NCERT English solutions

  Q1. The value of the limit Lim x→0  (cos x) cot2 x  is (a) 1 (b) e (c) e 1/2 (d) e -1/2 Q2. The value of limit Lim x→0  {sin (a + x) – sin (a – x)}/x is (a) 0 (b) 1 (c) 2 cos a (d) 2 sin a Q3. Lim x→-1  [1 + x + x² + ……….+ x 10 ] is (a) 0 (b) 1 (c) -1 (d) 2 Q4. The value of Lim x→01  (1/x) × sin -1  {2x/(1 + x²) is (a) 0 (b) 1 (c) 2 (d) -2 Q5. Lim x→0  log(1 – x) is equals to (a) 0 (b) 1 (c) 1/2 (d) None of these Q6. Lim x→0  {(a x  – b x )/ x} is equal to (a) log a (b) log b (c) log (a/b) (d) log (a×b) Q7. The value of lim y→0  {(x + y) × sec (x + y) – x × sec x}/y is (a) x × tan x × sec x (b) x × tan x × sec x + x × sec x (c) tan x × sec x + sec x (d) x × tan x × sec x + sec x Q8. Lim y→∞  {(x + 6)/(x + 1)} (x+4)  equals (a) e (b) e³ (c) e 5 (d) e 6 Q9. The derivative of [1+(1/x)] /[1-(1/x)] is (a) 1/(x-1)² (b) -1/(x-1)² (c) 2/(x-1)² (d) -2/(x-1)² Q10. The expansion of log(1 – x) is (a) x – x²/2 + x³/3 – …….. (b) x + x²/2 + x³/

  Q1. Sum of two rational numbers is ______ number. (a) rational (b) irrational (c) Integer (d) Both 1, 2 and 3 Q2. If x² = -4 then the value of x is (a) (-2, 2) (b) (-2, ∞) (c) (2, ∞) (d) No solution Q3. Solve: (x + 1)² + (x² + 3x + 2)² = 0 (a) x = -1, -2 (b) x = -1 (c) x = -2 (d) None of these Q4. If (x + 3)/(x – 2) > 1/2 then x lies in the interval (a) (-8, ∞) (b) (8, ∞) (c) (∞, -8) (d) (∞, 8) Q5.The region of the XOY-plane represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 10 is (a) unbounded (b) a polygon (c) none of these (d) exterior of a triangle Q6.The interval in which f(x) = (x – 1) × (x – 2) × (x – 3) is negative is (a) x > 2 (b) 2 < x and x < 1 (c) 2 < x < 1 and x < 3 (d) 2 < x < 3 and x < 1 Q7. If -2 < 2x – 1 < 2 then the value of x lies in the interval (a) (1/2, 3/2) (b) (-1/2, 3/2) (c) (3/2, 1/2) (d) (3/2, -1/2) Q8. The solution of the inequality |x – 1| < 2 is (a) (1, ∞) (b) (-1, 3)