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Page 1
UTTAR PRADESH NTSE STAGE 1 (2020-21)
SAT ANSWER KEY
Physics
101. 4 102. 2 103. 3 104. 2
105. 3 106. 4 107. 1 108. 3
109. 2 110. 2 111. 3
Chemistry
112. 2 113. 1 114. 3 115. 2
116. 2 117. 3 118. 4 119. 4
120. 1 121. 4 122. 2 123. 2
124. 3 125. 3 126. 4
BIO
127. 1 128. 2 129. 3 130. 4
131. 1 132. 3 133. 2 134. 4
135. 1 136. 2 137. 1 138. 2
139. 2 140. 3
Social Studies
141. 4 142. 1 143. 3 144. 2
145. 2 146. 2 147. 2 148. 3
149. 4 150. 1 151. 3 152. 4
153. 4 154. 2 155. 3 156. 2
157. 4 158. 3 159. 1 160. 4
161. 2 162. 3 163. 4 164. 1
165. 3 166. 1 167. 1 168. 2
169. 1 170. 2 171. 2 172. 2
173. 3 174. 1 175. 1 176. 1
177. 2 178. 2 179. 1 180. 3
Page 2
UTTAR PRADESH NTSE STAGE 1 (2020-21)
SAT ANSWER KEY
Physics
101. 4 102. 2 103. 3 104. 2
105. 3 106. 4 107. 1 108. 3
109. 2 110. 2 111. 3
Chemistry
112. 2 113. 1 114. 3 115. 2
116. 2 117. 3 118. 4 119. 4
120. 1 121. 4 122. 2 123. 2
124. 3 125. 3 126. 4
BIO
127. 1 128. 2 129. 3 130. 4
131. 1 132. 3 133. 2 134. 4
135. 1 136. 2 137. 1 138. 2
139. 2 140. 3
Social Studies
141. 4 142. 1 143. 3 144. 2
145. 2 146. 2 147. 2 148. 3
149. 4 150. 1 151. 3 152. 4
153. 4 154. 2 155. 3 156. 2
157. 4 158. 3 159. 1 160. 4
161. 2 162. 3 163. 4 164. 1
165. 3 166. 1 167. 1 168. 2
169. 1 170. 2 171. 2 172. 2
173. 3 174. 1 175. 1 176. 1
177. 2 178. 2 179. 1 180. 3
Mathematics
181. 2
Sol. ( ) x 0.7 0.7777....... i ==
( ) 10x 7.777......... ii =
(ii) – (i)
9x 7
x 7 / 9
14
2x
9
2x 1.5
=
=
?=
=
182. 1
Sol.
x y z
a b,b c,c a = = =
xy xyz 1
a c a a
xyz 1
= ? =
=
183. 1
Sol.
( ) ( )
( ) ( )
3 1 3 1
a b 3
3 1 3 1
--
=+
+-
3 1 2 3
a b 3
31
4 2 3
a b 3
2
+-
=+
-
-
=+
2 3 a b 3
a 2,b 1
- = +
= = -
184. 4
Sol.
a b b c c a 2a 2b 2c
2a 2b 2c 2a 2b 2c
xx
1
xx
+ + + + + + +
+ + + +
==
185. 3
Sol.
1 x 1 x
7 7 50
+-
+=
x
x
x
7
7.7 50
7
Let7 y
7
7y 50
y
+=
=
+=
Page 3
UTTAR PRADESH NTSE STAGE 1 (2020-21)
SAT ANSWER KEY
Physics
101. 4 102. 2 103. 3 104. 2
105. 3 106. 4 107. 1 108. 3
109. 2 110. 2 111. 3
Chemistry
112. 2 113. 1 114. 3 115. 2
116. 2 117. 3 118. 4 119. 4
120. 1 121. 4 122. 2 123. 2
124. 3 125. 3 126. 4
BIO
127. 1 128. 2 129. 3 130. 4
131. 1 132. 3 133. 2 134. 4
135. 1 136. 2 137. 1 138. 2
139. 2 140. 3
Social Studies
141. 4 142. 1 143. 3 144. 2
145. 2 146. 2 147. 2 148. 3
149. 4 150. 1 151. 3 152. 4
153. 4 154. 2 155. 3 156. 2
157. 4 158. 3 159. 1 160. 4
161. 2 162. 3 163. 4 164. 1
165. 3 166. 1 167. 1 168. 2
169. 1 170. 2 171. 2 172. 2
173. 3 174. 1 175. 1 176. 1
177. 2 178. 2 179. 1 180. 3
Mathematics
181. 2
Sol. ( ) x 0.7 0.7777....... i ==
( ) 10x 7.777......... ii =
(ii) – (i)
9x 7
x 7 / 9
14
2x
9
2x 1.5
=
=
?=
=
182. 1
Sol.
x y z
a b,b c,c a = = =
xy xyz 1
a c a a
xyz 1
= ? =
=
183. 1
Sol.
( ) ( )
( ) ( )
3 1 3 1
a b 3
3 1 3 1
--
=+
+-
3 1 2 3
a b 3
31
4 2 3
a b 3
2
+-
=+
-
-
=+
2 3 a b 3
a 2,b 1
- = +
= = -
184. 4
Sol.
a b b c c a 2a 2b 2c
2a 2b 2c 2a 2b 2c
xx
1
xx
+ + + + + + +
+ + + +
==
185. 3
Sol.
1 x 1 x
7 7 50
+-
+=
x
x
x
7
7.7 50
7
Let7 y
7
7y 50
y
+=
=
+=
( ) ( )
2
2
2
x
x
7y 7 50y
7y 50y 7 0
7y 49y y 7 0
7y y 7 1 y 7 0
y 1/ 7,7
1
7 x 1
7
7 7 x 1
+=
- + =
- - + =
- - - =
=
? = ? = -
= ? =
186. 3
Sol. Let the men salary Rs. 100
After 10% reduction salary = Rs 90
Amount increased Rs. 10 to bring it on original salary that is Rs
100.
Percentage increased =
10 1
100 11 %
90 9
?=
187. 3
Sol.
10 10 20
500 1.50 Rs.
100 100 100
? ? ? =
188. 4
Sol. C.P of pen (each)
10
Rs.
11
=
S.P of pen (each)
11
Rs.
10
=
So it is clean its profit
11 10 21
profit Rs.
10 11 110
? = - =
21
so now profit% = 100
110 10
10 11
??
??
?
??
??
?
??
??
21 11
100 21%
10 110
?
= ? =
?
189. 4
Sol.
1 1 1 1
x
3 4 3 4
??
+ = -
??
??
71
x x 7
12 12
= ? ? =
Page 4
UTTAR PRADESH NTSE STAGE 1 (2020-21)
SAT ANSWER KEY
Physics
101. 4 102. 2 103. 3 104. 2
105. 3 106. 4 107. 1 108. 3
109. 2 110. 2 111. 3
Chemistry
112. 2 113. 1 114. 3 115. 2
116. 2 117. 3 118. 4 119. 4
120. 1 121. 4 122. 2 123. 2
124. 3 125. 3 126. 4
BIO
127. 1 128. 2 129. 3 130. 4
131. 1 132. 3 133. 2 134. 4
135. 1 136. 2 137. 1 138. 2
139. 2 140. 3
Social Studies
141. 4 142. 1 143. 3 144. 2
145. 2 146. 2 147. 2 148. 3
149. 4 150. 1 151. 3 152. 4
153. 4 154. 2 155. 3 156. 2
157. 4 158. 3 159. 1 160. 4
161. 2 162. 3 163. 4 164. 1
165. 3 166. 1 167. 1 168. 2
169. 1 170. 2 171. 2 172. 2
173. 3 174. 1 175. 1 176. 1
177. 2 178. 2 179. 1 180. 3
Mathematics
181. 2
Sol. ( ) x 0.7 0.7777....... i ==
( ) 10x 7.777......... ii =
(ii) – (i)
9x 7
x 7 / 9
14
2x
9
2x 1.5
=
=
?=
=
182. 1
Sol.
x y z
a b,b c,c a = = =
xy xyz 1
a c a a
xyz 1
= ? =
=
183. 1
Sol.
( ) ( )
( ) ( )
3 1 3 1
a b 3
3 1 3 1
--
=+
+-
3 1 2 3
a b 3
31
4 2 3
a b 3
2
+-
=+
-
-
=+
2 3 a b 3
a 2,b 1
- = +
= = -
184. 4
Sol.
a b b c c a 2a 2b 2c
2a 2b 2c 2a 2b 2c
xx
1
xx
+ + + + + + +
+ + + +
==
185. 3
Sol.
1 x 1 x
7 7 50
+-
+=
x
x
x
7
7.7 50
7
Let7 y
7
7y 50
y
+=
=
+=
( ) ( )
2
2
2
x
x
7y 7 50y
7y 50y 7 0
7y 49y y 7 0
7y y 7 1 y 7 0
y 1/ 7,7
1
7 x 1
7
7 7 x 1
+=
- + =
- - + =
- - - =
=
? = ? = -
= ? =
186. 3
Sol. Let the men salary Rs. 100
After 10% reduction salary = Rs 90
Amount increased Rs. 10 to bring it on original salary that is Rs
100.
Percentage increased =
10 1
100 11 %
90 9
?=
187. 3
Sol.
10 10 20
500 1.50 Rs.
100 100 100
? ? ? =
188. 4
Sol. C.P of pen (each)
10
Rs.
11
=
S.P of pen (each)
11
Rs.
10
=
So it is clean its profit
11 10 21
profit Rs.
10 11 110
? = - =
21
so now profit% = 100
110 10
10 11
??
??
?
??
??
?
??
??
21 11
100 21%
10 110
?
= ? =
?
189. 4
Sol.
1 1 1 1
x
3 4 3 4
??
+ = -
??
??
71
x x 7
12 12
= ? ? =
190. 3
Sol. Let B ’s income = Rs. 100
A ’s income = 100 + 20=120 Rs.
It is clear that if A ’s income is Rs. 120, B ’s income is 100 Rs.
which is less than Rs. 20.
B's ? income less by
20
A 100
120
=?
100 2
16 %
63
==
191. 1
Sol. 52 – complete weeks
Two days can be Monday Tuesday, Tuesday Wednesday,
Wednesday Thursday, Thursday Friday, Friday Saturday, Saturday
Sunday, Sunday Monday.
F sat Sat S, SM
Total case = 7, fordable case = 2
Prob = 2/7
192. 3
Sol.
2 2sin cos sin2
sin cos
2 2 2
? ? ?
? ? = =
Min value of sin = - 1
sin2 1
min value of
22
?
? = -
193. 2
Sol. It following a particular pattern
36
12
10 1 10 1
Quotient 9, 9009
111 111
10 1
similarly 9009009009
111
--
= = =
-
=
194. 4
Sol.
x4
log3 log729
+
=
x 4 6
33
x 4 6 x 2
+
?=
+ = ? =
195. 1
Sol. We all known that
1 1 1 2 2 2
12
M TD M T D
WW
=
2
p p p q q q
pw
? ? ? ?
=
Page 5
UTTAR PRADESH NTSE STAGE 1 (2020-21)
SAT ANSWER KEY
Physics
101. 4 102. 2 103. 3 104. 2
105. 3 106. 4 107. 1 108. 3
109. 2 110. 2 111. 3
Chemistry
112. 2 113. 1 114. 3 115. 2
116. 2 117. 3 118. 4 119. 4
120. 1 121. 4 122. 2 123. 2
124. 3 125. 3 126. 4
BIO
127. 1 128. 2 129. 3 130. 4
131. 1 132. 3 133. 2 134. 4
135. 1 136. 2 137. 1 138. 2
139. 2 140. 3
Social Studies
141. 4 142. 1 143. 3 144. 2
145. 2 146. 2 147. 2 148. 3
149. 4 150. 1 151. 3 152. 4
153. 4 154. 2 155. 3 156. 2
157. 4 158. 3 159. 1 160. 4
161. 2 162. 3 163. 4 164. 1
165. 3 166. 1 167. 1 168. 2
169. 1 170. 2 171. 2 172. 2
173. 3 174. 1 175. 1 176. 1
177. 2 178. 2 179. 1 180. 3
Mathematics
181. 2
Sol. ( ) x 0.7 0.7777....... i ==
( ) 10x 7.777......... ii =
(ii) – (i)
9x 7
x 7 / 9
14
2x
9
2x 1.5
=
=
?=
=
182. 1
Sol.
x y z
a b,b c,c a = = =
xy xyz 1
a c a a
xyz 1
= ? =
=
183. 1
Sol.
( ) ( )
( ) ( )
3 1 3 1
a b 3
3 1 3 1
--
=+
+-
3 1 2 3
a b 3
31
4 2 3
a b 3
2
+-
=+
-
-
=+
2 3 a b 3
a 2,b 1
- = +
= = -
184. 4
Sol.
a b b c c a 2a 2b 2c
2a 2b 2c 2a 2b 2c
xx
1
xx
+ + + + + + +
+ + + +
==
185. 3
Sol.
1 x 1 x
7 7 50
+-
+=
x
x
x
7
7.7 50
7
Let7 y
7
7y 50
y
+=
=
+=
( ) ( )
2
2
2
x
x
7y 7 50y
7y 50y 7 0
7y 49y y 7 0
7y y 7 1 y 7 0
y 1/ 7,7
1
7 x 1
7
7 7 x 1
+=
- + =
- - + =
- - - =
=
? = ? = -
= ? =
186. 3
Sol. Let the men salary Rs. 100
After 10% reduction salary = Rs 90
Amount increased Rs. 10 to bring it on original salary that is Rs
100.
Percentage increased =
10 1
100 11 %
90 9
?=
187. 3
Sol.
10 10 20
500 1.50 Rs.
100 100 100
? ? ? =
188. 4
Sol. C.P of pen (each)
10
Rs.
11
=
S.P of pen (each)
11
Rs.
10
=
So it is clean its profit
11 10 21
profit Rs.
10 11 110
? = - =
21
so now profit% = 100
110 10
10 11
??
??
?
??
??
?
??
??
21 11
100 21%
10 110
?
= ? =
?
189. 4
Sol.
1 1 1 1
x
3 4 3 4
??
+ = -
??
??
71
x x 7
12 12
= ? ? =
190. 3
Sol. Let B ’s income = Rs. 100
A ’s income = 100 + 20=120 Rs.
It is clear that if A ’s income is Rs. 120, B ’s income is 100 Rs.
which is less than Rs. 20.
B's ? income less by
20
A 100
120
=?
100 2
16 %
63
==
191. 1
Sol. 52 – complete weeks
Two days can be Monday Tuesday, Tuesday Wednesday,
Wednesday Thursday, Thursday Friday, Friday Saturday, Saturday
Sunday, Sunday Monday.
F sat Sat S, SM
Total case = 7, fordable case = 2
Prob = 2/7
192. 3
Sol.
2 2sin cos sin2
sin cos
2 2 2
? ? ?
? ? = =
Min value of sin = - 1
sin2 1
min value of
22
?
? = -
193. 2
Sol. It following a particular pattern
36
12
10 1 10 1
Quotient 9, 9009
111 111
10 1
similarly 9009009009
111
--
= = =
-
=
194. 4
Sol.
x4
log3 log729
+
=
x 4 6
33
x 4 6 x 2
+
?=
+ = ? =
195. 1
Sol. We all known that
1 1 1 2 2 2
12
M TD M T D
WW
=
2
p p p q q q
pw
? ? ? ?
=
3
2 2
q
w
p
=
196. 4
Sol. Using factor theorem,
Put x = - 1 in the equation
( ) ( )
100 99
1 2 1 k 0
1 2 k 0
k1
- + - + =
- + =
=
197. 2
Sol. If original radius r
then volume of cylinder
2
rh =?
New radius = 1. 1r
New volume
2
1.21 r h = ? ?
2
1.21 r h =?
So increase in height
1.21 1
100%
1.21
- ??
=?
??
??
=17.36%
198. 1
Sol. Square on both side
2
x 1 x 1 2 x 1 1 + + - - - =
( )
2
22
22
2x 1 2 x 1
again sqaure
4x 1 4x 4 x 1
4x 1 4x 4x 4
4x 5 x 5 / 4
- = -
+ - = -
+ - = -
= ? =
199. 2
Sol. Prime no from 1 to 30
2, 3, 5, 7, 11, 13, 17, 19, 23, 29 = 10
10 1
prob.
30 3
==
200. 3
Sol. In two day insect climb = 2 – 1 = 1 m.
So in 20 day, insect climb = 10 m.
In 21th day insect climb = 2m
?Total height = 10 + 2 = 12 m
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