{bmatrix}5&1&3\\4&2&6\\5&4&2\end{bmatrix}\)

12. Find the matrix M and N, if M+N = \(\begin{bmatrix}5&6\\7&8\end{bmatrix}\),M-N = \(\begin{bmatrix}4&5\\6&8\end{bmatrix}\).

13. What will be the value of x for which the value of cosx is minimum?

14. The rate of change of area of a square is 40 cm²/s. What will be the rate of change of side if the side is 10 cm.

15. Find the minor of the element 2 in the determinant Δ=\(\begin{vmatrix}1&9\\2&3\end{vmatrix}\)?

16. \(\int \frac{(x^2+x+1)dx}{(x+2)(x^2+1)}\) equals ______

17. What is the value of sin^-1(-x) for all x belongs to [-1, 1]?

18. Given, f(x) = x³ – 12x² + 45x + 8. At which point does f(x) has its maximum?

19. Which of the following formula is incorrect?

20. If the direction cosines of the line are \(\frac{1}{2},-\frac{\sqrt{3}}{2}\),x respectively, then find the value of x.

21. Evaluate \(\int_2^3\)cosx dx.

22. Find the second order derivative of y=3x² 1 + log⁡(4x)

23. What is the value of \(\begin{vmatrix}1 & cosx-sinx & cosx + sinx \\1 & cosy-siny & cosy + siny \\1 & cosz-sinz & cosz + sinz \end {vmatrix}\)?

24. Find \(\int \frac{5 cos^2⁡x}{1+sin⁡x} dx\).

25. (a₁, a₂) ∈R implies that (a₂, a₁) ∈ R, for all a₁, a₂∈A. This condition is for which of the following relations?

26. Which among the below matrices has the inverse A^-1=\(\begin{bmatrix}1&-\frac{5}{8}\\0&\frac{1}{8}\end{bmatrix}\)

27. What is the value of sin^-1(sin 6)?

28. A bag contains 4 red and 7 blue balls. What is the probability of drawing a blue ball if the first ball drawn is red? The balls drawn are replaced into the bag.

29. Given that E and F are events such that P(E) = 0.5, P(F) = 0.4 and P(E∩F) = 0.3, then what will be the value of P(F|E)?

30. Find the order and degree of the differential equation (y''')²+7(y')²-(cos⁡x)²=0

31. Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.

32. “It is impossible for a particle to move in a straight line so that its velocity varies at the distance from the commencement of motion”. Which one is correct for the given statement?

33. What is derivative of xⁿ?

34. If the direction ratios of a line are 5, 4, -7 respectively, then find the direction cosines.

35. The order of the matrix A=\(\begin{bmatrix}1&5&9\\4&8&6\end{bmatrix}\) is 2×3.

36. A particle moves along the straight-line OX, starting from O with a velocity 4 cm/sec. At time t seconds its acceleration is (5 + 6t) cm/sec². What will be the velocity of the particle from O after 4 seconds?

37. What is the mathematical expression for f is left continuous on (a,b)?

38. What will be the value of f(x) if \(\begin{vmatrix}2ab & a^2 & b^2 \\a^2 & b^2 & 2ab \\b^2 & 2ab & a^2 \end {vmatrix}\)?

39. _____ planes have an angle 90 degrees between them.

40. A box contains a pair of socks in colours blue, red, yellow, green and pink. You reach into the box and choose a pair of socks without looking. You replace this pair and then choose another pair of socks. What is the probability that you will choose the yellow pair of socks both times?

41. What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?

42. Find \(\int_3^45x^3 \,dx\).

43. If a, b, c are the direction ratios of the line and l, m, n are the direction cosines of the line, then which of the following is incorrect?

44. What is the mathematical expression for a function to be strictly increasing on (a,b)?

45. If, A and B are arbitrary constants then what will be the differential equation of y = Ax + B/x?

46. Find \(\int \frac{20x^3}{1+x^4} dx\).

47. Value after differentiating cos (sinx) is _________

48. Find \(\frac{dy}{dx}\), if x=2t² and y=6t⁶.

49. A bag contains 3 red, 2 white and 4 green balls. What is the probability of drawing the second ball to be green if the first ball drawn is red? The balls are replaced in the bag.

50. The condition \(\frac {a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}\) is for the planes whose normals are _____ to each other.