Chatargee Previous Years Solved Sample Placement Papers
-
C is associated with
(a) 1, 4, 6, 7, 9, 11 (Ans)
(b) 2, 4, 6, 8, 9
(c) 1, 4, 6, 7, 9
(d) None of these
-
If p and q are positive integers, then which one of the following equations has p - √q as one of its roots?
(a) x² - 2px - (p² - q) = 0
(b) x² - 2px + (p² - q) = 0 (Ans)
(c) x² + 2px - (p² - q) = 0
(d) x² + 2px + (p² - q) = 0
-
Given two squares of sides x and y such that y = x + x². What is the rate of change of area of the second square with respect to the area of the first square?
(a) 1 + 3x + 2x² (Ans)
(b) 1 + 2x + 3x²
(c) 1 - 2x + 3x²
(d) 1 - 2x - 3x²
-
The planes px + 2y + 2z - 3 = 0 and 2x - y + z + 2 = 0 intersect at an angle π/4. What is the value of p²?
(a) 24 (Ans)
(b) 12
(c) 6
(d) 3
-
If the angle between the vectors **a** and **b** is π/3, what is the angle between -5**a** and 6**b**?
(a) π/6
(b) 2π/3 (Ans)
(c) 2π/5
(d) 3π/7
-
What is the degree of the differential equation d²y/dx² - √(1 + (dy/dx)³) = 0?
(a) 1 (Ans)
(b) 2
(c) 3
(d) 6
-
If ∫x²/nx dx = x³/m nx + x³/n + c, then what are the values of m and n respectively?
(a) 1/3, -1/9
(b) 3, -9 (Ans)
(c) 3, 9
(d) 3, 3
-
What is the principal value of cosec⁻¹(-√2)?
(a) π/4
(b) π/2
(c) -π/4 (Ans)
(d) 0
-
If f : R → R, g : R → R and g(x) = x + 3 and (fog)(x) = (x + 3)², then what is the value of f(-3)?
(a) -9
(b) 0
(c) 9 (Ans)
(d) 3
-
What is the value of lim (x - 1)² / |x - 1| as x → 1?
(a) 0 (Ans)
(b) 1
(c) -1
(d) The limit does not exist
-
A balloon is pumped at the rate of 4 cm³ per second. What is the rate at which its surface area increases when its radius is 4 cm?
(a) 1 cm²/sec
(b) 2 cm²/sec (Ans)
(c) 3 cm²/sec
(d) 4 cm²/sec
-
What is the value of 1 + tan 150° / 1 - tan 150°?
(a) 1
(b) 1/√2
(c) 1/√3
(d) √3 (Ans)
-
If f(x) = kx³ - 9x² + 9x + 3 is monotonically increasing in every interval, then which one of the following is correct?
(a) k < 3
(b) k ≤ 3
(c) k > 3
(d) k ≥ 3 (Ans)