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Home> Class-12> Mathematics >2020 Solutions
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| 89. Choose and write the correct options : Let A = {1, 2, 3), then number of relations containing (1, 2) and (1, 3) which are reflexive and |
| 90. Fill in the blanks : (i) Every differentiable function is ………..... (ii) Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 |
| 91. Write true / false in the following statements : (i) If A and B are two events such that P(A) ≠ 0 and P(BIA)=1, then A ⊂ B. |
| 92. Match the correct pairs : (i) ∫ cot x dx = (a) 1/a tan-1 x/a + c |
| 93. Give answers in one word / sentence each : (i) What is the rate of change of the area of a circle with respect to its radius / at / = 6 cm ? |
| 94. Find X and Y, if X+Y= [(7 0,2 5)] and X+Y= [(7 0,2 5)] |
| 95. Compute the indicated product : |
| 96. Examine whether the function f given by f(x) = x2 is continuous at x = 0. |
| 97. Find dy / dx, if x–y = Π |
| 98. Evaluate : |
| 99. Evaluate : ∫(1-x) √x dx |
| 100. Find the angle between two vectors a ⃗ and b ⃗ with magnitudes 1 and 2 respectively and when a ⃗.b ⃗=1. |
| 101. Find a vector in the direction of vector a ⃗=i ̂-2j ̂ that has magnitude 7 units. |
| 102. Find the direction cosines of x, y and z-axis. |
| 103. Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector |
| 104. A stone is dropped into a quiet lake and waves move in circles at a speed of 4 cm per second. At the instant, when the radius of the |
| 105. Use differential to approximate √36.6. |
| 106. Find two positive numbers whose sum, is 15 and the sum of whose squares is minimum. |
| 107. If the radius of a sphere is measured as 9 cm with an error 0.03 cm, then find the approximate error in calculating its volume. |
| 108. Find a unit vector perpendicular to each of the vectors (a ⃗+b ⃗) and (a ⃗–b ⃗), where |
| 109. Show that the point A(-2i ̂+3j ̂+5k ̂),B(i ̂+2j ̂+3k ̂ )and C(7i ̂-k ̂)are collinears. |
| 110. Find the angle between the line x+1 / 2 = y/3 = z–3/6 and the plane 10x + 2y–11z = 3. |
| 111. Show that the lines x + 3 / –3 = y – 1 / 1 = z – 5 / 5 and x + 1 / - 1 = y – 2 / 2 = z – 5 / 5 are coplanar. |
| 112. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as ' R={(a, b): b = a +1} is reflexive, symmetric or transitive. |
| 113. Show that * : R×RR defined by a*b = a + 2b is neither commutative nor associative. |
| 114. Express tan^(-1)[(cosx/(1-sinx)),-3π/2 |
| 115. Show that sin^(-1)[3/5-sin^1 [8/17=cos^(-1) [84/85]]] |
| 116. Show that A=[(2 3,1 -4)]and B=[ (1 -2,-1 3)] then verify that (AB)–1= B–1 A–1 |
| 117. Prove that : |
| 118. Find the distance of a point (2, 5, –3) from the plane |
| 119. Find the vector and Cartesian equations of the plane which passes through the point (5, 2, 4) and perpendicular to the line with direction |
| 120. Solve the following linear programming problem graphically : |
| 121. A cooperative society of farmers has 50 hectares of land to grow two crops X and Y. The profit from crops X and X per hectare are |
| 122. Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results |
| 123. An unbiased die is thrown twice. Let the event A be "Odd number on the first throw" and B the event "Odd number on the second throw". |
| 124. From a lot of 30 bulbs which include 6 defective, a sample of 4 bulbs is drawn at random with replacement. Find the probability |
| 125. Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the |
| 126. Express the matrix B=[(2 -2 -4,-1 3 4,1 -2 -3)]as the sum of a symmetric and a skew symmetric matrix. |
| 127. By using elementary operations, find the inverse of the matrix A=[(2 1,1 1)]. |
| 128. Verily Rolle's theorem for the function f(x) = x2 + 2x – 8, x = ∈ [-4, 2] |
| 129. Differentiate ax w.r.t. x, where a is a positive constant. |
| 130. Evaluate ∫^(π/2) 0 [sin^4 x/sin^4[x+cos^4 x] dx] |
| 131. Evaluate ∫〖((x^2+1) e^x)/(x+1)^2 dx〗 |
| 132. Using integration find the area of region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3,1). |
| 133. Find the area of the parabola y2 = 4 ax bounded by its latus rectum. |
| 134. Solve the differential equation dy/dx + y/x = x2 |
| 135. Find the particular solution of the differential equation log(dy/dx) = 3x+4y given that y=0 when x=0. |
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